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IB Chemistry/Stoichiometry

1.1.1: Apply the mole concept to substances.
A mole is equivalent to 6.022 x 1023 (Avogadro's constant) units. Chemists refer to a mole of something much as we refer to a dozen eggs; it is a convenient unit for counting. The periodic table provides molar masses, i.e. the number of grams of an element equivalent to one mole of atoms of that specific element. This can be extrapolated to molecules of known molecular formula.

1.1.2: Determine the number of particles and the amount of substance (in moles).
Number of moles = mass / molar mass (Usually found on periodic table). The coefficients in chemical equations give the molar ratios of reactants and products i.e. 2A + 3B → C. There is 2/3 as much A as B, and 3 times more B than C involved in the reaction. Assuming the reaction goes to completion, there must be 3/2 times as much B as A for neither to remain. If this ratio is not followed, one will be a limiting reactant, and so the reaction will have some of the other reactant left over when it completes.

1.2.1: Define the term molar mass (M) and calculate the mass of one mole of a species.
The molar mass (M) is the mass of one mole's worth of a substance. To find the atomic/molecular mass, multiply the amount of moles by the molar mass.

1.2.2: Atomic mass, Molecular Mass, Formula Mass
The molar mass can be found in the periodic table, and will give the mass for 1 mol of the species (or rather the average accounting for different isotopes and their relative abundance).

1.2.3: Define the terms relative molecular mass (Mr) and relative atomic mass (Ar)
Mr is the ratio between the molar masses of two species. Ar is the ratio of the number of atoms between two species.

1.2.4: The difference between moles and mass
The number of moles refers to the amount of the substance, every mol being 6.02 x 1023 individual elements. Mass is the property which results in 'weight' in the presence of gravity. Given a molar mass, M a mass m and a number of mols n then n = m / M.

1.2.5: The difference between the molecular formula and the empirical formula
An 'empirical formula' is the formula describing the different atoms present in a molecules, and their ratios, but not the actual number present. For example, could be an empirical formula if x, y, and z are in lowest common terms. The molar mass can then be used to calculate the actual numbers of each atom present per molecule. The empirical formula can be determined by percentage composition, or anything else which gives the ratios of atoms present. A 'molecular formula', on the other hand, has the actual number of atoms present in each molecule. It will be an integer multiple of the empirical formula. For example,.

 * Example:
 * If you are given the empirical formula with an equation, and a mass of 30.08 g mol-1. What is the molecular formula of this compound?
 * We will compare the molecular mass of the molecular formula, 30.08 g mol-1, to that of the empirical formula, found to be 15.04 g mol-1. By dividing, we find the ratio to be 2, meaning that the molecular formula must be 2 times as large as the empirical formula.  The molecular formula is therefore.

1.3 Chemical Equations
Chemical equations are a convenient, standardised system for describing chemical reactions. They contain the following information.

 * The type of reactants consumed and products formed
 * The relative amounts of reactants and products
 * The electrical charges on ions
 * The physical state of each species (e.g. solid, liquid, gas)
 * The reaction conditions (e.g. temperature, catalysts)

The final two points are optional and sometimes omitted.

Anatomy of an Equation
$$\hbox{H}_{2 (g)} + \hbox{Cl}_{2 (g)} \to 2\hbox{HCl}_{(g)}$$

Hydrogen gas and chlorine gas will react vigorously to produce hydrogen chloride gas. The equation above illustrates this reaction. The reactants, hydrogen and chlorine, are written on the left and the products (hydrogen chloride) on the right. The large number 2 in front of HCl indicates that two molecules of HCl are produced for each 1 molecule of hydrogen and chlorine gas consumed. The 2 in subscript below H indicates that there are two hydrogen atoms in each molecule of hydrogen gas. Finally, the (g) symbols subscript to each species indicates that they are gases.

Reacting Species
Species in a chemical reaction is a general term used to mean atoms, molecules or ions. A species can contain more than one chemical element (HCl, for example, contains hydrogen and chlorine). Each species in a chemical equation is written:

$$\hbox{E}_{x}^y$$

E is the chemical symbol for the element, x is the number of atoms of that element in the species and y is the charge (if it is an ion).

For example, ethanol would be written $$\hbox{C}_2\hbox{H}_6\hbox{O}_{}$$ because each molecule contains 2 carbon, 6 hydrogen and 1 oxygen atom. A magnesium ion would be written $$\hbox{Mg}^{2+}$$ because it has a double positive charge. Finally, an ammonium ion would be written $$[\hbox{NH}_4]^+$$ because each molecule contains 1 nitrogen and 4 hydrogen atoms and has a charge of 1+.

Coefficients
The numbers in front of each species have a very important meaning - they indicate the relative amounts of the atoms that react. The number infront of each species is called a coefficient. In the above equation, for example, one H2 molecule reacts with one Cl2 molecule to produce two molecules of HCl. This can also be interpreted as moles (i.e. 1 mol H2 and 1 mol Cl2 produces 2 mol HCl).

Other Information
Occasionally, other information about a chemical reaction will be supplied in an equation (such as temperature or other reaction conditions). This information is often written above the reaction arrow. We will ignore this for now, as it only complicates matters (and it's hard to draw in TeX).

1.3.1 : The mole ratio of two species in a chemical equation is the ratio of their coefficients...ie aX + bY → cZ : The ratio of X/Y is a/b, Y/Z = b/c etc.

Chemical equations are useful because they give the relative amounts of the substances that react in a chemical equation. For example, from the chemical equation for the formation of ammonia, we can see that one mole of nitrogen gas will combine with three moles of hydrogen gas to form two moles of ammonia gas.

$$\hbox{N}_{2 (g)} + 3\hbox{H}_{2 (g)} \to 2\hbox{NH}_{3 (g)}$$

1.3.2 : Balancing equations...change only the coefficients, not the subscripts to make sure all atoms, and charge is conserved (half equations can be balanced by addition of electrons to either side...2 half equations can be added by making the number of electrons equal in each, then vertically adding.)

In some cases, however, we may not know the relative amounts of each substance that reacts. Fortunately, we can always find the correct coefficients of an equation (the relative amounts of each reactant and product) by applying the law of conservation of matter. Because matter can neither be created nor destroyed, the total number of each atom on one side of the equation must be the same as the total on the other. This process of finding the coefficients is known as balancing the equation.

For example, assume in the above equation that we do not know how many moles of ammonia gas will be produced:

$$\hbox{N}_{2 (g)} + 3\hbox{H}_{2 (g)} \to ?\hbox{NH}_{3 (g)}$$

From the left side of this equation, we see that there are 2 atoms of nitrogen gas in the molecule N2 (2 atoms per molecule x 1 molecule), and 6 atoms of hydrogen gas in the 3 H2 molecules (2 atoms per molecule x 3 molecules). Because of the law of conservation of matter, there must also be 2 atoms nitrogen gas and 6 atoms of hydrogen gas on the right side. Since each molecule of the resultant ammonia gas (NH3) contains 1 atom of nitrogen and 3 atoms of hydrogen, 2 molecules are needed to obtain 2 atoms of nitrogen and 6 atoms of hydrogen.

In a similar manner, you can use the law of conservation of matter to solve equations containing a greater number of unknown coefficients (the relative amounts of each reactant and product), or even subscripts (the number of each element in a molecule) on either side of the equation:

$$\hbox{N}_{2 (g)} + 3\hbox{H}_{2 (g)} \to ?\hbox{NH}_{3 (g)}$$

1.3.3 : State symbols -- (s)-Solid, (l)-liquid, (g)-gas, (aq)-aqueous solution...i.e. something dissolved in water. Should be included in all chemical reactions (but won't be penalized).

$$\hbox{E}_{(state)} \,$$

E is the chemical symbol for the element and (state) is the physical state.

Examples
$$\hbox{CH}_{4} + 2\hbox{O}_{2} \to \hbox{CO}_{2} + 2\hbox{H}_{2}\hbox{O}$$

Above is the equation for burning methane gas (CH4) in the presence of oxygen (O2) to form carbon dioxide and water: CO2 and H2O respectively.

$$\hbox{Pb}^{+2}_{(aq)} + 2\hbox{I}^{-}_{(aq)} \to \hbox{PbI}_{2 (s)}$$

This is a precipitation reaction in which dissolved lead cations and iodide anions combine to form a solid yellow precipitate of lead iodide (an ionic solid).

Simple Formulas
Moles to Particles: number of moles x (6.02 x 1023/1 mole)= number of Particles

ex: 2.50 mol Zn x (6.02*1023 atoms of Zn/1 mol Zn)= 1.51 x 1024 atoms of Zn

Particles to Moles: number of Particles * (1 mole/6.02 x 1023)= number of moles

ex: 1.204 x 1024 atoms Ag * (1 mol/6.02 x 1023 atoms Ag)= 2 moles of Ag

Moles to Mass: number of moles x (molar mass/ 1 mole)= number of grams (or other unit of measurement)

ex: 3.57 mol Al x (26.982 g Al/ 1 mol Al)= 96.3 g

Mass to Moles: number of grams * (1 mole/ molar mass)= number of moles

ex: 25.5 g Ag * (1 mol Ag/ 107.868 g Ag)= 0.236 mol

ex: Na2CO3 = 2(mass of Na)+ mass of C + 3(mass of O)
 * to find molar mass

=2(22.990)+12.011+3(15.999)

=45.98+12.001+47.997

=105.99 g Na2CO3

1.4 Mass relationships in chemical reactions
1.4.1 : Mass is conserved throughout reactions. This fact allows masses to be calculated based on other masses in the reaction eg burning Mg in air to produce MgO and so to find the mass or Mg present in the original sample (ie purity)...can be extended to concentrations...ie titration.

1.4.2 : When a reaction contains several reactants, some may be in excess...is more is present that can be used in the reaction. The first reactant to run out is the limiting reagent (or reactant). Knowing the number of mols of the limiting reagent allows all other species to be calculated, and so the yield, and remaining quantities of other reactants.

1.5 Solutions
1.5.1
 * Solvent - the fluid you're dissolving in e.g. water.
 * Solute - something which has been dissolved to form a solution e.g. an ionic compound such as sodium hydroxide.
 * Solution - a mixture of solvent and solute where the solute has dissolved into the solvent to form an indistinguishable liquid.
 * Concentration - the amount of solute per volume of solution. Measured in moles per dm3 (i.e. moles per liter) or grams per liter.

1.5.2 : Apply the equation concentration = moles/volume...rather obvious from the units of concentration, but remember to convert everything into the same units.

1.5.3 : Use chemical equations to relate the amount of one species to the amounts of others.

TOPIC 1: QUANTITATIVE CHEMISTRY (12.5 HOURS)
Notes below are based on the specification for exams in 2009

SOME COMMON CATIONS
N.B. Many metals, including some of those above, show more than one valency. The valency is then always given with the name of the compound. It is written in Roman Numerals after the name of the metal.

e.g. Iron may be Fe+2 or  Fe+3

Iron II Chloride is Fe+2(Cl-)2

Iron III Chloride is Fe+3(Cl-)3

Other examples which you may meet are

Chromium II or Chromium III	Cr+2 or Cr+3

Manganese II or Manganese IV	Mn+2 or Mn+4

Tin II or Tin IV	Sn+2 or Sn+4

Lead II or Lead IV	Pb+2 or Pb+4

Some Common Anions
Rules of thumb: Anions consisting of just one element have names ending -ide.

 * Anions consisting of an element plus oxygen have names ending in -ate.

 * Notable exception: OH- is hydroxide, not 'hydrate'.

