One mole of ethanol is mixed with one mole of acetic acid at $25^{o} C$ . One fourth of the acid consumed to give an ester at equilibrium, and the system is given as $C_{2} H_{5} O H_{(l)} + C H_{3} C O O H_{(l)} ⇌ C H_{3} C O O C_{2} H_{5 (l)} + H_{2} O_{(l)}$ . The equilibrium constant for the system is found to be $1 / x$ , what is the value of $x$ .

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answer is 9.

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Detailed Solution

$\underset{1}{C_{2} H_{5} O H_{(l)}} + \underset{1}{C H_{3} C O O H} ⇌_{(l)} C H_{3} C O O C_{2} H_{5 (l)} + H_{2} O_{(l)}$

At equation

$\begin{array}{l} \underset{1}{C_{2} H_{5} O H_{(l)}} + \underset{1}{C H_{3} C O O H} ⇌_{(l)} C H_{3} C O O C_{2} H_{5 (l)} + H_{2} O_{(l)} \\ 1 - 1 / 4 1 - 1 / 4 1 / 4 1 / 4 \end{array}$

$∴ K = \frac{\frac{1}{4} \times \frac{1}{4}}{\frac{3}{4} \times \frac{3}{4}} = \frac{1}{9} = \frac{1}{x} ∴ x = 9$

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