(b) Define / describe the following, and provide relevant equations where necessary:
(i) The collision frequency: The collision frequency refers to the number of collisions that occur per unit time between particles in a gas. It is denoted by the symbol Z and is calculated using the equation:
Z = n * σ * v
where:
- n represents the number density of particles in the gas
- σ is the collision cross-section, which represents the effective area that particles collide with
- v is the average velocity of the particles
(ii) The mean free path: The mean free path is the average distance traveled by a particle between successive collisions in a gas. It is denoted by the symbol λ and is calculated using the equation:
λ = 1 / (√2 * n * σ)
where:
- n represents the number density of particles in the gas
- σ is the collision cross-section, which represents the effective area that particles collide with
(iii) The collision flux, ZW: The collision flux, denoted by ZW, represents the number of collisions that occur per unit area per unit time. It is calculated using the equation:
ZW = Z * v
where:
- Z represents the collision frequency
- v is the average velocity of the particles
(iv) Effusion: Effusion refers to the process by which a gas escapes through a small hole or opening into a vacuum. It is governed by Graham's law of effusion.
(v) Fick's first law of diffusion: Fick's first law of diffusion describes the rate at which a substance diffuses through a medium. It states that the rate of diffusion is directly proportional to the concentration gradient of the substance. The equation for Fick's first law of diffusion is:
J = -D * (∂C/∂x)
where:
- J represents the diffusion flux, which is the amount of substance diffusing per unit area per unit time
- D is the diffusion coefficient, which represents the ability of the substance to diffuse through the medium
- ∂C/∂x is the concentration gradient of the substance
(vi) Graham's law of effusion: Graham's law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The equation for Graham's law of effusion is:
Rate1 / Rate2 = √(M2 / M1)
where:
- Rate1 represents the rate of effusion of gas 1
- Rate2 represents the rate of effusion of gas 2
- M1 represents the molar mass of gas 1
- M2 represents the molar mass of gas 2