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 H2 + O2 ---> 2 H2O
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 H2 + O2 ---> 2 H2O
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 H2 + O2 ---> 2 H2O 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 H2 + O2 ---> 2 H2O 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