Question

which of the following gases would you expect to move the fastest at 250 k?
n₂
c₂h₆
ar
hbr

Explanation:

Step1: Recall Graham's Law

Graham's Law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass, i.e., \( \text{Rate} \propto \frac{1}{\sqrt{M}} \), where \( M \) is the molar mass. So, the gas with the smallest molar mass will effuse/diffuse the fastest.

Step2: Calculate molar masses

• For \( \text{N}_2 \): Molar mass \( M = 2 \times 14.01 = 28.02 \, \text{g/mol} \)
• For \( \text{C}_2\text{H}_6 \): \( M = 2 \times 12.01 + 6 \times 1.008 = 24.02 + 6.048 = 30.068 \, \text{g/mol} \)
• For \( \text{Ar} \): \( M = 39.95 \, \text{g/mol} \) (atomic mass of Ar)
• For \( \text{HBr} \): \( M = 1.008 + 79.904 = 80.912 \, \text{g/mol} \)

Step3: Compare molar masses

Among the given gases, \( \text{N}_2 \) has the smallest molar mass (28.02 g/mol) compared to \( \text{C}_2\text{H}_6 \) (30.068 g/mol), \( \text{Ar} \) (39.95 g/mol), and \( \text{HBr} \) (80.912 g/mol).

Answer:

\( \text{N}_2 \) (the option with \( \text{N}_2 \))