Question

2.00 mol of Argon can effuse from an opening in a vessel in 3.626 seconds. 1.00 mol of gas X can effuse in 1.000 seconds. Use this information to identify gas X.

Answer 1

The rate at which a gas effuses depends on its speed, but when 2 gases effuse through the same system, they will do so at different rates. They will take different amounts of time to escape from the container, due to their shape, size, and speed. The heavier a gas is, the slower it travels, and the lower its rate of effusion (compared to a lighter gas). A lighter gas will effuse faster than a heavier gas for the same reasons. The equation that determines this is knowns as Graham's Law of Effusion. It states that:
\[\frac{R_2}{R_1} = \sqrt {(\frac{MM_1}{MM_2})}\]
the ratio of the 2 rates will be proportional to the square root of their molar masses. The catch is that you have to be comparing equal amounts of gas, so if 2mol of Ar escape in 3.626s, then 1mol of Ar should escape in half that time. Plug in the rates, plug in the molar massof Ar as MM2, and find MM1