Properties of Gases | General Chemistry 2
Gas Properties
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:
P =
F = force (in Newton = kg.m.s-2)
A = area (in m2)
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
Gas Laws
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
P1 V1 = P2 V2 (at T = cst)
Charles’s Law (V vs T):
At constant pressure: V and T are directly proportional
= (at P = cst)
Gay-Lussac’s Law (P vs T):
At constant volume: P and T are directly proportional
= (at V = cst)
Avogadro’s Law (V vs n):
At constant temperature and pressure: V and n are directly proportional
= (at T and P = cst)
Ideal Gas Equation
PV = nRT
P = pressure (in Pa)
V = volume (in m3)
n = number of moles (in mol)
R = ideal gas constant = 8.314 (in J.K-1.mol-1)
T = temperature (in K)
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
Ideal Gas Law – Molar Volume, Molar Mass and Density
Molar Volume Vm (in L.mol-1) in the Ideal Gas Law:
Vm = =
R = 8.314 J.mol-1.K-1
T = temperature (in K)
P = pressure (in Pa)
At standard temperature and pressure (STP): Vm = 22.41 L.mol-1
Molar Mass M (in g.mol-1) in the Ideal Gas Law:
M = =
m = mass (in g)
R = 8.314 J.mol-1.K-1
T = temperature (in K)
P = pressure (in Pa)
V = volume (in m3)
Density ρ (in g.m-3) in the Ideal Gas Law:
ρ = =
P = pressure (in Pa)
M = molar mass (in g.mol-1)
R = 8.314 J.mol-1.K-1
T = temperature (in K)
Dalton’s Law of Partial Pressures
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
Ptot = PA + PB + PC + … + Pi =
Kinetic Theory and Speed Distribution
Kinetic energy of a gas molecule (in J):
Ek = mv2
m = mass of the molecule (in kg)
v = velocity (in m.s-1)
Kinetic energy of a mole of gas molecules (in J.mol-1):
Ek = Mkgv2
Mkg = molar mass (in kg.mol-1)
v = velocity (in m.s-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 is proportional to the temperature
= Mkg = αT
A detailed analysis of the collisions shows:
α = R ⇒ =
Root-mean-square speed vrms (in m.s-1): square root of the mean of the square of the molecular speeds
vrms = =
R = molar gas constant = 8.314 J.K-1.mol-1
T = temperature (in K)
Mkg = molar mass of the gas (in kg.mol-1)
Graham’s Law of Effusion
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 vrms:
rate = α vrms = α
α = proportionality coefficient
The formula mass of a gas can be determined by using effusion:
=
MA = molar mass of the gas A (in kg.mol-1)
MB = molar mass of the gas B (in kg.mol-1)
Mean Free Path
Mean Free Path l (in m): average distance a molecule travels between collisions
I =
R = molar gas constant = 8.314 J.K-1.mol-1
T = temperature (in K)
d = diameter of the gas molecule (in m)
NA = Avogadro’s number = 6.022 x 1023
P = pressure (in Pa)
Collision frequency z (in collisions.s-1): number of collisions that a molecule undergoes per second
z =
vrms = root-mean-square speed (in m.s-1)
l = mean free path (in m)
Van der Waals Equation
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:
(P + a )(V - nb) = nRT
P = pressure (in Pa)
V = volume (in m3)
n = number of moles (in mol)
R = molar gas constant = 8.314 J.K-1.mol-1
T = temperature (in K)