EXERCISE 1
 * If an element has two anions whose names should end in -ate, the one with fewer oxygens ends in -ite.

Work out the formula for the following ionic chemicals

 * 1) 	Zinc Chloride ZnCl2
 * 2) 	Sodium Oxide Na2O
 * 3) 	Aluminium Fluoride AlF3
 * 4) 	Iron III Chloride FeCl3
 * 5) 	Aluminium Oxide	 Al2O3
 * 6) 	Zinc Hydroxide Zn(OH)2
 * 7) 	Copper (II) Nitrate Cu(NO3)2
 * 8) 	Barium Sulphate BaSO4
 * 9) 	Sodium Carbonate Na2SO4
 * 10) 	Calcium Hydrogencarbonate Ca(HCO3)2
 * 11) 	Lead Iodide	 PbI2
 * 12) 	Nickel (II) Sulphate NiSO4
 * 13) 	Ammonium Carbonate (NH4)2CO3
 * 14) 	Manganese IV Oxide MnO2
 * 15) 	Sodium Bromide NaBr
 * 16) 	Magnesium Ethanoate Mg(CH3COO)2
 * 17) 	Silver Nitrate AgNO3
 * 18) 	Mercury II Chloride HgCl2
 * 19) 	Magnesium Nitride Mg3N2
 * 20) 	Potassium Phosphate K3PO4

What are the names of the following chemicals?

 * 1) 	CuBr2 Copper II Bromide
 * 2) 	K2O Potassium Oxide
 * 3) 	K2Cr2O7 Potassium DiChromate (VI)
 * 4) 	KNO3 Potasium Nitrate
 * 5) 	AlCl3 Aluminium Chloride
 * 6) 	FeCl2 Iron II Chloride
 * 7) 	FeS	 Iron II Sulphide
 * 8) 	Na2S2O3 Sodium ThioSulphate
 * 9) 	Al2(SO4)3 Aluminium Sulphate
 * 10) 	Mg(OH)2 Magnesium Hydroxide
 * 11) 	Pb(CH3CO2)2 Lead (II) Ethanoate
 * 12) 	Na2Zn(OH)4 Sodium Zincate
 * 13) 	Pb(NO3)2 Lead (II) Nitrate
 * 14) 	KMnO4 Potassium Manganate (VII)
 * 15) 	PbO2	 Lead (IV) Oxide
 * 16) 	Ni(NO3)2 Nickel Nitrate
 * 17) 	Na2SO3 Sodium Sulphite/Sodium Sulphate (IV)
 * 18) 	Ca(HCO3)2	 Calcium HydrogenCarbonate
 * 19) 	CuO	 Copper II Oxide
 * 20) 	MgCO3 Magnesium Carbonate

Relative molecular mass (Mr) and relative atomic mass (Ar).
Definition: The relative isotopic mass of 12C = 12

All other relative isotopic masses are measured relative to this standard and are not whole numbers e.g.

13C 13.003	19F 18.998	35Cl 34.97	37Cl 36.97

The IB requires you to use whole numbers as an approximation to the relative isotopic mass of every isotope.

The relative atomic mass (Ar) is the average value of an element’s relative isotopic masses e.g. Ar (C) = 12 * 0.9889 + 13.0033 * 0.011 = 12.0098

What is Ar (Cl) if 75.77 % is 35Cl and the rest is 37Cl?

Relative atomic masses are in your data booklet, written beneath each element’s symbol in Table 5. e.g.

The relative molecular mass (Mr) is the sum of a compound’s relative atomic masses e.g.

Mr (CO) = 12.01 + 16.00

What is Mr (CO2)?

What is Mr (Al2(CO3)3)?

Calculating the mass of one mole of a species from its formula.
Another way of saying the same thing is to use the term ‘Molar mass’

The molar mass (M) of carbon-12 atoms is 12 g mol-1

NB Molar mass has units (it is not ‘relative’)

You must specify if it refers to atoms, isotopes, molecules, etc.

EXERCISE 2:

Calculate the Relative Molecular Mass, Mr, of the following

1.	Sodium Chloride

2.	Copper Sulphate

3.	Lead Nitrate

4.	Magnesium Oxide

5.	Potassium Hydroxide

6.	Sulphuric Acid

7.	Carbon Dioxide

8.	Calcium Carbonate

9.	Aluminium Sulphate

10.	Sulphur Trioxide

11.	Ammonium Nitrate

12.	Zinc Chloride

13.	Iron II Bromide

14.	Iron III Iodide

15.	Oxygen

16.	Aluminium Zincate

17.	Nitric Acid

18.	Dilead II lead IV Oxide Pb3O4.

19.	Magnesium Sulphate - 7 – water MgSO4.7H2O

20.	Ammonium Iron II Sulphate - 6 – water (NH4)2SO4.FeSO4.6H2O

Calculate M for :-

1.	Copper Carbonate

2.	Potassium Dichromate

3.	Magnesium Hydroxide

4.	Sodium Phosphate

5.	Calcium Hydrogencarbonate

6.	Potassium Oxalate

7.	Sodium Cyanide

8.	Nitrogen Dioxide

9.	Ethanol

10.	Lead Chromate

11.	Potassium Permanganate

12.	Tin IV Chloride

13.	Ethane

14.	Lithium Carbonate

15.	Ammonia

16.	Butane

17.	Sodium Chromate

18.	Hydrochloric Acid

Applying the mole concept to substances.
Definition: A mole of particles contains the same number of particles as there are atoms in 12 g of carbon-12.

It turns out that there are 6.02 x 1023 particles per mole.

6.02 x 1023 mol-1 is Avogadro’s constant

Solving problems involving amount, mass and molar mass.
Maths (learn this thoroughly):

Mass = Amount x Molar mass

or

m = nM

or

Grams = Moles x Grams per mole

EXERCISE 3

1.	What is the mass of 0.5 moles of calcium carbonate (CaCO3)?

2.	What is the amount of 27 g of water?

3.	What is the relative molecular mass of fullerene if 2/3 mole has a mass of 480 g?

4.	What mass of magnesium contains the same number of atoms as there are in 4 grams of calcium?

5.	Calculate the mass of iron which contains the same number of atoms as there are molecules in 16 grams of oxygen.

6.	What is the mass of copper sulphate (CuSO4 ) which contains the same number of copper atoms as there are atoms in 6.5 grams of zinc?

7.	How much nitrogen contains the same number of atoms as there are sulphur atoms in 3.96 grams of ammonium sulphate ([NH4]2SO4)?

8.	What mass of manganese contains twice the number of atoms that there in 0.6 grams of carbon?

Empirical formula and molecular formula.
Empirical formula: the simplest expression of the proportions of the elements in a compound. The empirical formula can be obtained from the proportions of masses of each element.

Molecular formula: the numbers of atoms of each element in a molecule of a compound.

Sometimes the two formulae are the same: H2O, for example, is both the molecular and empirical formula.

Hydrogen peroxide has an empirical formula of HO but its molar mass is 34 g mol-1. Its molecular formula is H2O2

EXERCISE 4 1.	Analysis of two compounds showed that they contained the following proportions of elements: A: Carbon 26.1%	Oxygen 69.6%	Hydrogen 4.3% B: Carbon 52.2%	Oxygen 34.8%	Hydrogen 13.0% Calculate the empirical formula of each compound

2. If the empirical formula of methane is CH4, and its relative molecular mass is 16, what is the molecular formula?

3. If the empirical formula of ethane is CH3, and its relative molecular mass is 30, what is the molecular formula?

4. What is the mass of carbon dioxide that is produced when 50 g of calcium carbonate decomposes?

CaCO3 → CaO + CO2

5. If 12 g of magnesium react with oxygen to produce 20 g of magnesium oxide: a. What is the formula of magnesium oxide? b. What is the equation for the reaction?

6.	Determine the empirical formula and the molecular formula of the following compounds from the given information. a.	0.36 mol S are combined with 0.72 mol oxygen atoms. Mr of this compound is measured to be 64. b.	0.193 mol Fe combined with 0.2895 mol O and its molar mass is 160 g mol-1 c.	0.3285 mol Pb combined with 0.438 mol O. Mr = 685 d.	0.309 mol carbon combined with 0.618 mol H. Molar mass is 42 g mol-1 e.	0.379 mol H combined with 0.379 mol O. Mr = 34

7.	A compound was shown by qualitative analysis to contain nitrogen and hydrogen as the only elements. It was found by quantitative analysis that 0.02 mol of nitrogen are combined with 0.04 mol of hydrogen. Its relative molecular mass is approximately 30. Determine its empirical formula and its molecular formula.

8.	The relative molecular mass of a compound of boron and hydrogen was measured as just under 28. Every 0.25 mol of boron are combined with 0.75 mol hydrogen atoms. Find its empirical and its molecular formula.

9.	Calculate the empirical formulae of the following substances whose compositions are given below: a.	5g of an oxide of magnesium which contains 3g magnesium b.	7g nitrogen combined with 16g oxygen c.	0.6g magnesium combined with 1.2g oxygen and 0.3g of carbon d.	3.5g nitrogen combined with 2g oxygen e.	4.8 g oxygen combined with 3.2 g copper and 1.4 g nitrogen f.	28.2 g of an oxide of potassium which contains 23.4 g potassium g.	0.08 mol uranium combined with 3.413 g oxygen h.	1 mol zinc combined with 32 g oxygen and 2 g hydrogen i.	A chloride of lead in which 1.302 g of the compound contains 0.530 g chlorine j.	Aluminium bromide which contains 2.4 g bromine in every 2.67 g of bromide

10.	Determine the molecular formula of the following from the given information: a. 	8 g carbon are combined with 2 g hydrogen and the molar mass is 30 g mol-1. b. 	1.56 g of a hydrocarbon contains 1.44 g carbon and its relative molecular mass is 78 c. 	0.2 mol nitrogen atoms are combined with every 6.4 g oxygen and the molar mass of this compound is 92 g mol-1. e. 	3.55 g of an oxide of phosphorus contain 1.55 g phosphorus. Its relative molecular mass is estimated to be a little below 300.

Find the formula for each of the following substances whose percentage composition is given

11.	40% calcium, 12% carbon & 48% oxygen

12.	40% copper, 40% oxygen & sulphur

13.	the oxide of copper which contains 88.9% Cu by mass

14.	the hydrocarbon which contains 85.7% carbon and has a relative molecular mass of 96

15.	the carbohydrate which has a molar mass of 180 g mol-1 and contains 53.33% oxygen and 6.67% hydrogen.

Balancing chemical equations
Once you know the formulae of the chemicals in a reaction, you need to make a balanced chemical equation.

You cannot change the formulae of the chemicals.

You can only add coefficients to indicate how many molecules of each chemical react.

