11.1 Volume Mass Relationships of Gases 11.1 Avogadro's Law 11.1 Molar Volume of Gases 11.2 The Ideal Gas Law 11.2 Derivation of the Ideal Gas Law 11.2 The Ideal Gas Constant 11.2 Finding Molar Mass or density from the Ideal Gas Law 11.4 Effusion Chapter 11 Kevin Arcos

Mr. Escalona

AP Chemistry

Period 2

15 May 2013 Molecular Composition of Gases 11.1 Volume - Mass Relationships of Gases

11.2 The Ideal Gas Law

11.3 Stoichiometry of Gases

11.4 Effusion and Diffusion In the early 1800's, French chemist Joseph Gay-Lussac studied gas volume relationships.

Gay- Lussac's law of combining volumes of gases

Stated that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. Hydrogen Gas + Oxygen Gas -> water vapor

2 L 1 L 2 L

2 Volumes 1 Volume 2 Volumes 2:1:2 ratio between the volumes of the reactants and the product. The law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Hydrogen Gas + Chlorine Gas -> 2HCl

1 Volume 1 Volume 2 Volumes 1 Molecule 1 Molecule 2 Molecules

Hydrogen molecules combine with chlorine molecules in a 1:1 volume ratio to produce 2 volumes of hydrogen chloride. The volume occupied by one mole of a gas at STP (Standard Temperture and Pressure) is know as the standard molar volume of a gas.

You could use 1mol/22.4 L as a conversion factor to find the number of moles, and therefore the mass of a given volume of a known gas at STP. Given Molar mass of Oxygen Gas = 0.0680 mol

What volume in liters is occupied by this gas sample at STP? 0.0680 mol O2 x 22.4 L = 1.52 L O2

mol02 The ideal gas law is the mathematicall relationship of pressure, volume, temperature, and the number of moles of gas.

Considered an equation of state for a gas, because the particular state of a gas can be defined by its pressure, volume, temperature, and number of moles. Boyle's Law : At constant temperature, the volume of a give mass of gas is inversely proportion to the pressure

Charle's Law : At constant pressure, the volume of a given mass of gas is directly proportional to the Kelvin Temperature(Directly proportional: as one amount increases, another amount increases at the same rate).

Avogadro's Law : At constant pressure and temperature, the volume of a given mass of a gas is directly proportional to the number of moles. The constant R is known as the ideal gas constant. Its value depends on the units chosen for pressure volume and temperature.

R= 0.0821 L x atm/(mol x K)

*Make sure that you check the known values to be sure you are working with the correct units.

^such as Joules or Kilojoules, the constant would change to be 8.314 The derivation of this formula as follows:

V = nRT/P R = 0.0821 atm L / mol K

P = nRT/V R= PV/nT

n = PV/RT

T = nR/PV Starting with the base formula PV = nRT replace moles with mass and divide by molar mass.

PV = mRT/M or M = mRT/PV

m = mass

M = molar mass

Density is mass per unit volume.

D = m/V

Introducing density into that equation gives the following:

M = mRT/PV = DRT/P

Solving for density gives this equation:

D = MP/RT 11.3 Stoichiometry of Gases Apply both Gay Lussac and Avogadro's discovery to calculate the stoichiometry of reactions involving gases. What mass of sulfur must be used to produce 12.61 L of gaseous sulfur dioxide at STP according to the following equation.

S(s) + O2(g) -> SO2(g) PV = mRT/M

m = RT/PV

m = 0.0821 x 273K/1atm x 12.61 L

m = 282.28746/M of S2

m = 17.61g of S 11.4 Effusion and Diffusion Diffusion is initially known as the gradual mixing of two gases due to their spontaneous, random motion.

Effusion is the process where the molecules of a gas confined in a container randomly pass through a tiny opening in the container. Graham's law of effusion states that the rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. A sample of hydrogen effuses through a porous container about 9 times faster than and unknown gas. Estimate the molar mass of the unknown gas. For example: 9 times faster

Work backwards from the initial formula with Graham's kaw

Square 9 and then multiply by 2

9 x 9 = 81 x 2 = 162 or approximately 160g/mol of unknown gas 11.2 Derivation of Gas Law Equation Start with Boyle's Law, Charles Law, and Avogadro's law.

Boyle's Law : Volume inversely proportional to pressure at constant mol and pressure.

Charles law : Volume is directly proportional to temperature at constant mols and pressure.

Avogadro's law : Volume is directly proportional to mols at constant pressure and temperature.

Combine these relationships to make a more general gas law

V proportional to nT/P

If we call R a constant then it becomes

V = R(nT/P)

Rearranging we have the relationship in its most familiar form

PV = nRT

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# Chapter 11 Molecular Composition of Gases

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