Question

At 300 K, a sample of 3.0 g of gas A occupies the same volume as 0.2 g of hydrogen at 200 K at the same pressure. The molar mass of gas A is _____ g mol–1. (nearest integer)
Assume that the behaviour of gases as ideal.
(Given: The molar mass of hydrogen (H2) gas is 2.0 g mol–1).

Answer 1

$V_1$, Volume of $0.2\ g$ $H_2$ at $200\ K$
$=\frac { 0.2 \times R \times 200}{2 \times P}$
$V_2$, Volume of $3.0\ g$ of gas A at $300\ K$
$= \frac {0.3 \times R \times 300}{M \times P}$
Given that, $V_1 = V_2$
$⇒ \frac {0.2 \times R \times 200 }{ 2 \times P} = \frac {0.3 \times R \times 300}{M \times P}$
$M = 45$ g mol-1

So, the answer is $45$.