Exactly of a gas A diffuses through a membrane in the same time as of a gas B under identical pressu — States of Matter and Gaseous State Chemistry Question
Question
Exactly $50\text{ mL}$ of a gas A diffuses through a membrane in the same time as $40\text{ mL}$ of a gas B under identical pressure and temperature conditions. If the molecular weight of gas A is $64\text{ g/mol}$, what is the molecular weight of gas B?
Answer: B
💡 Solution & Explanation
Rate of diffusion $r = V/t$. For the same time $t$, $r_A/r_B = V_A/V_B = \sqrt{M_B/M_A}$. Substituting the values: $50/40 = \sqrt{M_B/64} \implies 5/4 = \sqrt{M_B}/8 \implies M_B = (5 \times 8 / 4)^2 = 10^2 = 100\text{ g/mol}$.
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