1. Chapter 5
Gases
John A. Schreifels
Chemistry 211

2. Overview Gas Laws Kinetic and Molecular Theory
Gas Pressure and its measurement
Empirical gas laws
Ideal gas laws
Stoichiometry and gases
Gas Mixtures; Law of partial pressures
Kinetic and Molecular Theory
Kinetic theory of an Ideal gas
Molecular speeds: diffusion and effusion
Real gases
John A. Schreifels
Chemistry 211

3. Gases and Gas Pressure
They form homogeneous solutions. All gases dissolve in each other.
Gases are compressible.
Large molar volume.
Barometer usually mercury column in tube; mm Hg is a measure of pressure.
Manometer tube of liquid connected to enclosed container makes it possible to measure pressure inside the container.
Pressure
One of the most important of the measured quantities for gases
defined as the force/area P = f/area.
Pressure has traditionally been measured in units relating to the height of the Hg and is thus expressed as mm Hg = 1 Torr.
John A. Schreifels
Chemistry 211

4. P = dHgghHg = doilghoil or dHghHg = doilhoil.
Gas Pressure
Pressure is directly proportional to the height of the column in a barometer or manometer.
Mercury often used but other low density liquids are used for low pressure changes:
P = dHgghHg = doilghoil or dHghHg = doilhoil.
E.g. Water is sometimes used to determine pressure; determine the height of water if the barometer pressure was 750 mmHg. The density of Hg = g/cm3 and 1.00 g/cm3 respectively.
Solution:
John A. Schreifels
Chemistry 211

5. The Gas Laws
Boyle's Law: For a fixed amount of gas and constant temperature, PV = constant.
Charles's Law: at constant pressure the volume is linearly proportional to temperature. V/T = constant
Avagadro’s law for a fixed pressure and temperature, the volume of a gas is directly proportional to the number of moles of that gas. V/n = k = constant.
E.g. 1 The volume of some amount of a gas was 1.00 L when the pressure was 10.0 atm; what would the volume be if the pressure decreased to 1.00 atm?
E.g. 2 A gas occupied a volume of 6.54 L at 25°C what would its volume be at 100°C?
E.g. 3 The volume of mol of some gas was L; what would be the volume of 15.0 mol of the same gas at the same T and P?
John A. Schreifels
Chemistry 211

6. The Ideal Gas Equation
Ideal gas law the functional relationship between the pressure, volume, temperature and moles of a gas. PV = nRT; all gases are ideal at low pressure.
PV =nRT. Each of the individual laws is contained in this equation.
Boyle's Law: PV = k1 = nRT.
Charles's Law:
Avagadro’s law:
When any of the other three quantities in the ideal gas law have been determined the last one can be calculated.
E.g. Calculate the pressure inside a TV picture tube, if it's volume is 5.00 liters, it's temperature is 23.0C and it contains mg of nitrogen.
John A. Schreifels
Chemistry 211

7. Further Applications of Ideal-Gas Equation
The density of a gas the density of a gas can be related to the pressure from the ideal gas law using the definition of density: d = mass/vol.
E.g. Estimate the density of air at 20.0C and 1.00 atm by supposing that air is predominantly N2.
E.g. From the results above determine the density of He.
Rearrangement permits the determination of molecular mass of a gas from a measure of the density at a known temperature and pressure.
E.g. A certain gas was found to have a density of g/L at 260C and 103 Torr. Determine the FM of the compound.
John A. Schreifels
Chemistry 211

8. Stoichiometric Relationships with Gases
When gases are involved in a reaction, das properties must be combined with stoichiometric relationships.
E.g. Determine the volume of gas evolved at K and 1.00 atm if 1.00 kg of each reactant were used. Assume complete reaction (i.e. 100% yield)
CaO(s) + 3C(s)  CaC2(s) + CO(g).
Strategy:
Determine the number of moles of each reactant to which this mass corresponds.
Use stoichiometry to tell us the corresponding number of moles of CO produced.
Determine the volume of the gas from the ideal gas law.
John A. Schreifels
Chemistry 211

