Question
Heat of combustion $$\Delta {H^ \circ }$$ for $$C\left( s \right),{H_2}\left( g \right)$$ and $$C{H_4}\left( g \right)$$ are $$ - 94, - 68$$ and $$ - 213\,kcal/mol.$$ Then, $$\Delta {H^ \circ }$$ for $$C\left( s \right) + 2{H_2}\left( g \right) \to C{H_4}\left( g \right)$$ is
A.
$$ - 17\,kcal/mol$$
B.
$$ - 111\,kcal/mol$$
C.
$$ - 170\,kcal/mol$$
D.
$$ - 85\,kcal/mol$$
Answer :
$$ - 17\,kcal/mol$$
Solution :
$$\eqalign{
& {\text{For reaction,}} \cr
& C\left( s \right) + 2{H_2}\left( g \right) \to C{H_4}\left( g \right),\,\Delta {H^ \circ } = ? \cr
& C + {O_2} \to C{O_2},\,\Delta H = - 94\,kcal\,\,...{\text{(i)}} \cr} $$
$$2{H_2} + {O_2} \to 2{H_2}O,\,\Delta H$$ $$ = - 68 \times 2\,kcal\,\,...{\text{(ii)}}$$
$$C{H_4} + 2{O_2} \to C{O_2} + 2{H_2}O,$$ $$\Delta H = - 213\,kcal\,\,...{\text{(iii)}}$$
On adding Eqs. (i) and (ii) and then subtracting Eq. (iii)
$$\eqalign{
& = \left( { - 94} \right) + \left( { - 2 \times 68} \right) - \left( { - 213} \right) \cr
& = - 230 + 213 \cr
& = - 17\,k\,cal/mol \cr} $$