Compounds with carbon-carbon double bond, such as ethylene, `C_(2)H_(4)`, add hydrogen in a reaction called hydrogenation.
`C_(2)H_(4)(g)+H_(2)(g) rarr C_(2)H_(6)(g)`
Calculate enthalpy change for the reaction, using the following combustion data
`C_(2)H_(4)(g) + 3O_(2)(g) rarr 2CO_(2)(g) + 2H_(2)O(g)`, `Delta_("comb")H^(Θ) = -1401 kJ mol^(-1)`
`C_(2)H_(6)(g) + 7//2O_(2)(g)rarr 2CO_(2) (g) + 3H_(2)O(l)`, `Delta_("comb")H^(Θ) = -1550kJ`
`H_(2)(g) + 1//2O_(2)(g) rarr H_(2)O(l)`, `Delta_("comb")H^(Θ) = -286.0 kJ mol^(-1)`

Explanation

We are given
a. `C_(2)H_(4)(g)+3O_(2)(g) rarr 2CO_(2)(g)+2H_(2)O(l), DeltaH=-1401 kJ mol^(-1)`
b. `H_(2)(g)+1/2O_(2)(g)rarr H_(2)O(l), DeltaH=-286.0 kJ mol^(-1)`
c. `C_(2)H_(6)(g)+7/2O_(2)(g) rarr 2CO_(2)(g)+3H_(2)O(l), DeltaH=-1550 kJ mol^(-1)`
We aim at
`C_(2)H_(6)+H_(2)(g)rarr C_(2)H_(6)(g), DeltaH=?`
Equation (i) + Equation(ii) -Equation (iii)
`C_(2)H_(4)(g)+H_(2)(g)rarrC_(6)H_(6)(g)`
`DeltaH=-1401+(-286.0)-(-1550)=-137 kJ mol^(-1)`