Question
The $$\left( {{S^ \circ }} \right)$$ of the following substances are :
$$\eqalign{
& C{H_4}\left( g \right)\,\,186.2\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr
& {O_2}\left( g \right)\,\,205.2\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr
& C{O_2}\left( g \right)\,\,213.6\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr
& {H_2}O\left( g \right)\,\,69.9.\,J{K^{ - 1}}\,mo{l^{ - 1}} \cr} $$
The entropy change $$\left( {\Delta {S^ \circ }} \right)$$ for the reaction $$C{H_4}\left( g \right) + 2{O_2}\left( g \right) \to C{O_2}\left( g \right) + 2{H_2}O\left( l \right)$$ is :
A.
$$ - 312.5\,J\,{K^{ - 1}}\,mo{l^{ - 1}}$$
B.
$$ - 242.8\,J\,{K^{ - 1}}\,mo{l^{ - 1}}$$
C.
$$ - 108.1\,J\,{K^{ - 1}}\,mo{l^{ - 1}}$$
D.
$$ - 37.6\,J\,{K^{ - 1}}\,mo{l^{ - 1}}$$
Answer :
$$ - 242.8\,J\,{K^{ - 1}}\,mo{l^{ - 1}}$$
Solution :
$$\eqalign{
& \Delta {S^ \circ } = {S^ \circ }_{C{O_2}} + 2 \times {S^ \circ }_{{H_2}O} - \left( {{S^ \circ }_{C{H_4}} + 2 \times S_{{O_2}}^ \circ } \right) \cr
& = \left( {213.6 + 2 \times 69.9} \right) - \left( {186.2 + 2 \times 205.2} \right) \cr
& = - 242.8\,J\,{K^{ - 1}}\,mo{l^{ - 1}}. \cr} $$