Answer to Question #314511 in Chemistry for sael

Question

The rate of effusion of an unknown gas was measured to be 25.3 mL/min. Under similar conditions, a known gas with a density of 3.1 g/mL effuses at 19.5 mL/min. What is the density of the unknown gas?

Strategy: Let ρ1 be the density of the unknown gas.

Answer 1

rate of effusion of unknown gas = r₁ = 25.3 mL/min

rate of effusion of known gas = r₂ = 19.5 mL/min

density of unknown gas = ρ₁ = ???

density of known gas = ρ₂ = 3.1 g/mL

Solution:

According to Graham's Law:

"When compared at hte same temperature and pressure, the rates of diffusion (or effusion) of any two gases are inversely proportional to the square roots of their densities"

Graham's Law can be expressed as: rate ∝ 1 / (density)^1/2

Therefore,

(r₁ / r₂) = (ρ₂ / ρ₁)^1/2

(25.3 / 19.5) = (3.1 / ρ₁)^1/2

1.2974 = (3.1 / ρ₁)^1/2

1.683 = 3.1 / ρ₁

ρ₁ = 1.84 g/mL

Answer: The density of the unknown gas is 1.84 g/mL