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Q. At a certain temperature, $1.0\, mole$ of $PCl_{3(g)}$ and $2.0\, mole$ of $Cl_{2(g)}$ were placed in a $3.0 \,litre$ container. When equilibrium is reached, only $0.70\, mole$ of $PCl_3$ remained unreacted. Calculate the value of $K_c$ for the reaction :
$PCl_{3(g)} +Cl_{2(g)} \rightleftharpoons PCl_{5(g)}$

Equilibrium

Solution:

image
$K_{c}=\frac{\left[PCl_{5}\right]}{\left[PCl_{3}\right]\left[Cl_{2}\right]}=\frac{0.3 / 3}{\frac{0.7}{3}\times\frac{1.7}{3}}=\frac{0.9}{0.7\times1.7}=0.76$