Question

A sample of hydrogen effuses through a porous container about 9 times faster than an unknown gas. Estimate the molar mass of the unknown gas.

Answer 1

Answer:

164 g/mol

Explanation:

According to Graham's law, the rate of effusion of a gas (r) is inversely proportional to the square root of its molar mass (M).

rH₂/rX = √[M(X)/ M(H₂)]

(rH₂/rX)² = M(X)/ M(H₂)

M(X) = (rH₂/rX)² × M(H₂)

M(X) = (9)² × 2.02 g/mol

M(X) = 164 g/mol

The molar mass of the unknown gas is 164 g/mol.

Answer 2

The molar mass of the unknown gas is 64 g/mol.

According to Graham's law:

The rate of effusion of a gas (r) is inversely proportional to the square root of its molar mass (M).

It is given by:

$rH_2/rX = \sqrt{[M(X)/ M(H_2)]} \\\\(rH_2/rX)^2 = M(X)/ M(H_2)\\\\M(X) = (rH_2/rX)^2 * M(H₂)\\\\M(X) = (9)^2 * 2.02 g/mol\\\\M(X) = 164 g/mol$

Thus, the molar mass of the unknown gas is 164 g/mol.

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