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)` .

Options

A. `-54.2` Kcal
B. `+54.2` Kcal
C. `-27.1` Kcal
D. `+27.1` Kcal

Explanation

We have to calulate
`2C_("Graphite")+H_(2)(g)rarr C_(2)H_(2)(g) , Delta H = ?`
Given,
`{:(C_(2)H_(2)(g)+(5)/(2)O_(2)(g) rarr 2CO_(2)(g)+H_(2)O(g), " " Delta H=-310.62 "kcal " ....(1)),(C_("Graphite")+O_(2)(g)rarr CO_(2)(g), " " Delta H=-94.05 "kcal "....(2)),(H_(2)(g)+(1)/(2)O_(2)(g)rarr H_(2)O(g) ," " Delta H=-68.32 "kcal " ....(3)),("Multiply Eq. (2) by 2 and add in Eq. (3)"),(2C_("Graphite")+2O_(2)(g)rarr 2CO_(2)(g)," " Delta H=-188.10 "kcal"),(ul(H_(2)(g)+(1)/(2)O_(2)(g)rarr H_(2)O(g)," " Delta H=-68.32"kcal ")),(2C_("Graphite")+(5)/(2)O_(2)(g)+H_(2)(g)rarr 2CO_(2)(g)+H_(2)O(g)," " Delta H=-256.42 "kcal "....(4)),("Subtract Eq. (1) from Eq. (4)"),(ul(C_(2)H_(2)(g)+(5)/(2)O_(2)(g)rarr 2CO_(2)(g)+H_(2)O(g), " " Delta H=-310.62 "kcal ")" "....(1)),(2C_("Graphite")+H_(2)(g)rarr C_(2)H_(2)(g), " " Delta H=+54.2 "kcal"):}`