The molar heats of combustion of `C_(2)H_(2)(g)`, C (graphite), and `H_(2)` 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

The thermochemical equations corresponding to the given data are :
`C("graphite") + O_2(g) to CO_2(g) , Delta_c H = - 94.05 kcal`….(i)
`H_2(g) + 1/2 O_2(g) to H_2O (l), Delta_c H = - 68.32 kcal …(ii)`
`C_2H_2(g) + 5/2 O_2(g) to 2CO_2(g) + H_2O(l), Delta_c H = -310.62 kcal`...(iii)
The required equation is
`2C ("graphite") + H_2(g) to C_2H_2 (g) , Delta_f H = ?`
Multiplying eq. (1) by 2 and adding to eq. (ii), we get
`2C("graphite") + H_2(g) + 5/2O_2(g) to 2CO_2(g) + H_2O(l),`
`DeltaH = 2 xx (-94.05) + (-68.32) kcal`...(iv)
Subtracting eq. (iii) from eq. (iv) and transposing, we get
`2C ("graphite") + H_2(g) to C_2H_2 (g) ,`
`Delta_f H = 2 xx (-94.05) + (-68.32) - (-310.62) = + 54.20 kcal`
Hence, the standard heat of formation of `C_2H_5` (g) is `54.20 kcal mol^(-1)`.