The heat of combustion at constant volume at 27°C of Benzene and acetylene are -800 k. cal and  -310 k cal. Find the heat of polymerization of acetylene to ${\mathrm{C}}_6{\mathrm{H}}_6$ at constant pressure

$\begin{array}{l}3{\mathrm{C}}_2{\mathrm{H}}_2+\frac{15}{2}{\mathrm{O}}_2\to 6{\mathrm{CO}}_2+3{\mathrm{H}}_2\mathrm{O};\Delta U=3\times (-310)=-930\mathrm{k}.\mathrm{cal}\\ {\mathrm{C}}_6{\mathrm{H}}_6+\frac{15}{2}{\mathrm{O}}_2\to 6{\mathrm{CO}}_2+3{\mathrm{H}}_2\mathrm{O};\Delta \mathrm{U}=-800\mathrm{k}.\mathrm{cal}\end{array}$

The following polymerization reaction can be obtained by (1)-(2)

$\begin{array}{l}3{\mathrm{C}}_2{\mathrm{H}}_2( \mathrm{g})\to {\mathrm{C}}_6{\mathrm{H}}_6\left(l\right)\\ \Delta U=-930-(-800)=-130\mathrm{k}.\mathrm{cal}\\ 3{\mathrm{C}}_2{\mathrm{H}}_2( \mathrm{g})\to {\mathrm{C}}_6{\mathrm{H}}_6\left(l\right);\Delta n_g=0-3=-3\end{array}$

The relationship between heat of a reaction at constant pressure and heat of a reaction at constant volume for a chemical process is given as

$\begin{array}{l}\Delta H=\Delta U+\Delta n_{g}RT\\ \Delta H=-130-3\times 2\times 300\times {10}^{-3}=-131.8\mathrm{k}.\mathrm{cal}\end{array}$