04 The Gaseous State

Question 1

Characteristics of Gases

Answer 1

1. No fixed volume or shape
2. Highly compressible
3. Volume changes greatly with pressure
4. Pressure exerted by gases is in all directions
5. Gases mix evenly and completely when confined to the same container
6. Lower density compared to (s) & (ℓ)
7. Poor heat conductors aka good heat insulators

Question 2

Avogadro’s Law

Definition

Derived from Avogadro’s Hypothesis

Answer 2

For a gas at constant temperature, T, and pressure, p, the volume of the gas, V, is directly proportional to the number of moles of the gas, n.

Question 3

Avogadro’s Law

Formula

Answer 3

At constant T & p,
V ∝ n

V₁/ n₁ = V₂/ n₂

n = amount of gas

V = volume occupied by the gas

Question 4

Gay-Lussac’s Law

Definition

Answer 4

For a fixed mass of gas at constant volume, V, the pressure of the gas, p, is directly proportional to its absolute temperature, T.

Question 5

Gay-Lussac’s Law

Formula

Answer 5

At constant V & n,
p ∝ T
p₁/ T₁ = p₂/ T₂

T = temperature of the gas

p = pressure exerted by the gas

Question 6

Charles’ Law

Definition

Answer 6

For a fixed mass of gas, n, at constant pressure, p, the volume of the gas, V, is directly proportional to its absolute temperature, T.

Question 7

Charles’ Law

Formula

Answer 7

At constant p & n,
V ∝ T
V₁/ T₁ = V₂/ T₂

T = temperature of gas

V = volume of gas

Question 8

Boyle’s Law

Definition

Answer 8

For a fixed mass of gas, n, at constant temperature, T, the volume of the gas, V, is inversely proportional to the pressure, p.

Question 9

Boyle’s Law

Formula

Answer 9

At constant T & n,
V ∝ 1/p

V₁p₁ = V₂p₂

V = volume of gas
p = pressure of gas

Question 10

Ideal Gas Equation

Answer 10

pV = nRT

R = molar gas constant of 8.31 J K_-1 mol_-1

Units:
p: Pa/ Nm_-2
V: m₃
n: mol
T: K

Question 11

The Kinetic Theory of Gases

Assumptions

Answer 11

1. An ideal gas consists of particles of negligible volume.
2. Gas particles exert negligible attractive forces on each other.
3. Gas particles are in constant random motion, colliding with one another and with the walls of the container. Between collisions, they move in a straight line.
4. Collisions between gas particles are perfectly elastic, i.e. no loss of kinetic energy occurs but kinetic energy can be transferred to another particle.
5. The average kinetic energy of particles in a gas is constant at constant temperature and is proportional to the absolute temperature. At the same temperature, all gases have the same average kinetic energy.

1 & 2 are the most important

Question 12

Ideal Gas
Definition

Answer 12

A gas that is assumed to be one where the gas particles have negligible volume and exert negligible attractive forces on one another.

Question 13

Real Gas

Answer 13

A gas which has a finite volume, size and attractive forces between gas particles.

Question 14

Approaching Ideality

Conditions

Answer 14

1. Low Pressure
   
   • Particles are far apart
   • Volume occupied by the gas particles can be considered negligible volume when compared to the volume to the container
   • Intermolecular attractive forces between the widely spaced gas particles are negligible
2. High Temperature
   
   • Gas particles possess sufficiently high kinetic energy to overcome the intermolecular attractive forces, making it negligible.

Question 15

Deviating from Ideality

Conditions

Answer 15

1. High Pressure
   
   • Particles closer together
   • Gas occupies smaller volume
   • Volume of gas particles is not negligible when compared to the volume of the container
   • Intermolecular attractive forces between the closely-spaced particles is significant
2. Low Temperature
   
   • Particles possess less kinetic energy
   • Intermolecular attractive forces are significant

Question 16

Intermolecular Repulsion Forces

Answer 16

affected by M_r
- larger e^- cloud
- more easily polarised
- stronger id-id interactions
- deviates more ideality

Question 17

Dalton’s Law of Partial Pressures

Formula

Answer 17

P_total = P_A + P_B + …

Question 18

Dalton’s Law of Partial Pressures

Definition

Answer 18

The total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases in the mixture.

Question 19

Mole Fraction, x_A

Definition

Answer 19

The ratio of the number of moles of gas A to the total number of all gaseous components present in the mixture.

Question 20

Mole Fraction, x_A

Formula

Answer 20

x_A = number of moles of component A/ total number of moles of all components in mixture = n_A/ n_total

Question 21

Partial Pressure of a gas

Formula

Answer 21

p_A = x_A x p_total

Question 22

Vapour Pressure

Definition

Answer 22

The pressure exerted by the gaseous particles on the liquid surface and on the walls of the container.

Question 23

Saturated Vapour Pressure

Definition

Answer 23

A dynamic equilibrium is set up when the number of particles leaving the surface is equal to that of those rejoining. The fixed number of gaseous particles in the space above the liquid is the saturated vapour pressure.

Question 24

Relating Intermolecular Forces, Boiling Points and Vapour Pressures

Answer 24

• Stronger intermolecular forces
• Lower saturated vapour pressure
• Lower volatility
• Higher boiling point