Example 1

 * C10H16 + Cl2 → C + HCl

This is unbalanced. Let’s balance the carbons first:

 * 1 C10H16 + Cl2 → 10 C + HCl

Now let’s try the hydrogens:

 * 1 C10H16 + Cl2 → 10 C + 16 HCl

Finally, time for the chlorines:

 * C10H16 + 8 Cl2 → 10 C + 16 HCl

Example 2

 * Si2H3 + O2 → SiO2 + H2O

This is unbalanced. Let’s balance the silicon first:

 * 1 Si2H3 + O2 → 2 SiO2 + H2O

Now let’s try the hydrogens:

 * 2 Si2H3 + O2 → 4 SiO2 + 3 H2O

Finally, time for the oxygens:

 * 4 Si2H3 + 11 O2 → 8 SiO2 + 6 H2O

Here is a trick you can use to guide you in steps 2 and 3:

 * 1 Si2H3 + O2 → 2 SiO2 + 3/2 H2O

Example 3

 * Ca10F2(PO4)6 + H2SO4 → Ca(H2PO4)2 + CaSO4 + HF

I don’t like the calcium. It appears in more than two compounds here. Next in line is fluorine:

 * 1 Ca10F2(PO4)6 + H2SO4 → Ca(H2PO4)2 + CaSO4 + 2 HF

The phosphate and sulphate can be treated as units:

 * 1 Ca10F2(PO4)6 + H2SO4 → 3 Ca(H2PO4)2 + CaSO4 + 2 HF

 * 1 Ca10F2(PO4)6 + 1 H2SO4 → 3 Ca(H2PO4)2 + 1 CaSO4 + 2 HF

Note that although we have coefficients for every substance, the coefficients 1, 3 and 2 are not balanced with the coefficients 1 and 1 – so I write them in two different colours.

The hydrogens look tricky too, but it’s either them or the calcium now:

1 Ca10F2(PO4)6 + 7 H2SO4 → 3 Ca(H2PO4)2 + 7 CaSO4 + 2 HF

Better do the calcium now…

Ca10F2(PO4)6 + 7 H2SO4 → 3 Ca(H2PO4)2 + 7 CaSO4 + 2 HF

EXERCISE 5 Balance these equations: 1.	   Cu +     O2 →     CuO 2.	   Fe +     O2 →     Fe3O4 3.	   Mg +     HCl →    MgCl2 +     H2 4.	    Al +     HCl →     AlCl3 +     H2 5.	    P +     O2 →     P2O5 6.	   NaHCO3 →     Na2CO3 +     CO2 +     H2O 7.	   KClO3 →     KCl +     O2 8.	    NaNO3 →     NaNO2 +     O2 9.	    Cu(NO3)2 →     CuO +     NO2 +     O2 10. PbO +    C →     Pb +     CO2 11.	   C4H8 +     O2 →     CO2 +     H2O 12.	   C4H10 +     O2 →     CO2 +     H2O 13.	   Na2CO3 +     HCl →     NaCl +     H2O +     CO2 14.	   KOH +     H2SO4 →    K2SO 4 +     H2O 15.	    (NH4)2SO4 +     NaOH →     NH3 +     Na2SO4 +     H2O 16.	   Mg +     H2O →    MgO +     H2 17. Na +    H2O →    NaOH +     H2 18. Pb3O 4 +    H2 →     Pb +     H2O 19.	   Fe2O3 +     CO →     Fe +     CO2 20.	   Fe(OH)3 →    Fe2O 3 +     H2O 21.	   CuO +     H2 →    Cu +     H2O 22.	   Zn +     HCl →     ZnCl2 +     H2 23. KClO3 →    KCl +     O2 24. S8 +    F2 →     SF6 25.	   Fe +     O2 →     Fe2O3 26.	   C2H6 +     O2 →     CO2 +     H2O

The mole ratios of any species in a chemical equation.
EXERCISE 6

1.	What is the amount (unit : mole) of hydrochloric acid needed to react with 1 mol Mg and how much magnesium chloride is formed?

2.	What is the amount of chlorine which will react with 4 mol Fe? How much iron III chloride is formed?

3.	How much carbon dioxide can be produced by reacting 0.1 mol CuCO3 with hydrochloric acid? What is the minimum amount of acid required?

4.	What is the amount of sodium hydrogencarbonate which should be heated to produce 0.2 mol Na2CO3?

5.	What amount of barium sulphate can be precipitated from a solution containing 0.01 mol barium chloride? What amount of potassium sulphate will be required to react with this barium chloride? What would be the effect of adding twice the amount of potassium sulphate?

The state symbols (s), (l), (g) and (aq).
EXERCISE 7 Can you add state symbols to the equations above? Aqueous solutions and Ionic equations Many substances dissolve in water to form aqueous solutions. Ionic substances are usually soluble, separating into their component ions: Al2(SO4)3 (s)  2 Al+3(aq) + 3 SO4-2(aq) The mobility of the ions in solution means that these solutions will conduct electricity (though the solid substance will not). Covalent substances do not usually dissolve in water. If they do dissolve, the molecules remain intact: C6H12O6(s)  C6H12O6(aq) When no more solute can be dissolved in a solvent, the solution is said to be saturated.

Ionic equations describe only the ions that react, omitting other (‘spectator’) ions. AgNO3 (aq) + NaCl(aq) ® AgCl(s) + NaNO3 (aq) Each aqueous compound can be treated as a pair of ions: Ag+(aq) + NO-3 (aq) + Na+(aq) + Cl-(aq) ® AgCl(s) + Na+(aq) + NO-3 (aq) The sodium and nitrate ions do not take part in the reaction Ag+(aq) + Cl-(aq) ® AgCl(s) This treatment simplifies the equation and makes it more generally applicable. E.g. What if silver fluoride and potassium chloride solutions were mixed? When an acid and an alkali react, ionic equations can be very useful: Sodium hydroxide (NaOH) and hydrochloric acid (HCl) react to form sodium chloride and water Magnesium hydroxide (Mg(OH)2) and sulphuric acid (H2SO4) react to form magnesium sulphate (MgSO4) and water Treating Na+, Mg2+, Cl- and SO42- as spectator ions, what is the common ionic equation when a hydroxide reacts with an acid? EXERCISE 8 Write balanced equations for the following reactions. Put in the physical states in the appropriate manner and write the ionic equation as well where this is appropriate (numbers 1, 2, 5, 11, & 15). Occasionally, oxygen appears as reactant but is not in any of the named products. In these cases, assume it is converted into water. 1. Iron filings reacting with dilute hydrochloric acid to give hydrogen plus iron II chloride solution. 2. Zinc oxide powder dissolves in dilute hydrochloric acid to give zinc chloride and water. 3. In the Contact process, sulphur dioxide and oxygen combine to form sulphur trioxide in the presence of vanadium V oxide catalyst and at a temperature of 450°C. 4. When crystalline potassium nitrate [nitrate (V)] is heated, oxygen is given off and a residue of potassium nitrite [nitrate (III)] remains. 5. When chlorine is bubbled into aqueous potassium iodide, a ppt. of iodine is formed along with a solution of potassium chloride. 6. The effect of heat on dilead II lead IV oxide (Pb3O4) is to produce oxygen, leaving lead II oxide behind. 7. Baking soda, sodium hydrogen carbonate, is used in cooking and when heated it decomposes to form sodium carbonate, carbon dioxide and steam. 8. When carbon dioxide is bubbled through lime water (calcium hydroxide solution), milkiness is observed due to the formation of a ppt of calcium carbonate. 9. If carbon dioxide is allowed to continue to bubble through the solution from (8) for a long time, the ppt redissolves, forming calcium hydrogencarbonate. 10. In the blast furnace, carbon monoxide reduces iron III oxide to molten iron while being oxidised itself into carbon dioxide. 11. The chemical test for a sulphate is to add barium chloride solution to a solution of the test sample. A white ppt. of barium sulphate indicates a positive result. 12. Magnesium burns in an extremely exothermic reaction in which magnesium oxide is the product. 13. When conc. sulphuric acid (a liquid) is poured onto common salt, fumes of hydrogen chloride are observed, while sodium hydrogensulphate remains in the test tube. 14. A solution of hydrogen peroxide will decompose spontaneously, in the presence of manganese IV oxide catalyst, to liberate oxygen. 15. When solutions of ammonium chloride and sodium hydroxide were heated together, the smell of ammonia was observed. Sodium chloride was one of the other products.

Calculating theoretical yields from chemical equations.
EXERCISE 9

1	What is the amount of sodium nitrate (nitrate V) (NaNO3) in 17.0g ? What mass of sodium nitrite (nitrate III) will be obtained by heating this if it decomposes according to the equation :- 2 NaNO3  2 NaNO2 + O2

2.	What mass of zinc oxide remains after heating 9.45g zinc nitrate? 2 Zn(NO3)2  2 ZnO + 4 NO2 + O2

3.	What mass of sodium carbonate remains after heating 4.2g sodium hydrogencarbonate?

4.	What mass of powdered zinc would react with 0.96 g of sulphur? What is the expected yield of zinc sulphide?

5.	What will be the loss in mass on heating 6.2g copper carbonate until no further reaction takes place? CuCO3 (s)  CuO (s) + CO2 (g)

6.	A solution contained 6.62g of lead nitrate. A solution of sodium chloride was added in order to precipitate lead chloride. What is the expected yield of lead chloride?

7.	What is the amount of Mg contained in 4.8g magnesium? If this reacts with hydrochloric acid, what is the amount of hydrogen gas which will be produced?

8.	An aqueous solution contains 12.6 g HNO3. What amount of HNO3 is this? Find the amount and the mass of potassium hydroxide which will just neutralise this. What mass of potassium nitrate could you expect as product?

9.	5.05 g of copper nitrate decomposes according to the following equation when it is heated 2 Cu(NO3)2  2 CuO + 4 NO2 + O2 (a)	What mass of copper oxide is produced? (b)	What amount of nitrogen dioxide is formed?

The limiting reactant and the reactant in excess: Theoretical, experimental and percentage yield.
EXERCISE 10

1.	What mass of zinc will be required to react completely with 5g of copper sulphate and what mass of copper will be formed?

2.	How much iron II sulphate will be required to react with 4g sodium hydroxide and what mass of iron II hydroxide will be formed?

3.	8g of calcium are dissolved in excess hydrochloric acid. How many molar masses of acid will actually react? What amount of calcium chloride can you expect? If this crystallises out of solution as CaCl2.6H2O, what is the maximum mass of crystals that can be produced?

4.	A technician used 2.4g of magnesium ribbon to produce crystals of magnesium sulphate - 7 - water by reaction with dil. sulphuric acid. What should his yield (in grams) have been? If he managed to make only 16.4 g, calculate his percentage yield.

5.	A portable gas stove burns butane at the rate of 116 g per hour. What mass of water will be produced after one hour? In what physical state will this water first appear? What will eventually happen to it? If the appliance is used in a confined space, state what problems or dangers might result.

6.	8.0 g of copper oxide were dissolved in dilute sulphuric acid and after suitable treatment 20 g copper II sulphate - 5 - water were obtained. What is the percentage yield?

7.	Ethanol (20 cm3) was heated with an equal volume of ethanoic acid in the presence of concentrated sulphuric acid catalyst. The yield of ethyl ethanoate was 8 cm3. (a)	Calculate the mass and the amount of each reagent. (b)	Which of the two reagents, ethanol or ethanoic acid is the limiting reagent i.e. which is not in excess? (c)	Calculate the percentage yield of ester. [ densities in g cm-3 :- ethanol 0.79; ethanoic acid 1.05; ethyl ethanoate 0.9]

8.	8.4g of sodium hydrogen carbonate are mixed with 15g of hydrochloric acid. Explain which reagent is in excess. Find the amount of carbon dioxide produced in the reaction. Would more or less carbon dioxide have been produced by heating the hydrogencarbonate?

9.	On heating 4.2g of a metal carbonate, XCO 3, 0.05 mol carbon dioxide was produced. Calculate the relative atomic mass, A r, of the metal X. XCO 3  XO + CO 3

10.	Bath salts (sodium carbonate crystals) (9.53g) were gently heated in a crucible in order to drive off all their water of crystallisation. 3.53g of anhydrous salt remained. Calculate the number of molecules of water of crystallisation in the sodium carbonate and hence its formula. However when 12 g of the crystals were left in a hot room, the loss in mass was only 6.80g. What can you deduce about the formula of the sodium carbonate after it had undergone efflorescense in these conditions?

