The molar heats of combustion of `C_(2)H_(2)(g),C` (graphite) and `H_(2)(g)` are 310.62 kcal, 94.05 kcal and 68.32 kcal respectively. Calculate the standard heat of formation of `C_(2)H_(2)(g)` .

Explanation

Given that,
(i) `{:(C(s)+O_(2)(g) to CO_(2)(g),,DeltaH=-94.05"kcal"):}`
(ii) `{:(H_(2)(g)+(1)/(2)O_(2)(g) to H_(2)O(g),,DeltaH=-68.32"kcal"):}`
(iii) `{:(C_(2)H_(2)(g)+2(1)/(2)O_(2)(g) to 2CO_(2)(g)+H_(2)O(g),,DeltaH=-310.62"kcal"):}`
We have to calculate `DeltaH` of the equation
`2C(s)+H_(2)(g) to C_(2)H_(2)(g),DeltaH=?`
Proceeding the same way as in Example 9, we apply,
[2xx Eqn. (i)+Eqn.(ii) - Eqn. (iii)] and we get,
`2C(s)+2O_(2)(g)+H_(2)(g)+(1)/(2)O_(2)(g)-C_(2)H_(6)(g)-2(1)/(2)O_(2)(g) to 2CO_(2)(g)+H_(2)O(g)-2CO_(2)(g)-H_(2)O(g),DeltaH=2xx(-94.05)+(-68.32)-(-310.62)`
or `2C(s)+H_(2)(g) to C_(2)H_(2)(g),DeltaH=54.20"kcal"`