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

`C_(2)H_(2)(g)+(5)/(2)O_(2)(g) to 2CO_(2)(g)+H_(2)O(l), Delta H^(0)= - 310.62 ` kcal ..(1)
`C("graphite")+O_(2)(g) to CO_(2)(g), Delta H^(0)= - 94.05` kcal ..(2)
`H_(2)(g)+(1)/(2)O_(2)(g)to H_(2)O(l), Delta H^(0)= - 68.32` kcal ..(3)
Adding the equation obtained by multiplying equation (2) by 2 to equation (3), we have
`2C("graphite")+H_(2)(g)+(5)/(2)O_(2)(g) to 2CO_(2)(g)+H_(2)O(l)`
`Delta h^(0)= [2(-94.05)-68.32] `kcal ..(4)
Subtracting equation (1) from equation (4), we have
`2C("graphite")+H_(2)(g) to C_(2)H_(2)(g)`
`Delta H^(0)= [2(-94.05)-68.32] " kcal " + 310.62 " kcal " = 54.2 " kcal "` . ..(5)
Equation (5) represents the formation reaction of `C_(2)H_(2)(g)`. So, the standard heat of formation for `C_(2)H_(2)(g)` is `54.2 " kcal mol"^(-1)`.