Avogadro’s law of volumes of gases.
Avogadro’s law: Equal volumes of gases, at the same pressure and temperature, contain equal amounts of molecules. The law can be used to find the volumes of gases in a reaction: e.g. 1 dm3 of hydrogen will react with 1 dm3 of chlorine to give 2 dm3 of hydrogen chloride. EXERCISE 11 What volume of CO2 will be produced when 1 dm3 of methane (CH4) combines with 3 dm3 of oxygen? What volume of CO2 will be produced when 1 dm3 of ethene (C2H4) combines with 3 dm3 of oxygen?

Graphs relating to the ideal gas equation.
This section meets many criteria for Topic 11.3 Graphical techniques EXERCISE 12

1. A sample of gas was heated while the pressure was kept constant. The changes in volume were recorded. Graph the following data:

Use a scale which starts at -300 °C and 0 dm3.

Estimate the temperature required for the gas to have a zero volume.

2. Another gas sample was pressurized and the effect on its volume was recorded. The temperature was kept constant. Graph the following data:

What is the relationship between pressure and volume? 3. A gas was gradually introduced to a rigid, constant temperature, vacuum-filled container, and the pressure recorded as more gas was added. Graph the following data:

What is the relationship between pressure and amount?

4. One mole of a gas was kept in a 1 m3 (1000 dm3) container as the temperature was varied. The effect on the pressure was recorded:

What is the relationship between pressure and temperature?

What is the gradient of the graph?

Use the gradient to estimate the temperature required for the pressure to be 101325 Pa (1 atm).

Molar volume of a gas
A mole of any gas at 298 K and 1 atmosphere pressure occupies 24 dm3. At 273 K the volume is 22.4 dm3. E.g. 2 moles of argon atoms occupy 48 dm3 0.5 moles of oxygen molecules occupy 12 dm3 What is the volume of carbon dioxide that is produced when 50 g of calcium carbonate decomposes? CaCO3 ® CaO + CO2

The relationship between temperature, pressure and volume for a fixed mass of an ideal gas.
We can summarize the behavior of an ideal gas with this equation:

PV = nRT

P is the pressure (in Pa or N m-2)

V is the volume (m3)

n is the number of moles of the gas

R is the ideal gas constant (=8.31 J K-1 mol-1)

T is the absolute temperature (K)

You can see from this that if pressure increase, either the volume must decrease or the temperature increases. Similarly, increasing temperature causes increased volume and/or pressure. EXERCISE 12

Use PV = nRT to calculate: a)	The volume occupied by 1 mol of a gas at 25 oC (298 K) and 100000 Pa (1 bar) pressure.

b)	The pressure required to make 5 mol of gas occupy 50 dm3 (50 x 10-3 m3) at 35 oC.

c)	The number of moles of gas which occupy 25 dm3 at 85 oC and 1.05 bar.

d)	The temperature of a 3 mol gas sample which has a volume of 18 dm3 at 1 atm (1.013 bar) pressure.

If we change the conditions for a given sample of gas, we can simplify the equation considerably. Call the initial pressure, temperature and volume P1, T1 and V1, and the values after the conditions have changed are called P2, T2 and V2. The amount of gas, n, and the constant, R, are the same in both cases. This gives us the formula: = P1*V1 / T1 = P2*V2 / T2 The ‘1’ and ‘2’ refer to the volume (V) of the gas under different conditions of Pressure (P) and Absolute Temperature (T - measured in kelvins) Helpfully, the pressure and volume do not now have to measured in Pa and m3. Any units are suitable, so long as the same units are used for P1and P2, and for T1 and T2.

EXERCISE 13

1. Use the simplified equation (and answers to the previous exercise) to calculate:

a)	The volume occupied by 1 mol of a gas at 0 oC and 100000 Pa (1 bar) pressure.

b)	The pressure required to make 5 mol of gas occupy 40 dm3 (50 x 10-3 m3) at 35 oC.

c)	The temperature of a 3 mol gas sample which has a volume of 25 dm3 at 1 atm (1.013 bar) pressure.

d)	If a sample of gas which occupies 26.25 dm3 at 120.8 oC and 1.10 bar could be the same as a sample which occupies 25 dm3 at 85 oC and 1.05 bar.

2. If 1 dm3 of gas is warmed from 298 to 745 K, while the pressure is kept constant at 1 atm, what is its new volume?

3. What pressure is now required to pressurize the hot gas until it reaches its original volume?

Solute, solvent, solution and concentration
Concentration (c) is measured as the quantity of solute per unit volume (usually per dm3 i.e. dm-3) of solution (not solvent). Remember that 1 dm3 = 1000 cm3 The solute quantity can be measured as mass, so the units are g dm-3. cm = m/v	mass concentration = mass / volume The solute quantity can be measured as amount, so the units are mol dm-3. cn = n/v	molar concentration = amount / volume The molar concentration of a substance is often written in the shorthand form [substance]. E.g. Instead of writing ‘The molar concentration of NaCl’ we can write [NaCl].

EXERCISE 14

1)	Write down all the possible mathematical expressions which might be needed when doing calculations based on volumetric analysis (titrations).

2)	What is the mass concentration if 5 g of NaCl are dissolved in 500 cm3 of solution?

3)	What is the amount of 5 g of NaCl?

4)	What is the molar concentration if 5 g of NaCl are dissolved in 500 cm3 of solution?

5)	25 cm3 of hydrochloric acid (0.12 mol dm-3) were just neutralized by 28.4 cm3 of sodium hydroxide solution. Calculate the concentration of the base.

6)	23.2 cm3 of hydrochloric acid were required to cause the formation of the very pale grey colour - almost colourless - of screened methyl orange indicator in 25.0 cm3 of potassium hydroxide solution. Determine the concentration of the acid given that the potassium hydroxide was made by dissolving 1.372 g in 250.0 cm3 of solution.

7)	A sample of lithium hydroxide was weighed as 0.62 g. It was dissolved in water & made up to 250.0 cm3. 25.00 cm3 aliquots were titrated and 21.25 cm3 of standard hydrochloric acid (0.100 mol dm-3) were required. The lithium hydroxide is thought to be contaminated with lithium chloride. Calculate the mass of lithium hydroxide in the sample and hence its percentage purity.

8)	Butanedioic acid is a dibasic acid (diprotic acid) of molecular formula C4H6O4. 1.0073 g were weighed, dissolved in water and the solution made up to 250 cm3. 25 cm3 portions required 23.95 cm3 of potassium hydroxide solution to cause the colour change of a suitable indicator. Calculate the concentration of the alkali.

 * a)	What amount of butanedioic acid was used (how many moles)?

 * b)	What amount was used in each titration?

 * c)	What amount (mol) of potassium hydroxide was present in each titration?

 * d)	What is the concentration of potassium hydroxide?

9)	A technician was asked to analyse a solution of commercial caustic soda for its sodium hydroxide & sodium carbonate content. She did this by titrating a 25.00 cm3 portion with hydrochloric acid solution (0.100 mol dm-3.) using firstly phenolphthalein and then, as part of the same titration, by adding methyl orange.

Results obtained were 16.90 cm3 of acid to bring about the colour change of the phenolphthalein and a total end point of 24.55 cm3.

At the first colour change (phenolphthalein goes pink to colourless), the reactions taking place are:

OH- + H+  H2O & also CO3-2 + H+  HCO3-2.

At the second colour change (methyl orange turns green to red), the reaction taking place is

HCO3-2 + H+  CO2 + H2O

Thus the first part of the titration relates to the concentration of hydroxide plus carbonate. The second part refers to the concentration of the carbonate (in its hydrogencarbonate form) only.

 * a)	Calculate the number of moles of acid used in the first part and thus the total number of moles of hydroxide plus carbonate in the 25.00 cm3 portion.

 * b)	Calculate the volume and hence the number of moles of acid used in the second part of the titration and thus the number of moles of hydrogencarbonate (and thus carbonate).

 * c)	From a) & b) calculate the number of moles of hydroxide and of carbonate in the 25.00 cm3 portion. From these results calculate the concentrations of the sodium hydroxide & sodium carbonate in the solution. Give your answer in each case in mol dm-3 & also in g dm-3.

10)	1.483 g of the mineral Dolomite were added to excess hydrochloric acid (50 cm3, 1.0 mol dm-3). After reaction was complete, the solution was filtered and made up to 250 cm3. 25 cm3 portions of this solution containing unreacted acid were titrated against 0.1 mol dm-3 KOH when a mean titre of 26.3 cm3 was obtained. Assuming that Dolomite is essentially magnesium carbonate plus insoluble silica, calculate its percentage composition.

 * a)	What amount of potassium hydroxide was in the 26.3 cm3?

 * b)	What amount of hydrochloric acid would have reacted with this?

 * c)	What amount of hydrocloric acid was in the 250 cm3 solution?

 * d)	What amount of acid was taken at the start?

 * e)	What amount of acid reacted with the Dolomite?

 * f)	Calculate the amount and hence the mass of magnesium carbonate which would have reacted with the hydrochloric acid.

 * g)	Calculate the percentage by mass of magnesium carbonate in Dolomite.

title: IB Chemistry/Stoichiometry


text:
User:Akaemi73

Emi Maniatopoulou Brighton, UK Interests: The Criminal Justice System, Drugs - law, social cost, psychology

source: wikimedia

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Akaemi73


text:
Talk:Harold Guskin

Notability
Established by cited sources:, ~Kvng (talk) 22:09, 14 November 2019 (UTC)

title: Talk:Harold Guskin


text:
Fish Magic

Fish Magic is a 1925 Surrealist painting by Swiss-German artist Paul Klee. The painting belonged to the collection of Walter and Louise Arensberg before being donated in 1950 to the Philadelphia Museum of Art where it is currently held.

Analysis
Fish Magic is seen as an intermingling of aquatic, celestial, and earthly entities. The painting is covered by a delicate surface of black paint, under which lies a dense layer of multicolored pigments. The colorful figures were then scratched and scrawled out by Klee on the dark background. A square of muslin was glued to the painting in the center, giving the painting the sense of a collage. The painting's dark palette and the muslin's fragility create a mysterious and inky atmosphere.

Ker writes that "Fish Magic is set squarely within the tradition of German Romanticism, with its blend of fantasy and natural empiricism, of poetry and pragmatics." She points to the technique used to draw out the various fish, flora, human beings, and clock tower as "a sophisticated version of the games children play with wax crayons."

According to Ann Temkin, Fish Magic is a masterpiece in which the intellectual and imaginative forces of Klee's artistic gifts are reconciled, producing a "sense of magic". Specifically, Temkin points to the thin diagonal line extending from the middle right of the canvas to the top of the clock tower, writing that the "long painted line from the side seems ready to pull the [square of muslin] off to reveal something underneath."

title: Fish Magic


text:
Calculus/Sequences

A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence.

For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...).

Examples and notation
There are various and quite different notions of sequences in mathematics, some of which (e.g., exact sequence) are not covered by the notations introduced below.

A sequence may be denoted (a1, a2, ...). For shortness, the notation (an) is also used.

A more formal definition of a finite sequence with terms in a set S is a function from {1, 2, ..., n} to S for some n ≥ 0. An infinite sequence in S is a function from {1, 2, ...} (the set of natural numbers without 0) to S.

Sequences may also start from 0, so the first term in the sequence is then a0.

A finite sequence is also called an n-tuple. Finite sequences include the empty sequence that has no elements.

