Question
Given that,
$$C\left( s \right) + {O_2}\left( g \right) \to C{O_2}\left( g \right),$$ $$\Delta {H^ \circ } = - x\,kJ$$
$$2CO\left( g \right) + {O_2}\left( g \right) \to 2C{O_2}\left( g \right),$$ $$\Delta {H^ \circ } = - ykJ$$
The enthalpy of formation of carbon monoxide will be
A.
$$y - 2x$$
B.
$$2x - y$$
C.
$$\frac{{y - 2x}}{2}$$
D.
$$\frac{{2x - y}}{2}$$
Answer :
$$\frac{{y - 2x}}{2}$$
Solution :
$$C + {O_2} \to C{O_2},\,\,\Delta {H^ \circ } = - x\,kJ...{\text{(i)}}$$
On reversing given second equation we get,
$$\eqalign{
& 2C{O_2} \to 2CO + {O_2},\,\Delta {H^ \circ } = + y\,kJ \cr
& {\text{or}}\,\,C{O_2} \to CO + \frac{1}{{2{O_2}}},\,\Delta {H^ \circ } = + \frac{y}{2}kJ...{\text{(ii)}} \cr} $$
From Eqs. (i) and (ii) ( by addition )
$$\eqalign{
& C + \frac{1}{2}{O_2} \to CO, \cr
& \Delta {H^ \circ } = \frac{y}{2} - x \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{y - 2x}}{2}kJ \cr} $$