Question
What will be the heat of reaction for the following reaction ? Will the reaction be exothermic or endothermic ?
$$\eqalign{
& F{e_2}{O_{3\left( s \right)}} + 3{H_{2\left( g \right)}} \to 2F{e_{\left( s \right)}} + 3{H_2}{O_{\left( l \right)}} \cr
& {\Delta _f}{H^ \circ }\left( {{H_2}O,l} \right) = - 285.83\,kJ\,mo{l^{ - 1}}, \cr
& {\Delta _f}{H^ \circ }\left( {F{e_2}{O_3},s} \right) = - 824.2\,kJ\,mo{l^{ - 1}} \cr} $$
A.
$$ - 824.2\,kJ\,mo{l^{ - 1}},{\text{exothermic}}$$
B.
$$ + 33.3\,kJ\,mo{l^{ - 1}},{\text{endothermic}}$$
C.
$$ - 33.3\,kJ\,mo{l^{ - 1}},{\text{exothermic}}$$
D.
$$ + 824.2\,kJ\,mo{l^{ - 1}},{\text{endothermic}}$$
Answer :
$$ - 33.3\,kJ\,mo{l^{ - 1}},{\text{exothermic}}$$
Solution :
$$\eqalign{
& {\Delta _f}{H^ \circ }\left( {F{e_{\left( s \right)}}} \right) = 0,{\Delta _f}{H^ \circ }\left( {{H_{2\left( g \right)}}} \right) = 0 \cr
& {\Delta _f}{H^ \circ } = 3\left( { - 285.83} \right) - 1\left( { - 824.2} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - 857.5 + 824.2 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - 33.3\,kJ\,mo{l^{ - 1}} \cr
& {\text{Reaction is exothermic}}{\text{.}} \cr} $$