Question

The heat of combustion of $H_2\left(g\right)$ at constant pressure and $300K$ is -280 kJ mol${}^{-1}$.
What will be the heat of combustion at constant volume and $300K$?

• A. $\Delta U=$ -276.2587 kJ
• B. $\Delta U=$ +276.2587 kJ
• C. $\Delta U=$ -27.63 kJ
• D. None of these

Answer 1

Answer: (A)

$\Delta U=$ -276.2587 kJ

The combustion reaction is as shown below.

$H_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)⟶H_{2}O\left(l\right)$

The heat of combustion at constant pressure is $\Delta H=-280$ kJ mol${}^{-1}$

$\Delta H=\Delta U+\Delta nRT$ ,

$\Delta n=0-\frac{3}{2}$

$\Delta n=-\frac{3}{2}$ ,

Here $\Delta U$ is the heat of combustion at constant volume.

Substitute values in the above expression.

$\Delta H=\Delta U-\frac{3}{2}\times 8.314\times 300$

$-280kJ=\Delta U-\frac{74826}{20}\times \frac{1}{1000}kJ$

$\Rightarrow \Delta U=-276.2587kJ$

Hence, the correct option is $A$