Question
$${\Delta _f}{U^ \circ }$$ of combustion of $$C{H_{4\left( g \right)}}$$ at certain temperature is $$ - 393\,kJ\,mo{l^{ - 1}}.$$ The value of $${\Delta _f}{H^ \circ }$$ is
A.
$${\text{zero}}$$
B.
$$ < {\Delta _f}{U^ \circ }$$
C.
$$ > {\Delta _f}{U^ \circ }$$
D.
$${\text{equal to}}\,\,{\Delta _f}{U^ \circ }$$
Answer :
$$ < {\Delta _f}{U^ \circ }$$
Solution :
The balanced equation for combustion of methane is $$C{H_{4\left( g \right)}} + 2{O_{2\left( g \right)}} \to C{O_{2\left( g \right)}} + 2{H_2}{O_{\left( l \right)}}$$
$${\text{Here}},\Delta {n_g} = 1 - 3 = - 2$$
$${\Delta _f}{H^ \circ } = {\Delta _f}{U^ \circ } + \Delta {n_g}RT;$$ $${\Delta _f}{H^ \circ } = - 393 - 2RT$$
$$\therefore \,\,{\Delta _f}{H^ \circ } < {\Delta _f}{U^ \circ }$$