Chapter 11 Molecular Composition of Gases

Volume-Mass Relationships of Gases

a) relationships between volume of gases in balanced equations

b) relationship between volume, density and molar mass

Measuring and Comparing the Volumes of Reacting Gases

Gay-Lussac in the early 1800's studied volume relationships of gases in chemical reactions

hydrogen + oxygen ---> water vapor

2 L of hydrogen reacted with 1 L of oxygen ---> 2 L of water vapor

2 volume of hydrogen + 1 volume of oxygen ---> 2 volumes of water vapor

2 H_{2} + O_{2} ---> 2 H_{2}O

2:1:2 volume ratio for this reaction

can be 2 mL + 1 mL ---> 2 mL or

can be 10 L + 5 L ---> 10 L

found the same situation in

hydrogen + chlorine ---> hydrogen chloride gas

1 L + 1 L ---> 2 L or

1 volume + 1 volume ---> 2 volumes

Led to Gay-Lussac's Law of Combining Volumes of Gases - statement

Avogadro's Law

Dalton originally thought that atoms were indivisible and that particles of gases exist as isolated single atoms.

He also believed that one atom of one element combined with one atom of another element to form a compound.

This idea created a problem for situation like the reaction to create water vapor:

hydrogen + oxygen ---> water vapor

2 L of hydrogen reacted with 1 L of oxygen ---> 2 L of water vapor

2 volume of hydrogen + 1 volume of oxygen ---> 2 volumes of water vapor

2 H_{2} + O_{2} ---> 2 H_{2}O

2:1:2 volume ratio for this reaction

It led scientists to believe that the oxygen split into two parts to explain what was happening.

Explained by Avogadro in 1811. He suggested that the particles of hydrogen and oxygen and water consisted of more that one atom joined together.

Also postulated what is called Avogadro's Law - statement.

Figure 11-1

At the same temperature and pressure, the volume of any given gas varies directly with the number of molecules.

For the reaction of hydrogen and chlorine to produce hydrogen chloride:

hydrogen + chlorine ---> hydrogen chloride gas

1 L + 1 L ---> 2 L or

1 volume + 1 volume ---> 2 volumes

Hydrogen chloride was analyzed to contain one hydrogen and one chlorine and so to explain how we get two volumes it is necessary to postulate the diatomic nature of both hydrogen and chlorine.

Figure 11-2

Gas volume is directly proportional to the number of moles or

V = kn

2 H_{2} + O_{2} ---> 2 H_{2}O where

2 molecules + 1 molecule ---> 2 molecules or

2 mol + 1 mol --->2 mol or

2 volumes + 1 volume ---> 2 volumes

Molar Volume of Gases

Avogadro's law states that at the same temperature and pressure one mole of any gas will occupy the same volume as one mole of another gas even though their mass may be different.

That volume is called the standard molar volume of a gas or simply the molar volume - definition.

Use 22.4 L concept as a conversion factor to calculate the number of moles (and therefore the mass) if you know the volume a gas occupies at STP.

Figure 11-3

Sample Problem 11-1 page 336

Sample Problem 11-2 page 337

Homework: 11.1

The Ideal Gas Law

This gas law brings the idea of moles into calculations for gases.

Figure 11-4 page 340

The Ideal Gas Law - statement

The equation is called 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.

Derivation of the Ideal Gas Law

Will not go into detail about the derivation.

PV = nRT

The Ideal Gas Constant

Figure 11-5

The ideal gas constant is represented by the R in the ideal gas equation.

Its value depends on the units used for pressure, volume, temperature, and number of particles.

Usually the value we use is 0.082 L - atm / mol - K or

62.4 L - mm Hg / mol - K

**Note: the dashes are dashes -- not subtraction operators.**

Finding P, V, T, or n from the Ideal Gas Law

a) If you know three of the four variables, you can calculate the fourth, using the ideal gas law, since R is a constant.

b) can calculate the molar mass if you remember that moles = g / molar mass

c) can calculate density by manipulating the ideal gas law, keeping in mind that moles = g / molar mass and density is mass / volume. We get

D = M x P / R x T

Sample Problem 11-3 page 343

Sample Problem 11-5 page 344

Homework: 11.2

Finding Molar Mass or Density from the Ideal Gas Law

for molar mass: M = m RT / PV

for density: D = M P / RT

Sample Problem 11-6

Homework: 11.3

Stoichiometry of Gases

2 H_{2} + O_{2} ---> 2 H_{2}O where

2 molecules + 1 molecule ---> 2 molecules or

2 mol + 1 mol --->2 mol or

2 volumes + 1 volume ---> 2 volumes

2 l + 1 l ----> 2 L

2 mL + 1 ML -----> 2 mL

Volume ratios: 2 volumes of hydrogen: 1 volume of oxygen

2 volumes of hydrogen: 2 volumes of water etc.

can use these volume ratios only if both gases are at the same temperature and pressure

Volume-Volume Calculations

Sample Problem 11-7 page 347

Homework: 11.4

Volume-Mass and Mass-Volume Calculations

SAMPLE PROBLEM 11-8 PAGE 349

Homework: 11.5

Effusion and Diffusion

Diffusion - definition

Effusion- definition

This section deals with calculating the molar mass of a gas using effusion

Graham's Law of Effusion

Figure 11-6

Rates of effusion and diffusion depend on the relative velocities of gas molecules.

Figure 11-7

The velocity of a gas varies inversely with its mass. Lighter molecules move faster than heavier molecules at the same temperature.

Using the equation for K.E. we can derive Graham's Law of Effusion which is

Graham's Law of Effusion - statement

Applications of Graham's Law

Graham worked on densities of gases.

The density of a gas varies directly with its molar mass.

That means we can restate the equation of Graham's Law as

Figure 11-8

Sample Problem 11-10 page 355

Homework: 11.6

end of notes

Gay-Lussac's Law of Combining Volumes of Gases states that at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. back

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain equal number of molecules. Back

The standard molar volume of a gas is the volume occupied by one mole of a gas at STP and whose value is 22.4 L. back

The ideal gas law is the mathematical relationship of pressure, volume, temperature, and the number of moles of a gas. Back

Diffusion is the gradual mixing of two gases due to their spontaneous, random motion. Back

Effusion is the process whereby the molecules of a gas confined in container randomly pass through a tiny opening in the container. Back

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. Back