An unknown gas effuses at one half the speed of oxygen. What is the molar mass of the unknown? It is either HBr or HI. Which gas is it?

HI.

Explanation:

Thomas Graham found that, at a constant temperature and pressure the rates of effusion of various gases are inversely proportional to the square root of their masses.

Rate of effusion ∝ 1/√molar mass.

(Rate of effusion of O₂) / (Rate of effusion of unknown gas) = (√molar mass of unknown gas) / (√molar mass of O₂). An unknown gas effuses at one half the speed of that of oxygen.

∵ Rate of effusion of unknown gas = 1/2 (Rate of effusion of O₂)

∴ (Rate of effusion of O₂) / (Rate of effusion of unknown gas) = 2.

Molar mass of O₂ = 32.0 g/mol.

∵ (Rate of effusion of O₂) / (Rate of effusion of unknown gas) = (√molar mass of unknown gas) / (√molar mass of O₂).

∴ 2.0 = (√molar mass of unknown gas) / √32.0.

(√molar mass of unknown gas) = 2.0 x √32.0

By squaring the both sides:

∴ molar mass of unknown gas = (2.0 x √32.0) ² = 128 g/mol.

∴ The molar mass of sulfur dioxide = 80.91 g/mol and the molar mass of HI = 127.911 g/mol.

So, the unknown gas is HI.