Question

A glass box holds equal amounts of hydrogen, nitrogen, oxygen, and bromine. The gases are allowed to exit the container through a tiny hole. Which gas will exit the hole the fastest?

Answer 1

According to Graham's law of diffusion, the rate of diffusion $r$ of a gas is inversely proportional to the square root of its molar mass $M$ :

$$r = \frac{k}{\sqrt{M}}$$

Let's calculate the molar mass of each of the gases:

M(H₂) = 2.02 g/mol

M(N₂) = 28.01 g/mol

M(O₂) = 32.00 g/mol

M(Br₂) = 159.81 g/mol.

As you can note, the molar mass of hydrogen is the smallest, so this gas will exit the hole the fastest. Furthermore, the times of diffusion of the gases can be compared as (from the fastest to the slowest): H₂<N₂<O₂<Br₂, and the rates of diffusion of these gases as H₂>N₂>O₂>Br₂.

Answer: Hydrogen gas (H₂) will exit the hole the fastest.