One mole of ethanol is treated with one mole of ethanoic acid at ${25}^{\circ }C$. Half of the acid changes into ester at equilibrium. The equilibrium constant for the reaction will be ‘x’, then the value of ‘x’ is______.

$\begin{array}{l}{C}_2{H}_{5}OH+C{H}_{3}COOH\rightleftharpoons C{H}_{3}COO{C}_2{H}_5+H_{2}O\\ Intial 1 10 0\\ Atequ I-\frac{1}{2}I-\frac{1}{2}\frac{1}{2}\frac{1}{2}\\ K=\frac{\left[C{H}_{3}COO{C}_2{H}_5\right]\left[H_{2}O\right]}{\left[C_2{H}_{5}OH\right]\left[C{H}_{3}COOH\right]}=\frac{\frac{1}{2}\times \frac{1}{2}}{\frac{1}{2}\times \frac{1}{2}}=1\end{array}$