Question

2 moles each of $C{H}_{3}OH$ and $C{H}_{3}COOH$ are taken and heated in the presence of conc. $H_{2}S{O}_4$ so that equilibrium is established . If $K_c$ for esterification is 4, moles of ester present at equilibrium is:

• A. $1.33$
• B. $1.6$
• C. $0.67$
• D. $0.33$

Answer 1

The correct option is A $1.33$

$C{H}_{3}C{O}_{2}H+C_2{H}_{5}OH\rightleftharpoons C{H}_{3}C{O}_2{C}_2{H}_5+H_{2}O$

$t=0$ $2$ $2$ $0$ $0$

At $t=t_{eqm}$ $2-x$ $2-x$ $x$ $x$

Given $K_C=4$

$\Rightarrow K_C=\frac{\left[C{H}_{3}C{O}_2{C}_2{H}_5\right]\left[H_{2}O\right]}{\left[C{H}_{3}C{O}_{2}H\right]\left[C_2{H}_{5}OH\right]}$

$\Rightarrow K_C=\frac{\left(x/v\right)\left(x/v\right)}{\left(\frac{4-x}{v}\right)\left(\frac{4-x}{v}\right)}$

$=\frac{x^2}{(2-x{)}^2}$

$\Rightarrow K_C=4=\frac{x^2}{(2-x{)}^2}$

$\Rightarrow 2=\frac{x}{2-x}$

$\Rightarrow x=4/3$

Moles of ester present= $x=4/3=1.33$