Chemistry - Thermochemistry Question with Solution | TestHub

${\mathrm{C}}_2{\mathrm{H}}_4( \mathrm{g})+3{\mathrm{O}}_2( \mathrm{g})\to 2{\mathrm{CO}}_2( \mathrm{g})+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$
$\mathrm{\Delta U}=-1406 \mathrm{kJ} {\mathrm{mol}}^{-1}$

$\mathrm{T}=300\mathrm{K}$

$\mathrm{\Delta H}=\mathrm{\Delta U}+{\mathrm{\Delta n}}_{\mathrm{g}}\mathrm{RT}$

$\mathrm{\Delta U}$ is the change in the internal energy of the system, which is the sum of the kinetic and potential energies of all the molecules in the system. $\mathrm{R}$ is the gas constant ($8.314 \mathrm{J}/(\mathrm{mol} \mathrm{K})$ and $\mathrm{T}$ is the temperature in Kelvin.
$$\begin{gathered} ∆\mathrm{H} = –1406 + (–2) \times 8.3 \times 300 = –1406 – 4.98 \\ = –1410.98 \mathrm{KJ} \mathrm{mol}–1 \approx –1411 \\ \mathrm{The} \mathrm{minimum} \mathrm{value} \mathrm{of} \mathrm{T}∆\mathrm{S} \mathrm{at} \mathrm{equilibrium} ∆\mathrm{H} \\ ∆\mathrm{H} = \mathrm{T}∆\mathrm{S} = –1411 \mathrm{KJ} {\mathrm{mol}}^{–1} \end{gathered}$$