A function from all integers into a set is sometimes called a bi-infinite sequence, since it may be thought of as a sequence indexed by negative integers grafted onto a sequence indexed by positive integers.

The sequence $$a_n \ = \ \frac{1}{n}$$ is called the harmonic sequence.

If c and d are given numbers, the sequence $$a_n \ = \ c + nd$$ is an arithmetic sequence.

If b and r ≠ 0 are given, the sequence $$a_n \ = \ b r^n$$ is a geometric sequence.

Types and properties of sequences
A subsequence of a given sequence is a sequence formed from the given sequence by deleting some of the elements (which, as stated in the introduction, can also be called "terms") without disturbing the relative positions of the remaining elements.

If the terms of the sequence are a subset of an ordered set, then a monotonically increasing sequence is one for which each term is greater than or equal to the term before it; if each term is strictly greater than the one preceding it, the sequence is called strictly monotonically increasing. A monotonically decreasing sequence is defined similarly. Any sequence fulfilling the monotonicity property is called monotonic or monotone. This is a special case of the more general notion of a monotonic function. A sequence that both increases and decreases (at different places in the sequence) is said to be non-monotonic or non-monotone.

The terms non-decreasing and non-increasing are often used in order to avoid any possible confusion with strictly increasing and strictly decreasing, respectively. If the terms of a sequence are integers, then the sequence is an integer sequence. If the terms of a sequence are polynomials, then the sequence is a polynomial sequence.

If S is endowed with a topology (as is true of real numbers, for example), then it becomes possible to consider the convergence of an infinite sequence in S. Such considerations involve the concept of the limit of a sequence.

It can be shown that bounded monotonic sequences must converge.

Sequences in analysis
In analysis, when talking about sequences, one will generally consider sequences of the form
 * $$(x_1, x_2, x_3, ...)\,$$ or $$(x_0, x_1, x_2, ...)\,$$

which is to say, infinite sequences of elements indexed by natural numbers. (It may be convenient to have the sequence start with an index different from 1 or 0. For example, the sequence defined by xn = 1/log(n) would be defined only for n ≥ 2. When talking about such infinite sequences, it is usually sufficient (and does not change much for most considerations) to assume that the members of the sequence are defined at least for all indices large enough, that is, greater than some given N.)

The most elementary type of sequences are numerical ones, that is, sequences of real or complex numbers.

title: Calculus/Sequences


text:
Poole Silver Company

Poole Silver Company was an American silver manufacturing company, active in Taunton, Massachusetts from 1892 to 1971.

The Poole Silver Company was formed in 1892 by George Poole and Edward Roche in Taunton as Poole, Roche & Co., then established as a corporation on May 21, 1895, as an early manufacturer of silver products made with electroplating techniques. In 1900 it operated in a small two-room factory at 106 Whittenton Street, and later moved to 320 Whittenton Street. From 1946 the firm began to produce sterling silver flatware, holloware, and cutlery. In 1971 the company was bought by Towle Silversmiths. The intellectual property currently belongs to Lifetime Brands.

title: Poole Silver Company


text:
Rostov Defensive Operation

The Rostov Defensive Operation on November 5–16, 1941 was a front–line defensive operation of the Soviet troops of the Southern Front, an integral part of the Donbas–Rostov Strategic Defensive Operation of the Great Patriotic War.

Previous events and plans of the parties
Having suffered a heavy defeat in the Donbas Defensive Operation in October 1941, the troops of the Soviet Southern Front (commanded by Colonel General Yakov Cherevichenko) withdrew to the Debaltsevo–Bolshekrepinskaya–Khapry line by the beginning of November 1941. At this line, the heavily weakened armies of the front were hastily consolidated: the 12th Army (Major General Konstantin Koroteev), the 18th Army (Major General Vladimir Kolpakchi), the 9th Army (Major General Fyodor Kharitonov).

All armies had a large shortage of personnel, and especially in military equipment. After a heavy defeat in the Donbas operation, they demanded a significant replenishment, but all Soviet reserves were sent to Moscow and to form Reserve Armies.

Since Rostov-on-Don remained the main target of the German offensive, the 56th Separate Army (Lieutenant General Fyodor Remezov) was deployed on the approaches to the city, which hastily created the Rostov–Novocherkassk fortified region and was responsible for the immediate defense of Rostov.

The command of Army Group South (General Field Marshal Gerd von Rundstedt), after a short pause to pull up the rear, was preparing to resume the operation to capture Rostov. However, having received intelligence information about the strengthening of the Soviet defense on the shortest route to Rostov along the Taganrog–Rostov-on-Don railway along the Azov Sea coast, it decided to change the direction of the main attack and carry out a deep enveloping maneuver from the north and northeast, through Dyakovo, Shakhty, Novocherkassk. If successful, the troops of the 9th and 56th Separate Armies would fall into the encirclement northwest of Rostov. Then it was planned to turn part of the forces of the 1st Tank Army to the north and, together with the troops of the 17th Army, close a new encirclement ring in the Voroshilovgrad area for complete encirclement and elimination of the entire Southern Front in the eastern part of Donbas.

In addition, the 1st Panzer Army (Colonel General Ewald von Kleist) was to seize a bridgehead on the southern bank of the Don. After that, it was supposed to develop an offensive to the south and, first of all, to capture Maykop and Tuapse in order to send oil through the pipeline and further by sea for refining to Romania. In March – April 1942, German troops expected to completely occupy the Caucasus up to the border with Iran.

To carry out the operation, the 14th Motorized Corps (General of the Infantry Gustav von Wietersheim of the 1st Panzer Army (14th and 16th Panzer Divisions, SS Viking Motorized Division) was deployed to the eastern part of Donbas. From the south, he was assisted by the 3rd Motorized Corps (60th Motorized Division and SS Adolf Hitler Motorized Division), from the north by the 49th Mountain Corps (1st and 4th Mountain Divisions). In the south, the 13th Panzer Division delivered a diversionary blow to Rostov along the shortest route. The offensive of the strike group was supported by the troops of the 17th German Army and the Italian Expeditionary Corps (General Giovanni Messe).

The Soviet command was able to timely reveal the transfer of the strike forces of the 1st Tank Army to the north, accurately determine the direction of the main attack (in the zone of the 9th Soviet Army) and unravel the German plans. Not having in their reserve tank forces to parry a German strike and not counting on replenishing their significantly weakened troops, the Commander–in–Chief of the South–West Direction, Marshal of the Soviet Union Semyon Timoshenko and Cherevichenko focused on exhausting the enemy with stubborn defense. In the defensive zone of the 9th Army, a system of anti–tank strong points and anti–tank areas was built in the Dyakovo area, which became one of the first experiments with a powerful anti-tank defense in the Great Patriotic War. These points mutually covered each other with fire, were echeloned in depth and provided crossfire from several artillery positions on each target. The infantry personnel allocated for the defense of these points were tested with tanks and were trained in actions when repelling tank attacks.

Operation progress
On November 5, the German 1st Panzer Army launched an offensive in the 9th Army's defense zone. The German command did not succeed in achieving a surprise; the battle immediately took on an extremely fierce character. On the 9th Army's right flank, relying on the anti–tank areas at Dyakovo, two Soviet rifle divisions pinned down three 1st Panzer Army divisions and inflicted heavy losses on them. German tanks, with great difficulty, slowly moved forward, storming one Soviet position after another. Parts of the 9th Army of General Fyodor Kharitonov combined stubborn defense with active actions, inflicted three powerful counterattacks on the wedged enemy. By the end of November 8, in four days of fighting, the enemy, at the cost of heavy losses, had managed to push the 9th Army 30–35 kilometers away.

From November 11 to 16, German troops advanced another 25 kilometers in the Novocherkassk direction. The advance on the main direction to Shakhty was only 15 kilometers, on the auxiliary one (to Krasny Sulin) – a little more than 10 kilometers, and in a diversionary attack on Rostov, the German 13th Panzer Division did not advance at all. To the north, in the zone of the 18th Army, the advance of the German infantry divisions in 12 days of fighting ranged from 2 to 10 kilometers. During the entire battle, the enemy never managed to break through the Soviet defenses.

The penetration of German troops into the line of the Soviet defense forced them to stretch out their northern flank. A front line configuration favorable for the Soviet side was formed, convenient for striking the flank and rear of the 1st German Tank Army. On November 8, the Commander–in–Chief of the troops of the South–Western direction, Semyon Timoshenko, reported to the Supreme Commander–in–Chief Joseph Stalin the plan of an offensive operation with the aim of defeating the 1st German Tank Army. Already on November 9, the Headquarters of the Supreme Command decided to prepare and conduct this operation. In the area of Shakhty – Kamensk-Shakhtinsky, the striking force of the front – the 37th Army – was quickly formed and concentrated.

Results of the operation
Both sides suffered significant losses in manpower, and the German side in tanks. As a result of losses, the command of Army Group South had to make adjustments to the plan for a further offensive, which again led to a regrouping of troops and a suspension of the offensive. The plan for a new encirclement of the troops of the Southern Front was thwarted by the Red Army at the very beginning.

Under cover of the stubborn heroic defense of the armies of the Southern Front, and above all the troops of the 9th Army, the Soviet command regrouped its forces. On November 15–16, troops of the 37th Army moved out of the concentration area to the front line and occupied the starting lines for the launch of a counteroffensive on the Rovenki–Pavlovka line.

Without the slightest operational pause, on November 17, Soviet troops went on the offensive – the Rostov Offensive Operation began. In the course of it, the course of the battle on the entire southern flank of the Soviet–German front was turned around and the largest defeat was inflicted on German troops in the entire history of World War II.

title: Rostov Defensive Operation


text:
Probability/Probability Spaces

Terminologies
The name of this chapter,, is a mathematical construct that models a random experiment. To be more precise:

Let us first give the definitions related to sample space. For the definitions of event space and probability, we will discuss it in later sections.

Probability interpretations
In this chapter, we will discuss probability mathematically, and we will give an axiomatic and abstract definition to probability (function). By axiomatic definition, we mean defining probability to be a function that satisfying some axioms, called probability axioms. But such axiomatic definition does not tell us how should we interpret the term "probability", so the definition is said to be from the interpretation of probability. Such independence make the formal definition always applicable, no matter how you interpret probability.

However, the axiomatic definition does not suggest a way to construct a probability measure (i.e., assigning probabilities to events): it just states that probability is a function satisfying certain axioms, but how can we construct such function in the first place? In this section, we will discuss two main types of probability interpretations: subjectivism and frequentism, where the method of assigning probabilities to events is mentioned in each of them.

Subjectivism
Intuitively and naturally, of an event is often regarded as a numerical measure of the "chance" of the occurrence of the event (that is, how likely the event will occur). So, it is natural for us to assign probability to an event based on our own assessment on the "chance". (In order for the probability to be valid according to the axiomatic definition, the assignment needs to satisfy the .) But different people may have different assessment on the "chance", depending on their personal opinions. So, we can see that such interpretation of probability is somewhat , since different people may assign different probabilities to the same event. Hence, we call such probability interpretation as (also known as ).

The main issue of the subjectivism is the lack of objectivity, since different probabilities can be assigned to the same event based on personal opinion. Then, we may have difficulties in choosing which of the probabilities should be used for that event. To mitigate the issue of the lack of objectivity, we may adjust our degrees of belief on an event from time to time when there are more observed data through, which will be discussed in later chapter, so that the value is assigned in a more objective way. However, even after the adjustment, the assignment of value is still not in an objective way, since the adjusted value (known as ) still depends on the initial value (known as ), which is assigned subjectively.

