Question

If $\Delta H_f^o{(C}_2{H}_4)$ and $\Delta H_f^o{(C}_2{H}_6)$ are $x_1$ and $x_2$ Kcal ${mol}^{-1}$, then heat of hydrogenation of $C_2{H}_4$ is:

• A. $x_1+x_2$
• B. $x_1-x_2$
• C. $-(x_1+x_2)$
• D. none of the above

Answer 1

The correct option is D none of the above

$2C+2H_2⟶C_2{H}_4{\Delta H^0}_f=x_{1}kcal/mol$

$C_2{H}_4⟶2C+2H_2{\Delta H^0}_f=-x_{1}kcal/mol.....\left(1\right)$

$2C+3H_2⟶C_2{H}_6{\Delta H^0}_f=x_{2}kcal/mol.....\left(2\right)$

Adding ${eq}^n\left(1\right)\&\left(2\right)$, we have

$C_2{H}_4+2C+3H_2⟶C_2{H}_6+2C+2H_2{\Delta H^0}_R=-x_1+x_2$

$C_2{H}_4+H_2⟶C_2{H}_6{\Delta H^0}_R=(x_2-x_1)kcal/mol$

Hence the heat of hydrogenation of $C_2{H}_4$ is $(x_2-x_1)kcal/mol$.