Question

In a constant volume calorimeter, $5$g of a gas with molecular weight $40$ was burnt in excess of oxygen at $298$K. The temperature of the calorimeter was found to increase from $298$K to $298.75$K due to combustion process. Given that the heat capacity of the calorimeter is $2.5$ kJ $K^{-1}$, the numerical value for the $\Delta U$ of combustion of the gas in kJ $mo{l}^{-1}$ is:

• A. $15$
• B. $12$
• C. $90$
• D. $8$

Answer 1

The correct option is A $15$

As we know that, for ideal gas under any process,

$\Delta U=\frac{\text{heat capacity}\times \text{change in temprature}}{\text{no.of moles}}$

Given:-

Mol. wt. of gas $=40g$

Wt. of gas $=5g$

$\therefore$ No. of moles $=\frac{5}{40}=0.125\text{mole}$

Heat capacity $=2.5kJ/K$

Change in temperature $=298-298.75=0.75K$

$\therefore \Delta U=\frac{2.5\times 0.75}{0.125}=15kJ/mol$

Hence the numerical value for the $\Delta U$ of combustion is $15kJ/mol$.

Hence, the correct option is $\text{A}$