Question

An unkown gas diffuses four times as oxygen. calculate the molar mass of the gas

Answer 1

rate1 / rate2 = sqrt(M2 / M1)

So let's make oxygen "Gas 2" and we'll call the mystery gas "Gas 1". Since Gas 1 diffuses 4 times as fast as oxygen, we know that:

rate1 / rate2 = 4

Substituting that into the Graham's Law equation:

4 = sqrt(M2 / M1)

The molar mass (M2) of oxygen gas, O2, is 32 g/mol.

4 = sqrt(32 / M1)

Square both sides.

16 = (32 / M1)

M1 = 32 / 16 = 2

The only gas that has a molar mass of 2 g/mol is hydrogen gas, H2.

I hope that helps. Good luck!