Frequentism
Another probability interpretation, which is objective, is called. We denote by $$n(E)$$ the number of occurrences of an event $$E$$ in $$n$$ repetitions of experiment. (An is any action or process with an  that is subject to uncertainty or randomness.) Then, we call $$\frac{n(E)}{n}$$ as the of the event $$E$$. Intuitively, we will that the relative frequency fluctuates less and less as $$n$$ gets larger and larger, and approach to a constant limiting value (we call this as ) as $$n$$ tends to infinity, i.e., the limiting relative frequency is $$\lim_{n\to \infty}\frac{n(E)}{n}$$. It is thus natural to take the limiting relative frequency as the probability of the event $$E$$. This is exactly what the definition of probability in the frequentism. In particular, the of such limiting relative frequency is an assumption or  in frequentism. (As a side result, when $$n$$ is large enough, the relative frequency of the event $$E$$ may be used to approximate the probability of the event $$E$$.)

However, an issue of frequentism is that it may be infeasible to conduct experiments many times for some events. Hence, for those events, no probability can be assigned to them, and this is clearly a limitation for frequentism.

Because of these issues, we will instead use a modern axiomatic and abstract approach to define probability, which is suggested by a Russian mathematician named Andrey Nikolaevich Kolmogorov in 1933. By, we mean defining probability quite broadly and abstractly as something that satisfy certain axioms (called ). Such probability axioms are the mathematical foundation and the basis of modern probability theory.

Probability axioms
Since we want use the probability measure $$\mathbb P$$ to assign probability $$\mathbb P(E)$$ to every event $$E$$ in the sample space, it seems natural for us to set of the probability measure $$\mathbb P$$ to be the set containing subsets of $$\Omega$$, i.e., the power set of $$\Omega$$, $$\mathcal P(\Omega)$$. Unfortunately, this situation is not that simple, and there are some technical difficulties if we set the domain like this, when the sample space $$\Omega$$ is.

This is because the power set of such uncountable sample space includes some "badly behaved" sets, which causes problems when assigning probabilities to them. (Here, we will not discuss those sets and these technical difficulties in details.) Thus, instead of setting the domain of the probability measure to be $$\mathcal P(\Omega)$$, we set the domain to be a (sigma-algebra) containing some "sufficiently well-behaved" events:

We have seen two examples of $$\sigma$$-algebra in the example above. Often, the "smallest" $$\sigma$$-algebra is not chosen to be the domain of the probability measure, since we usually are interested in events $$\varnothing$$ and $$\Omega$$.

For the "largest" $$\sigma$$-algebra, on the other hand, it contains every event, but we may not be interested in some of them. Particularly, we are usually interested in events that are "well-behaved", instead of those "badly behaved" events (indeed, it may be even impossible to assign probabilities to them properly (those events are called )).

Fortunately, when the sample space $$\Omega$$ is, every set in $$\mathcal P(\Omega)$$ is "well-behaved", so we can take this power set to be a $$\sigma$$-algebra for the domain of probability measure.

However, when the sample space $$\Omega$$ is, even if the power set $$\mathcal P(\Omega)$$ is a $$\sigma$$-algebra, it contains "too many" events, particularly, it even includes some "badly behaved" events. Therefore, we will not choose such power set to the domain of the probability measure. Instead, we just choose a $$\sigma$$-algebra that includes the "well-behaved" events to be the domain, so that we are able to assign probability properly to every event in the $$\sigma$$-algebra of the domain. Particularly, those "well-behaved" events are often the events of interest, so all events of interest are contained in that $$\sigma$$-algebra, that is, the domain of the probability measure.

To motivate the probability axioms, we consider some properties that the "probability" in frequentism (as a limiting relative frequency) possess: $$ \begin{align} \lim_{n\to \infty}\frac{n(\bigcup_{i=1}^{\infty}E_i)}{n} &=\lim_{n\to \infty}\frac{n(\bigcup_{i=1}^{\infty}E_i)}{n}\\ &=\lim_{n\to \infty}\frac{n(E_1)+n(E_2)+\dotsb}{n}&(\text{the events are pairwise disjoint})\\ &=\lim_{n\to \infty}\frac{n(E_1)}{n}+\lim_{n\to \infty}\frac{n(E_2)}{n}+\dotsb&(\text{every limit exists by the axiom in frequentism})\\ &=\sum_{i=1}^{\infty}\lim_{n\to \infty}\frac{n(E_i)}{n}, \end{align} $$
 * 1) The limiting relative frequency must be nonnegative. (We call this property as .)
 * 2) The limiting relative frequency of the whole sample space $$\Omega$$ ($$\Omega$$ is also an event) must be 1 (since by definition $$\Omega$$ contains all sample points, this event must occur in every repetition). (We call this property as .)
 * 3) If the events $$E_1,E_2,\dotsc$$ are pairwise disjoint (i.e., $$E_i\cap E_j=\varnothing$$ for every $$i,j$$ with $$i\ne j$$), then the limiting relative frequency of the event $$\bigcup_{i=1}^{\infty}E_i\overset{\text{ def }}=E_1\cup E_2\cup\dotsb$$ (union of subsets of $$\Omega$$ is a subset of $$\Omega$$, so it can be called an event) is
 * which is the sum of the limiting relative frequency of each of the events $$E_1,E_2,\dotsc$$. (We call this property as .)

It is thus very natural to set the probability axioms to be the three properties mentioned above:

Using the probability axioms alone, we can prove many well-known properties of probability.

Basic properties of probability
Let us start the discussion with some simple properties of probability.

Using this result, we can obtain from the countable additivity of probability:

Finite additivity makes the proofs of some of the following results simpler.

Constructing a probability measure
As we have said, the axiomatic definition does not suggest us a way to construct a probability measure. Actually, even for the same experiment, there can be many ways to construct a probability measure that satisfies the above probability axioms if there are not sufficient information provided:

However, we have previously mentioned that we may assign probabilities to events subjectively (as in subjectivism), or according to its limiting relative frequency (as in frequentism). Through these two probability interpretations, we may provide some background information for a random experiment, by assigning probabilities to some of the events before constructing the probability measure, to the extent that there is way to construct a probability measure. Consider the coin tossing example again:

In general, it is not necessary to assign probability to event in the event space in the background information for us to able to construct the probability measure in exactly one way. Consider the following example.

We can see from this example that to provide sufficient background information to the extent that the probability measure can be constructed in exactly one way, we just need the probability of each of the singleton events (which should be nonnegative and sum to one to satisfy the probability axioms). After that, we can calculate the probability for each of the other events in the event space, and hence construct the only possible probability measure.

This is true when the sample space is countable, in general:

The following is an important special case for the above theorem.

More advanced properties of probability
Recall the in combinatorics. We have similar results for probability:

The following is a classical example for demonstrating the application of inclusion-exclusion principle.

title: Probability/Probability Spaces


text:
Potez 40

The Potez 40 was a French three-engine, braced high-wing monoplane designed and built in response to a French government programme for colonial transport and policing aircraft duties.

Design and development
The Potez 40 was an all-metal aircraft covered with duralumin, longitudinally corrugated at approximately 100 mm pitch throughout. The wing was rectangular in plan apart from its rounded tips and was built around two I-section spars. On each side a parallel pair of airfoil section struts braced the wing from the forward and rear spars to the lower fuselage longeron.

The fuselage was in three demountable parts. The nose region forward of the pilot was smooth and slightly rounded but merged into a corrugated, flat sided and rectangular cross-section fuselage. The central Salmson 9Ab 230 hp nine cylinder radial engine was mounted on the extreme nose, completely uncowled and driving a two bladed propeller. The pilot's compartment had a shallow, framed and angled pair of plane windscreens just ahead of the wing leading edge with an internal door to the main cabin, which was lit by long, shallow side windows and accessed by a large triangular door defined by the lattice fuselage structure. Just behind the wing trailing edge there was an open dorsal gunner's position, which at some point in the Type 40's development housed a pair of machine guns on a standard rotatable mounting The detachable rear section carried the empennage, which was constructed in a similar way to the wings. In early drawings the fin was triangular and the rudder unbalanced though this was modified by the time the Potez 40 was displayed, unflown, at the 1930 Paris Salon into a taller vertical tail with a clearly extended tip. The horizontal tail was mounted near the base of the fin and was semi-elliptical, with straight leading edges and recessed elevators. It was braced from below with a pair of struts on both sides

The two outer Salmson engines were mounted, uncowled, on the forward wing bracing struts, with extended streamlined bodies behind them which connected to the rear bracing strut; the forward struts were reinforced by jury struts to the wing roots and the rear bracing struts by vertical jury struts to the rear spar. The Potez 40 had a tailwheel undercarriage with its main legs with rubber shock absorbers mounted vertically below the outer engine extensions; the mainwheels were hinged on widely spaced V-Struts from the lower fuselage and were sometimes enclosed under spats.

The Potez 40 made it first flight at Méaulte around the end of February 1931 and after satisfactory initial trials was flown to the military test centre at Villacoublay at the end of May 1931. After a long period of modification, it returned to Villacoublay for competitive tests in late 1932. In the interval it was tested with two other makes of engines and proposed as a commercial transport. It was Potez's last three-engine design. By 1935, the development of the Potez 40 had been abandoned, and the airframe was offered for sale.

Variants

 * Type 40-01: Salmson 9AB 9-cylinder radial engine.
 * Type 40-02: Lorraine Algol 9-cylinder radials.
 * Type 40-03: Commercial transport version with Gnome-Rhône 7K Titan Major 7-cylinder radials.

title: Potez 40


text:
SOR CN 12

SOR CN12 is a low-entry intercity bus produced by Czech bus manufacturer SOR since 2004.

Construction features
SOR CN 12 is two-axle, while the space ahead of the rear axle is a low-floor. The driven axle is the rear axle and engine with gearbox is located under the floor in the rear. Vehicle body is welded from steel sections, outside is flashing, inside lined with plastic sheeting. Cab is closed. The front axle is a brand SOR, rear solid axle is brand DANA.

Low-floor is approximately in two thirds of the bus, while in the low-floor section located at a height of 360 mm above the ground. To the rear of the vehicle, under which is hidden drivetrain, has two steps (as part of a low-floor and the last door). A similar solution is quite common for other producers and indicates the general concept of low-entry (loosely translated as "vehicle with low starting edge"), respectively. abbreviation LE. In the case of the bus SOR CN 12 However, this solution is unique variable height of the roof of the vehicle, popularly known as "hump".

Production and operation
CN 12 is two-door model of SOR BN 12, which is more suitable for intercity transportation, and was later renamed to SOR CN 12. Initially, however, was SOR CN 12 known as "SOR BN 12 two-door".

title: SOR CN 12


text:
User:FertChervu

Hello. I am a Mexican, 1983-born, professional librarian. I also am a self-taught composer of music, and I volunteered as an amateur choral singer for years.

I think Wikipedia could be a powerful information resource with proper support by professional librarians, so here I am. I created my user account years ago, but I didn't had a serious concern about Wikipedia before. Now, I will not leave. ;)

Have a good reading.

title: User:FertChervu


text:
Mary Jane Watson (Sam Raimi film series)

Mary Jane "MJ" Watson is a fictional character in Sam Raimi's Spider-Man film series. Based on the character of the same name, she is portrayed by Kirsten Dunst. In the films, Mary Jane is Peter Parker's next-door neighbor, childhood crush, and primary love interest. Though Mary Jane dates several other men in the first two films, she ultimately falls in love with Peter and Spider-Man and discovers they are one and the same. Despite his strong feelings for her, Peter initially declines a relationship with her in order to keep her safe, but they eventually become a couple in the end.

