Question

A gas cylinder is filled with hydrogen gas which weighs $40$ g. The same cylinder holds 880 g of a gas $A$ and $560$ g of a gas $B$ under the same conditions of temperature and pressure. Calculate the relative molecular masses of $A$ and $B$.

• A. $A\to 44,B\to 28$
• B. $A\to 32,B\to 64$
• C. $A\to 46,B\to 28$
• D. $A\to 44,B\to 32$

Answer 1

The correct option is A $A\to 44,B\to 28$

$PV=nRT=\frac{W}{M}RT$
$\frac{W}{M}=\frac{PV}{RT}$
Volume of the container, temperature and pressure are same for all the gases.
$\frac{W}{M}=$ constant
Hence, $\frac{W_{H2}}{M_{H2}}=\frac{W_A}{M_A}=\frac{W_B}{M_B}$
$\frac{\text{40 g}}{\text{2 g/mol}}=\frac{\text{880 g}}{M_A}=\frac{\text{560 g}}{M_B}$
$M_A=\text{880 g}\times \frac{\text{2 g/mol}}{\text{40 g}}=\text{44 g/mol}$
$M_B=\text{560 g}\times \frac{\text{2 g/mol}}{\text{40 g}}=\text{28 g/mol}$
Hence, the relative molecular masses of $A$ and $B$ are 44 g/mol and 28 g/mol respectively.