9. Partial Pressure and Dalton’s Law
Dalton's Law = the sum of the partial pressures of the gases in a mixture = the total pressure or P = PA + PB + PC + ...where Pi = the partial pressure of component i.
Dalton found that gases obeying the ideal gas law in the pure form will continue to act ideally when mixed together with other ideal gases.
The individual partial pressures are used to determine the amount of that gas in the mixture, not the total pressure, PA = nART/V.
Since they are in the same container T and V will be the same for all gases.
E.g g of air consists of approximately 0.76 g nitrogen and 0.24 g oxygen. Calculate the partial pressures and the total pressure when this sample occupies a 1.00 L vessel at 20.0C.
Solution:
Determine the number of moles of each gas.
Using the ideal gas law determine the pressure of each and sum to determine the total pressure.
John A. Schreifels
Chemistry 211

10. Partial Pressure and Dalton’s Law2
Mole fraction another quantity commonly determined for gas mixtures. It is defined the number of moles of one substance relative to the total number of moles in the mixture or
X can be calculated from
moles of each gas in the mixture or
the pressures of each gas
E.g. determine the mole fraction of N2 in the above example.
Collection of a gaseous product over water is another example of Dalton's Law. Subtract the vapor pressure of water to find the pressure of the gaseous product.
E.g. Suppose KClO3 was decomposed according to
2 KClO3(s)+   2KCl(s) + 3O2(g).
PT = Torr and mL of gas was collected over water at 20.0C. Determine the number of moles of O2 if the vapor pressure of water is 17.5 torr at this temperature.
John A. Schreifels
Chemistry 211

11. The Behavior of Real Gases
The molar volume is not constant as is expected for ideal gases.
These deviations due to an attraction between some molecules.
Finite molar molecular volume.
For compounds that deviate from ideality the van der Waals equation is used:
where a and b are constants that are characteristic of the gas.
Applicable at high pressures and low temperatures.
John A. Schreifels
Chemistry 211

12. The Kinetic Theory – Molecular Theory of Gases
Microscopic view of gases is called the kinetic theory of gases and assumes that
Gas is collection of molecules (atoms) in continuous random motion.
The molecules are infinitely small point-like particles that move in straight lines until they collide with something.
Gas molecules do not influence each other except during collision.
All collisions are elastic; the total kinetic energy is constant at constant T.
Average kinetic energy is proportional to T.
John A. Schreifels
Chemistry 211

13. The Kinetic Theory – Molecular Theory of Gases
Theory leads to a description of bulk properties i.e. observable properties.
The average kinetic energy of the molecule is
where NA = Avagadro’s number.
Average kinetic energy of moving particles can also be obtained from
where u = average velocity
All speeds are possible giving really a distribution of speeds.
Combine 1 & 2 to get a relationship between the velocity, temperature and molecular mass.
Express M in kg/mol and R = J/mol*K.
E.g. determine average velocity of He at 300 K.
E.g.2 predict the ratio of the speeds of some gas if the temperature increased from 300 K to 450 K.
John A. Schreifels
Chemistry 211

14. Graham’s Law: Diffusion and Effusion of Gases
Diffusion the process whereby a gas spreads out through another gas to occupy the space with uniform partial pressure.
Effusion the process in which a gas flows through a small hole in a container.
Graham’s law of Effusion the rate of effusion of gas molecules through a hole is inversely proportional to the square root of the molecular mass of the gas at constant temperature and pressure.
E.g. determine the molecular mass of an unknown compound if it effused through a small orifice if it effused 3.55 times slower than CH4.
E.g. A compound with a molecular mass of 32.0 g/mol effused through a small opening in 35 s; determine the effusion time for the same amount of a compound with a molecular mass of 16.0.
John A. Schreifels
Chemistry 211