Despite being criticized for adhering to the damsel in distress archetype in each installment of the film series, Dunst's interpretation of the character has been generally well-received.

Comic book origins
Mary Jane Watson was first introduced into Spider-Man comics story-lines in The Amazing Spider-Man #42 in 1966, despite being mentioned earlier in the comics. She was conceived as competition to Gwen Stacy as Spider-Man's primary love interest, and is characterized as a free-spirited, outgoing personality as opposed to Gwen's more serious, academic nature. Peter Parker initially dates Gwen after he stops going out with Mary Jane due to what he sees as her shallow personality while Mary Jane refuses to be tied down in one relationship. Despite this, Mary Jane became more popular with fans and following Gwen's death in the comics, Peter and MJ begin to rekindle their relationship and eventually marry despite ups and downs in the comics.

Casting and execution
Actress Kirsten Dunst was cast as Mary Jane Watson for the 2002 Spider-Man film, with Mary Jane having been cemented in comics lore as Peter Parker's primary love interest by then. Before director Sam Raimi cast Dunst, he had expressed his interest in casting Alicia Witt. Dunst decided to audition after learning Tobey Maguire had been cast as Peter Parker/Spider-Man, feeling the film would have a more independent feel. Dunst earned the role a month before shooting in an audition in Berlin. In the first two films in the trilogy, Dunst wore a red wig for the part, dying part of her hair in the first film, before dying her full head of blond hair red for the third film. Dunst was also allegedly asked to change her teeth for the films, a demand that she refused. She also declined to do certain stunts in the films.

The set-up for Spider-Man and Mary Jane's famous "upside-down kiss" involved several rain-machines at the studio lot, and saw some difficulty as Maguire was hung upside down with water pouring into his nostrils. To achieve the look of Mary Jane pulling Spider-Man's mask down, Dunst was described by Sam Raimi as "doing some hand trickery" as the mask was not pliable in those conditions.

Having initially signed on for three Spider-Man films, Dunst said that she would consider doing a fourth, but only if Raimi and Maguire also returned. In January 2010, it was announced that the fourth film was cancelled and that the Spider-Man film series would be restarted, and therefore dropping the trio from the franchise. Storyboard artist Jeffrey Henderson, who worked on the fourth Spider-Man film before the project's cancellation, disclosed in November 2022 that the fourth film would have established that Mary Jane had been "let go" by Peter Parker, leading him to now deeply enjoy being Spider-Man.

In 2021, while attending a screening of her latest film The Power of the Dog, Dunst expressed openness to reprising her role as Mary Jane in regards to rumors of her appeance in the Marvel Cinematic Universe (MCU) film Spider-Man: No Way Home: "I would do it. Why not? That would be fun. I would never say no to something like that". No Way Home screenwriters Erik Sommers and Chris McKenna wrote at various points versions of the film's story that included Mary Jane, alongside appearances of Sally Field's Aunt May and Emma Stone's Gwen Stacy, but Sommers and McKenna ultimately concluded that the story felt already overstuffed, ultimately choosing Zendaya's Michelle "MJ" Jones and Marisa Tomei's Aunt May to be the only female characters in the film with significant screen time.

Characterization and themes
As portrayed in the Sam Raimi trilogy, Mary Jane Watson is a kind, funny, beautiful, sweet, cheerful, passionate and energetic young woman who is an aspiring actress. She runs with the stereotypical popular crowd in school, being surrounded by people who have enticing physical features and great skills in ways of performing arts or sports. Mary Jane is somewhat naive, but always knows what's going on. While individuals in MJ's high school clique are rude, snobbish, arrogant, vain and uncaring, Mary Jane is a loyal friend and a warm individual, capable of intense love and real feelings. Mary Jane does not let the attention she gets from boys get to her head. Instead, she uses her looks merely as an advantage for acting and modelling and works to develop independence and smarts. Despite her popularity, MJ struggles with insecurity and an urge to impress people she deems important, both of which most likely come from her abusive father, and is an indecisive dater before Peter finally commits to her. She also deals with the harsh reality of being an actress and has her own struggles in each film.

She never bullies or judges Peter Parker and is friendly towards him, despite him being in the unpopular crowd, and even flirts with him and calls him "Tiger" (an homage to her catchphrase in the comics). MJ generally has no one treat her with respect for anything other than her looks, which she may not have noticed until after high school graduation, before she and Peter develop a stronger friendship. It is quite possibly because of this, Mary Jane becomes so smitten by Spider-Man so quickly and later falls for Peter (oblivious that they are one and the same) as he is very kind to her other than just for her looks. After her kiss with Spider-Man, MJ was shown to be a great deal happier and almost ecstatic, because it had perhaps been her first kiss with someone who loved her back for more than just aesthetic reasons. Unfortunately, her involvement with Spider-Man also makes her a common target by his enemies, making her require his rescue in all three films, as noted by Emily Kubincanek of Film School Rejects.

Writing in 2020 after the release of Spider-Man: Into the Spider-Verse, Adadora Asidianya of CBR.com looked back at Mary Jane's live-action portrayal in the Raimi films and noted that she provides a grounding presence for Peter in the films, also commending her positive outlook in life despite her toxic upbringings.

Spider-Man (2002)
Mary Jane first appears as Peter Parker narrates the first few minutes of the film. She is depicted as a popular girl at Midtown High School and the ex-girlfriend of star athlete Flash Thompson, while Peter, her next-door neighbor who has had a crush on her since they were in first grade, is an academically gifted but shy outsider. Peter struggles to catch the school bus until MJ asks the driver to stop for him. Later, their class attends a field trip to a lab at Columbia University. Peter's friend Harry Osborn flirts with MJ before Peter takes a picture of her for the school newspaper, after which a genetically-altered spider bites him, ultimately giving him his abilities. Peter then saves Mary Jane from slipping in the school cafeteria with his new abilities the next day and inadvertently triggers a fight with Flash, though he is able to easily dodge Flash's punches and knocks him out with one punch. Peter later apologizes to MJ for the fight while she confides in him about wanting to escape her abusive, alcoholic father and pursue an acting career.

She breaks up with Flash during high school graduation and takes up work as a waitress while looking for acting gigs. While Mary Jane starts dating Harry, she and Peter begin to form a closer friendship. Peter rescues her as Spider-Man when the Green Goblin attacks a parade she was attending with Harry, and again later on from a gang in an alley. Mary Jane thanks Spider-Man with a kiss without him revealing his identity. MJ grows distant from Harry due to his desire to please his father, Norman, at her expense and also subsequently develops feelings for Peter when she realizes how much he cares for her, causing Harry to break up with MJ upon seeing her and Peter holding hands.

Norman, who is the Green Goblin and has deduced Peter is Spider-Man, kidnaps Mary Jane upon realizing Peter loves her, thanks to his son's unwitting confession. The Goblin forces Peter to choose between saving Mary Jane and a Roosevelt Island Tramway car full of children, all of whom he holds hostage on top of the Queensboro Bridge. Spider-Man opts to save both, and despite a struggle, manages to lower MJ and the kids onto a boat, after which the Goblin whisks Spider-Man away for a final confrontation which results in the Goblin's death. At Norman's funeral, Mary Jane tells Peter that she loves him and they kiss. Peter, who decides that for her protection they can't be together, gently rejects her and insists they can only be friends. As he leaves, a saddened Mary Jane realizes that her kiss with Peter reminds her of the one she shared with Spider-Man and suspects that he is the superhero.

Spider-Man 2 (2004)
Two years after the events of the first movie, Mary Jane has found success as a model and Off-Broadway actress. Maintaining her friendships with both Peter and Harry, she continues to pine for Peter, but as he continues to reject her, she starts dating astronaut John Jameson, the son of Peter's boss J. Jonah Jameson. Struggling to balance his vigilantism as Spider-Man with his personal life, Peter fails to make it to one of Mary Jane's performances of The Importance of Being Earnest.

Fed up with being Spider-Man and after losing his powers, Peter tosses his suit away and is able to handle his job and studies and decides to pursue MJ, though she pushes him away when John proposes to her. After Mary Jane kisses John, in a manner that is reminiscent of the upside-down kiss between her and Spider-Man from the first film, she realizes that she does not love John and still wants a relationship with Peter. Later, she meets Peter in a coffee shop where she asks for a kiss to confirm her belief that he is Spider-Man. She even asks him if he loves her which he falsely replies, "I don't", for the sake of his superhero responsibilities and her safety. Before they can kiss, Doctor Octopus attacks the cafe, kidnapping Mary Jane.

Peter regains his abilities and takes up being the web-slinger once more, fighting Doc Ock on a runaway New York City Subway train before being subdued and delivered to Harry, who wants revenge on Spider-Man for allegedly killing his father. After Harry unmasks Peter, he reluctantly provides Doc Ock's and Mary Jane's location so Peter can save her. Peter defeats Doctor Octopus this time as the latter tries to create a fusion reactor capable of destroying the city, and unmasks himself to both Doctor Octopus and MJ, confirming her suspicions that Peter and Spider-Man are in fact one and the same. Peter finally confesses his love for MJ, rescuing her as Doctor Octopus regains control of himself from the malicious AI in his tentacles and repents of his prior actions, sacrificing himself to destroy the reactor. Peter explains his reasoning for not being with her, then allows her to reunite with John. However, MJ leaves John at the altar during their wedding and runs to Peter's apartment, stating that she is willing to accept any risks that come with being in a relationship with Peter. The two finally become a couple, and Mary Jane sees Peter off as he swings into action as Spider-Man to help out a situation, uttering her catchphrase "Go get 'em, Tiger!"

Spider-Man 3 (2007)
Having dated Peter for one year, Mary Jane experiences some struggles in her personal life, losing her Broadway role because of bad reviews and experiencing friction with her boyfriend when an alien symbiote takes him over and amplifies the negative traits of his personality which as a result makes him distance himself from her to focus on capturing and killing his uncle's actual killer, Flint Marko. She also faces competition for Peter's affections in the form of his lab partner Gwen Stacy. After she confides in Harry about her problems, Harry, who had suffered amnesia from a prior fight with Peter as the New Goblin, regains his memories after they unwittingly kiss and frightens MJ into breaking up with Peter, setting up a second confrontation between the two former friends which leaves Harry's face disfigured.

Peter, now under more influence from the symbiote, later brings Gwen to a jazz club where MJ has found work as a singer and waitress in order to make her jealous, though Gwen catches on and apologizes to Mary Jane. He then gets into a fight with the club's bouncers and unintentionally hits Mary Jane when she intervenes, leading him to realize what the symbiote suit has turned him into. He leaves and disposes of the symbiote suit, which subsequently falls onto Eddie Brock, Gwen's failed suitor and Peter's bitter rival and fellow photographer, to create Venom.

Although the symbiote was removed, Peter felt he did too much damage to amend things with Mary Jane as he feels inadequate to propose to her and stares at her apartment window before leaving, thinking she doesn't want to see him again. After she departs from her apartment, Mary Jane gets kidnapped by Brock, who holds a grudge against Peter for ruining his career as a photographer and taking away his girlfriend, teaming up with Flint Marko to lure and kill Spider-Man. Holding her in a web duct taxi as bait, Mary Jane is briefly able to protect herself this time. The subsequent battle pits Spider-Man and the New Goblin against Venom and the Sandman; the two villains are defeated, but Harry loses his life in the process after sacrificing himself to save his friends, dying with MJ and Peter at his side.

Sometime after Harry's funeral, Peter arrives at MJ's jazz club, and the two begin to mend their relationship, sharing a dance.

