Exactly of an unknown gas at occupies the same volume as of gas at and at the same constant pressure — States of Matter and Gaseous State Chemistry Question
Question
Exactly $3.7\text{ g}$ of an unknown gas at $25^\circ\text{C}$ occupies the same volume as $0.184\text{ g}$ of $H_2$ gas at $17^\circ\text{C}$ and at the same constant pressure. What is the molecular weight of the unknown gas (in $\text{g/mol}$)? (Round off to the nearest integer, assume ideal behaviour, $M(H_2) = 2\text{ g/mol}$).
Answer: 41
💡 Solution & Explanation
Since volume and pressure are the same, $V = n_1RT_1/P = n_2RT_2/P$, thus $n_1T_1 = n_2T_2$. For the unknown gas: $n_1 = 3.7/M$, $T_1 = 298\text{ K}$. For $H_2$: $n_2 = 0.184/2 = 0.092$, $T_2 = 290\text{ K}$. Therefore, $(3.7/M) \times 298 = 0.092 \times 290 \implies M = (3.7 \times 298) / (0.092 \times 290) = 1102.6 / 26.68 \approx 41.33$. The nearest integer is 41.
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