${\mathrm{\Delta }}_f{U}^{\ominus }$ of formation of ${\mathrm{CH}}_4\left(g\right)$ at a certain temperature is $-393 \mathrm{kJ} {\mathrm{mol}}^{-1}$. The value of $\mathrm{\Delta }{H}^{\ominus }$ is

The balanced equation for combustion of methane is

${\mathrm{CH}}_{4\left(\mathrm{g}\right)}+2{\mathrm{O}}_{2\left(\mathrm{g}\right)}\to {\mathrm{CO}}_{2\left(\mathrm{g}\right)}+2{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{l}\right)}$

$\mathrm{\Delta }{n}_g=1-3=-2$

$\begin{array}{l}{\mathrm{\Delta H}}^0={\mathrm{\Delta U}}^0+{\mathrm{\Delta n}}_{\mathrm{B}}\mathrm{RT}\\ {\mathrm{\Delta H}}^0=-393-2\mathrm{RT}\\ \therefore {\mathrm{\Delta H}}^0<{\mathrm{\Delta U}}^0\end{array}$

or

$\begin{array}{l}C\left(g\right)+2{\mathrm{H}}_2\left(g\right)⟶{\mathrm{CH}}_4\left(g\right)\\ \mathrm{\Delta }{n}_g=-1\\ \mathrm{\Delta }H=\mathrm{\Delta }U-1\times RT\end{array}$