Television

 * Mary Jane also appears in Spider-Man: The New Animated Series, an animated television series serving as a loose alternate continuation of the first Spider-Man film. She, Peter and Harry attend Empire State University together, and she attempts to start a relationship with Peter without much success, owing to his reluctance to endanger her due to his duties as Spider-Man. Mary Jane is voiced by Lisa Loeb.

Film

 * Dunst's Mary Jane Watson appears through archive material from Spider-Man in the Into the Spider-Verse sequel Spider-Man: Across the Spider-Verse (2023).

Video games

 * Mary Jane Watson appears in all three video game adaptations of the films. While she is voiced by Cat O'Conner in the first game, Kirsten Dunst reprises her role in a vocal capacity in the second game while Kari Wahlgren takes over the role in the third game.

Reception and legacy
Kirsten Dunst's portrayal of Mary Jane Watson in the Spider-Man films was generally well-received, as she was nominated for several awards for her performance, winning four, including the Empire Award for Best Actress in 2003. Owen Gleiberman of Entertainment Weekly remarked on Dunst's ability to "lend even the smallest line a tickle of flirtatious music". In the Los Angeles Times review, critic Kenneth Turan noted that Dunst and Maguire made a real connection on screen, concluding that their relationship "involved audiences to an extent rarely seen in films".

However, elements of her character were met with a mixed response. In his review of Spider-Man 3, Ryan Gilbey of the NewStatesman was critical of Dunst's character: "the film-makers couldn't come up with much for Mary Jane to do other than scream a lot". Allie Gemmill of Bustle wrote in 2017 that the films portray Mary Jane as a constant damsel in distress and gave the illusion that she was defined primarily through the men in her life. Conversely, Adadora Asidianya wrote that Mary Jane provides a voice of reason for Peter, whether as a friend or a love interest.

Spider-Man and Mary Jane's "upside-down kiss" in Spider-Man is now regarded as one of the most iconic moments in film history. Entertainment Weekly put "the kiss in Spider-Man" on its end-of-the-decade "best-of" list, saying: "There's a fine line between romantic and corny. And the rain-soaked smooch between Spider-Man and Mary Jane from 2002 tap-dances right on that line. The reason it works? Even if she suspects he's Peter Parker, she doesn't try to find out. And that's sexy."


text:
Halifax–Northampton Regional Airport

Halifax–Northampton Regional Airport is a public use airport located eight nautical miles (9 mi, 15 km) south of the central business district of Roanoke Rapids, a city in Halifax County, North Carolina, United States. It is owned by the Halifax–Northampton Regional Airport Authority. This airport is included in the National Plan of Integrated Airport Systems for 2011–2015, which categorized it as a general aviation facility.

Although most U.S. airports use the same three-letter location identifier for the FAA and IATA, this airport is assigned IXA by the FAA but has no designation from the IATA (which assigned IXA to Singerbhil Airport in Agartala, India). The airport's ICAO identifier is KIXA.

Facilities and aircraft
Halifax–Northampton Regional Airport covers an area of 797 acres (323 ha) at an elevation of 145 feet (44 m) above mean sea level. It has one runway designated 2/20 with an asphalt surface measuring 5,500 by 101 feet (1,676 x 31 m).

For the 12-month period ending July 17, 2009, the airport had 2,900 aircraft operations, an average of 241 per month: 90% general aviation and 10% military. At that time there were 20 aircraft based at this airport: 90% single-engine and 10% multi-engine.

title: Halifax–Northampton Regional Airport


text:
Talk:Party Never Ends/GA1

GA Review
The edit link for this section can be used to add comments to the review.''

Reviewer: Aoba47 (talk · contribs) 04:15, 18 September 2017 (UTC)

 * Lead and infobox
 * Please adjust the ALT text for the album cover. The phrase “topless shot” is not the best wording (i.e. the shot is not topless).
 * The languages do not need to be linked in the infobox.
 * Just a clarification question, but do you know if there is an executive producer for the album.
 * There is no executive producer credited. Cartoon network freak (talk) 20:12, 18 September 2017 (UTC)
 * I figured as much, but I wanted to double-check. That is not uncommon so I understand. Aoba47 (talk) 20:31, 18 September 2017 (UTC)

 * I do not see the need for the references for the singles in the infobox as all of this information should be in the body of the article and properly cited there.
 * I am a little confused by the information on the critical reception of the album. First, the reference for the Time of India does not need to be in the lead. And second, I would imagine that would be more reviews for this album than just one. The inclusion of only review is raising some red flags on the comprehensiveness of the article.
 * Removed ref; other than that, see my comments at the bottom of the page. Cartoon network freak (talk) 20:12, 18 September 2017 (UTC)
 * Thank you. Aoba47 (talk) 20:31, 18 September 2017 (UTC)

 * The following sentence is rather long and would benefit from revision (Six tracks from the record were released as singles along with several promotional singles, of which "More than Friends" experienced widespread commercial success.). Maybe, cut this sentence into two with one featuring the singles and the other on the promotional singles.
 * Specify the exact amount of promotional singles rather than “some” as you should be able to locate this information.
 * In the following sentence (During her first tour, she appeared in several television programmes and radio stations.), I am not sure the “during the first tour” part is necessary. It implies that these appearances were a part of the tour, while I would classify them as separate promotional endeavors done by Inna.
 * I would move the sentence on Frida Kahlo directly after the sentence on the tours in Mexico and the United States.

 * Background and release
 * For this part (The songs from Party Never Ends have been recorded in recording studios), avoid the repetitions of recording (i.e. “recorded” and “recording studios”).
 * Do you know the city in Mexico where the album was recorded? It just is a little odd to list primarily cities, and then have a single country.
 * I know it's odd (: but the source doesn't give any further information or context. Cartoon network freak (talk) 20:12, 18 September 2017 (UTC)
 * No worries. You at least got all of that information on where it was recorded so you should be proud of that. It can very difficult to locate all of that so be proud of it. Aoba47 (talk) 20:31, 18 September 2017 (UTC)

 * Is there any more information about the production/recording process? Has Inna ever talked about how she developed and recorded the album in interviews for instance? This is more of a clarification question, as the information on the background seems a little bare.
 * See my comment at the bottom of the page. Cartoon network freak (talk) 20:12, 18 September 2017 (UTC)

 * In this part (along with track "Take Me Higher" for), change “track” to “album track” and “for” to “from”
 * I would change “her Body and the Sun album from 2015” to “her fourth studio album Body and the Sun (2015)”.

 * Composition
 * This part is very awkwardly worded and constructed and requires revision (which serves as the third track as is of the house and Latin genres).
 * I am not certain about the sentence about “Inndia” and “Shining Star”. When you use “while”, you are suggesting some sort of contrast between the two things being discussed, and I do not see how the connection here. I would rephrase it to avoid the “while” construction.
 * I would make the information about “Caliente” into its own sentence to avoid longer sentences with a lot of references.
 * For this part (Deluxe edition track "Be My Lover" features), change “Deluxe edition track” to “The deluxe edition track”.
 * For this part (name, featured on her album Heartbreak on Hold (2012).), I would change “, featured on” to “from” to have more concise language.

 * Reception and accolades
 * Read my above comment on my concerns about the information included on the album’s reception. It seems a little odd to only have one review.
 * See my comment at the bottom of the page. Cartoon network freak (talk) 20:12, 18 September 2017 (UTC)

 * You use a lot of quotes in the first paragraph that it borders on being a quote farm. I would paraphrase more, specifically the short quotes used for the specific songs. You can say it better in your own words rather than the short quotes (i.e. “mediocre”, “upper”, “passable”, and “radio friendly”).
 * I would specify that the following (Deepcentral's O stea (2013) and Smiley's Acasă (2013)) are albums.
 * In the same sentence, the comma after (2013) is not needed so please remove it.

 * Promotion and singles
 * The Frida Kahlo image needs ALT text.
 * I am on the fence about the use of the Frida image. It is a rather large image and places a lot of emphasis on only one sentence of information in this article. I will allow it for this review, but I would suggest you think about the use of the image as it does seem to add undue weight to a rather small portion of the section. I would be fine with the image if more people talked about her tour wardrobe or if she talked more in-depth about it, but that does not appear to be the case.
 * Relaced with a picture from the tour. Cartoon network freak (talk) 20:12, 18 September 2017 (UTC)

 * Write out “Washington D.C. instead of just saying Washington to make it absolutely clear.
 * The phrase (Another tour in Mexico visited) needs to be completely revised. You can say that Inna visited these locations but neither the tour or Mexico did the visiting.
 * I would say “final concert” or “final show” instead of “closing concert”.
 * I would move the sentence on Frida directly after the first sentence on her going on a tour in Mexico to make it flow better in a more coherent/chronological manner.
 * I do not believe countries should be linked.
 * Not the countries are linked, but their respective singles chart. Cartoon network freak (talk) 20:12, 18 September 2017 (UTC)

 * The phrase “lyrics video” should be “lyric video”.
 * For the phrase (Multiple promotional singles), just say the amount rather than “multiple”.
 * I am confused by this sentence (All singles benefited of at least one music video, including a visual for promotional single "Spre mare" and a lyrics video for “J’Adore”.). I understand why you single out “J’Adore” as a lyric video is different from a music video, but I do not seem why you single out “Spre mare”. It is understand that “Spre mare” has a video from this part of the sentence “All singles benefited of at least one music video” so it is redundant to repeat this information. I would remove the part about “Spre mare” in this sentence for that reason.

 * Track listing
 * You mention multiple editions of this album in the article, so you should include the track listings for those here.
 * This isn't really necessary for an album-related article, and the main track listing suffices, according to Wikipedia policies. Also, we have all the different things on the other versions mentioned throughout the article. Cartoon network freak (talk) 20:24, 18 September 2017 (UTC)
 * Makes sense; thank you for letting me know. I need to read through all of these policies one day for real ><. Aoba47 (talk) 20:31, 18 September 2017 (UTC)

Great work with this article. Once my comments are addressed, I will pass this. Aoba47 (talk) 04:15, 18 September 2017 (UTC)
 * Final comments
 * Thank you very much for the review! In reply to your expanding suggestions, I have to say that there are no other sources on the web for expansion. That one review was written in 2017, so I'm glad we have at least one Sadly, Romanian websites don't write that much about a  new release, and Romanian songs/albums are not often analyzed/reviewed by international publications. Pre-2014 Inna/Alexandra Stan songs/albums are especially hard(er) to expand on an acceptable level; compare "Be My Lover" to "On the Floor" and you'll see the difference. I guess you're having "good life"; even promotional singles like "Ugly" that haven't charted anywhere get so much coverage that its article mostly triples that for Party Never Ends. I hope you got me ;) Best regards and THX again, Cartoon network freak (talk) 20:24, 18 September 2017 (UTC)
 * Thank you for addressing my comments and for your clarifications. I completely understand your points. I just wanted to double-check that all of the bases were covered. I will happily ✅ this. Great work. Aoba47 (talk) 20:31, 18 September 2017 (UTC)

title: Talk:Party Never Ends/GA1


text:
2010 Pan American Fencing Championships

The 2010 Pan American Fencing Championships were held in San José, Costa Rica from 2 to 7 July.

title: 2010 Pan American Fencing Championships


text:
Talk:Chulita Vinyl Club

Feedback from New Page Review process
I left the following feedback for the creator/future reviewers while reviewing this article: I think that this meets WP:GNG, but it needs significant copyediting for tone and neutrality..

signed,Rosguill talk 23:02, 22 September 2019 (UTC)

title: Talk:Chulita Vinyl Club