Question

a gas made up of homonuclear diatomic molecules escapes through a pinhole 0.936 times as fast as n₂ gas. write the chemical formula of the gas.

Explanation:

Step1: Recall Graham's Law

$\frac{v_1}{v_2} = \sqrt{\frac{M_2}{M_1}}$
Let gas 1 = unknown gas, gas 2 = $\text{N}_2$. $v_1 = 0.936v_2$, $M_2 = 28\ \text{g/mol}$.

Step2: Substitute values into the formula

$0.936 = \sqrt{\frac{28}{M_1}}$

Step3: Square both sides

$0.936^2 = \frac{28}{M_1}$

Step4: Calculate $0.936^2$

$0.936^2 ≈ 0.876$

Step5: Solve for $M_1$

$M_1 = \frac{28}{0.876} ≈ 31.96\ \text{g/mol}$

Step6: Identify homonuclear diatomic gas

Molar mass ~32 g/mol: $\text{O}_2$ (O atomic mass ≈16, 2×16=32).

Answer:

$\text{O}_2$