Answer:
1. 7.0 u; 2. 81 u; 3. 12.7 h.
Step-by-step explanation:
Graham’s Law applies to the diffusion of gases:
The rate of diffusion (r) of a gas is inversely proportional to the square root of its molar mass (M).
r = 1/√M
If you have two gases, the ratio of their rates of diffusion is
r₂/r₁ = √(M₁/M₂)
1. Molecular mass
r₂/r₁ = (2.5r₁)/r₁ = 2.5
2.5 = √(44.01/M₂)
Square both sides: 6.25 = 44.01/M₂
Multiply each side by M₂: 6.25M₂ = 44.01
Divide each side by 6.25: M₂ = 7.0 u
The molecular mass of the gas is 7.0 u.
2. Molecular mass
r₂/r₁ = (r₁/1.7)/r₁ = 1/1.7
1/1.7 = √(28.01/M₂)
Square both sides: 1/2.89 = 28.01/M₂
Multiply each side by M₂: M₂/2.89 = 28.01
Multiply each side by 2.89: M₂ = 81 u
The molecular mass of the gas is 81 u.
3. Time for diffusion
The time for effusion is inversely proportional to the rate. The faster the rate, the slower the time. Thus,
t₂/t₁ = √(M₂/M₁)
Multiply each side by t₁
t₂ = t₁√(M₂/M₁) = 4.5√(16.04/2.016) = 4.5√7.956 = 4.5 × 2.82 = 12.7 h
It would take methane 12.7 h to diffuse.
