Question

The standard heat of formation $\left({\Delta }_f{H}_{298}^{\circ }\right)$ of ethane (in kJ/mol), if the heat of combustion of ethane, hydrogen and graphite are -1560, -393.5 and -286 kJ/mol, respectively, is

Answer 1

$C_{graphite}+O_2\left(g\right)\to C{O}_2\left(g\right)\Delta H_c^{\circ }=-286\text{kJ/mol}\dots \dots \left(1\right)$
$H_2\left(g\right)+0.5O_2\left(g\right)\to H_{2}O\left(l\right)\Delta H_c^{\circ }=-393.5\text{kJ/mol}\dots \dots \left(2\right)$
$C_2{H}_6\left(g\right)+3.5O_2\left(g\right)\to 2C{O}_2\left(g\right)+3H_{2}O\left(l\right)\Delta H_c^{\circ }=-1560\text{kJ/mol}\dots \dots \left(3\right)$
$2C_{\left(graphite\right)}+3H_2\left(g\right)\to C_2{H}_6\left(g\right);\Delta H_f^{\circ }=?$
By inverting (3) and multiplying (1) by 2 and (2) by 3 and adding, we get,
$2\times (-286)+3\times (-393.5)-(-1560)=-192.5\text{kJ/mol}$