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Ideal Gas Law. Find the pressure exerted by 80.0 g of carbon monoxide in a volume of 40.0 L at 25 ºC. Ideal Gas Law. Find the volume occupied by 65.0 g of oxygen at a pressure of 1.43 atm at 36ºC. Ideal Gas Law.

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Ideal Gas Law

Find the pressure exerted by 80.0 g of carbon monoxide in a volume of 40.0 L at 25 ºC.

Ideal Gas Law

Find the volume occupied by 65.0 g of oxygen at a pressure of 1.43 atm at 36ºC.

Ideal Gas Law

Find the Celsius temperature required for 76.0 g of carbon dioxide to occupy 40.0 L at a pressure of 748 torr.

Ideal Gas Law

How many grams of argon are in a 50.0 L tank at a pressure of 4.00 x 106 Pa at 23 ºC?

Learning Check

What volume will 145 grams of fluorine gas occupy at a pressure of 1.20 x 105 Pa at 18 ºC?

Ideal Gas Law

What is the molar mass of a gas if 319 grams occupies 46.5 L at a pressure of 2.35 atm at 23 ºC?

Density and Molar Mass

Density for a gas is usually expressed in g/L.

Molar mass is g/mol.

Since moles of a gas are related to the volume of the gas (along with pressure and temperature), there should be a way to convert g/L to g/mol for a gas…

Density and Molar Mass

Starting with PV = nRT, let

n =

Then, PV = · RT

molar mass = · RT

mass

molar mass

mass

molar mass

mass

P·V

Density and Molar Mass

molar mass = · RT

molar mass =

d

P

dRT

Know this.

P

Density and Molar Mass

What is the molar mass of a gas with a density of 4.50 g/L at 862 torr and 27 ºC?

Density and Molar Mass

What is the density of krypton gas at 785 torr and 37 ºC?

Learning Check

What is the molar mass of a gas with a density of 3.84 g/L at 0.950 atm and 57 ºC?

Finding Moles

grams x or

numbers of molecules x

solution volume in L x

n = special case at STP:

mol

mass

g

molar mass

1 mol

6.022 x 1023 molecules

mol

L

PV

22.4 L

RT

1 mol

Stoichiometry with Gases

What volume of nitrogen at STP is needed to react with 165 g of hydrogen at STP to make ammonia?

N2(g) + 3 H2(g)  2 NH3(g)

Stoichiometry with Gases

What volume of nitrogen at 132 ºC and 1.12 atm is needed to produce 38.0 L of NH3 at 132 ºC and 1.12 atm?

N2(g) + 3 H2(g)  2 NH3(g)

Stoichiometry with Gases

What volume of nitrogen at 132 ºC and 1.12 atm is needed to produce 38.0 L of NH3 at 74 ºC and 1.40 atm?

N2(g) + 3 H2(g)  2 NH3(g)

Learning Check

What volume of hydrogen at 95 ºC and 786 torr is needed to produce 40.0 L of NH3 at 64 ºC and 766 torr?

N2(g) + 3 H2(g)  2 NH3(g)

Dalton’s Law of Partial Pressure

partial pressure – the pressure a gas in a mixture would exert if it were the only gas in the container.

Dalton’s Law:

The total pressure of a mixture of gases is equal to the sum of the partial pressures of all the gases in the mixture.

PT = PA + PB + PC + …

Dalton’s Law of Partial Pressure

Calculate the total pressure of a mixture of oxygen with a partial pressure of 614 torr, nitrogen with a partial pressure of 1.33 atm, and helium with a partial pressure of 1.80 x 105 Pa.

Dalton’s Law of Partial Pressure

Calculate the pressure of nitrogen in a tank with a total pressure of 2.32 atm if the only other gas in the tank, oxygen, has a pressure of 0.914 atm.

Collecting Gases over Water

One situation where we need to apply Dalton’s Law of Partial Pressures is when we collect gases “over water” in the lab.

gas + water vapor

Collecting Gases over Water

vapor pressure – the partial pressure of the gas phase (vapor) of a substance over a sample of the liquid phase of the substance at equilibrium.

Collecting Gases over Water

We know the pressure exerted by water vapor at different temperatures (see Appendix B).

Collecting Gases over Water

Calculate the dry pressure of hydrogen gas if the total pressure of the hydrogen gas collected over water at 24 ºC is 718 torr. (Vapor pressure of water is 29.8 mmHg at 24 ºC.

Partial Pressure and Mole Fraction

Because pressure is directly proportional to number of moles (when T and V are constant), we know:

PT = PA + PB + PC + …

just as we know

nT = nA + nB + nC + …

Partial Pressure and Mole Fraction

mole fraction (X) – the moles of a substance in a mixture compared to the total moles in the mixture.

XA = =

nA

PA

nT

PT

Partial Pressure and Mole Fraction

Calculate the mole fraction of oxygen in a scuba tank containing oxygen with a partial pressure of 0.800 atm if the total pressure in the tank is 3.81 atm.

Partial Pressure and Mole Fraction

Calculate the mole fraction of oxygen in a container if it contains 8.00 grams of oxygen, 22.0 grams of nitrogen, and 12.0 grams of helium. Calculate the partial pressure of the nitrogen if the total pressure in the container is 2.00 atm.

Partial Pressure and Mole Fraction

Calculate the volume occupied by 16.0 grams of oxygen mixed with 20.0 grams of nitrogen at 25 ºC at 1.16 atm.

Graham’s Law of Effusion

effusion – diffusion through a small orifice (hole).

Graham’s Law of Effusion – the rate of effusion of a gas is inversely proportional to the square root of the density of the gas.

effusion rate 

1

 d

Graham’s Law of Effusion

Since we know that density is related to the molar mass of gas, we can also say:

effusion rate 

Most important to understand: Heavier gases move (and effuse) more slowly. Lighter gases move (and effuse) more rapidly.

1

 molar mass

Graham’s Law of Effusion

Calculate the relative rate of effusion of He vs. N2 at the same temperature and pressure.

Real vs. Ideal Gases

While real gases approximate ideal behavior at high temperature and low pressure, how do we deal with real gases at low temperature and high pressure where behavior deviates from ideal?

Use an equation that corrects for the volume of the particles and the minute attractions between gas particles.

The van der Waals equation makes these corrections…

Real vs. Ideal Gases

(P +

) (V−nb) = nRT

n2a

V2

van der Waals equation: