Properties of Gases | General Chemistry 2

Gas: variable volume and shape ⇒ it expands to fill entire container
Most of the volume is empty space

Properties:

• Gas volume changes significantly with pressure and temperature
• Gases have relatively low densities
• Gases flow very freely
• Gases are miscible with each other ⇒ form solution in any proportions
• Gases exert pressure on the walls of any surface they touch

Pressure:
Pressure is defined as a force per unit area:
 

Pressure is measured in a variety of units:

• atm and torr are most commonly used in gas law problems
• Pa is used if SI units are needed

Conversion factor: 1 atm = 760 torr = 1.013 bar = 1.013 x 10⁵ Pa

4 important variables:

• Pressure P (in Pa)
• Temperature T (in K)
• Volume V (in L)
• Number of moles n (in mol)

Ideal gas: gas that exhibits linear relationships among these variables

Boyle’s Law (P vs. V):
At constant temperature: P and V are inversely proportional
 

Charles’s Law (V vs T):
At constant pressure: V and T are directly proportional
 

Gay-Lussac’s Law (P vs T):
At constant volume: P and T are directly proportional
 

Avogadro’s Law (V vs n):
At constant temperature and pressure: V and n are directly proportional
 

This equation is true for ideal gases, or gases behaving ideally
Better conditions for a gas to behave like an ideal gas: monoatomic gas, low pressure, high temperature

Molar Volume V_m (in L.mol^-1) in the Ideal Gas Law:
 

At standard temperature and pressure (STP): V_m = 22.41 L.mol^-1

Molar Mass M (in g.mol^-1) in the Ideal Gas Law:
 

Density ρ (in g.m^-3) in the Ideal Gas Law:
 

Dalton’s Law: at low pressures, the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of all the gases in the mixture

P_tot = P_A + P_B + P_C + … + P_i = $\sum _{} P_i$

Kinetic energy of a gas molecule (in J):
 

Kinetic energy of a mole of gas molecules (in J.mol^-1):
 

Kinetic theory of gases postulates:

• The gas molecules are constantly moving in random directions with a distribution of speeds

They collide randomly with one another and the walls of the container

• All collisions of molecules with the walls of the container are elastic ⇒ no energy is lost during a collision
• The average distance between the molecules in a gas is much larger than the size of the molecules ⇒ most of the gas is empty space
• The molecules exert no attractive or repulsive forces on each other except during collisions ⇒ between collisions they move in straight lines
• The mean kinetic energy of the gas molecules $\overline{E_k}$ is proportional to the temperature

Diffusion: gradual dispersal of one gas through another (equal pressure process)
Effusion: escape of a gas through one or more small holes from a region of high pressure to a region of lower pressure

Graham’s Law: for 2 gases at the same temp. and pressure, the rate of effusion is directly proportional to v_rms:
 

The formula mass of a gas can be determined by using effusion:
 

Mean Free Path l (in m): average distance a molecule travels between collisions
 

Collision frequency z (in collisions.s^-1): number of collisions that a molecule undergoes per second
 

Equation for non-ideal gas ⇒ it accounts for deviations from Gas Ideality

In the ideal-gas equation:

• V is substituted by V – nb, where b = cst
• P is substituted by P + a , where a = cst

The 2 constants a and b depend upon the particular gas and are called van der Waals constants

Van der Waals equation: