Question

The heats of combustion of $C_x{H}_y$, carbon and hydrogen are a, b and c $cal$ respectively. The heat of formation of $C_x{H}_y$ will be:

• A. $[-xb+\frac{yc}{2}+\frac{a}{2}]cal$
• B. $-[xb+\frac{yc}{2}-a]cal$
• C. $[xb-\frac{yc}{2}+\frac{a}{2}]cal$
• D. $[xb-\frac{yc}{2}-\frac{a}{2}]cal$

Answer 1

The correct option is B $-[xb+\frac{yc}{2}-a]cal$

Equation for combustion of $C_x{H}_y$,
$C_x{H}_y+\frac{1}{2}(2x+\frac{y}{2})O_2\to xC{O}_2+\frac{y}{2}{H}_{2}O;\Delta H=-acal---\left(1\right)$

Equation for combustion of $C\left(s\right)$,
$C\left(s\right)+O_2\to C{O}_2;\Delta H=-bcal---\left(2\right)$

Equation for combustion of $H_2\left(g\right)$
$H_2\left(g\right)+O_2\to H_{2}O;\Delta H=-ccal---\left(3\right)$

Equation for formation of $C_x{H}_y$,
$xC\left(s\right)+\frac{y}{2}{H}_{2}O\to C_x{H}_y;\Delta H=dcal---\left(4\right)$

$\left(4\right)=x\times \left(2\right)+\frac{y}{2}\times \left(3\right)-\left(1\right)$
$\Delta H_{formation}=x\times (-b)+\frac{y}{2}\times (-c)-(-a)$
$\Delta H_{formation}=-[xb+\frac{y}{2}c-a]$