Question

At 300 K , the standard enthalpies of formation of $C_6{H}_{5}COOH\left(s\right)$ , $C{O}_2\left(g\right)$ & $H_{2}O\left(l\right)$ are ; -408, -393 , & -286 kJ mol respectively.
Calculate the heat of combustion of benzoic acid at:
(i) constant pressure
(ii) constant value

Answer 1

$C_6{H}_{5}COOH\left(s\right)+7.5O_2\left(g\right)\to {7CO}_2\left(g\right)+3H_{2}O\left(l\right)$

$\Delta n=7-7.5=-0.5$

a) $\therefore$ Heat combustion at constant pressure

$=7\times (-393)+3\times (-286)+408+7.5\times 96.485$

$=(7\times {\Delta H}_{{CO}_2}+3\times {\Delta H}_{H_{2}O})-({\Delta H}_{C_6{H}_{5}COOH}+7.5\times {\Delta H}_{O_2})$

$=-2477kJmol$

$\therefore$ Heat combustion at constant volume

$=-2477-\Delta nRT$

$=-2477+0.5\times 8.314\times {10}^{-3}\times 300$

$=-2476kJ/mol$