Question

Match the List I (Mathematical process on equilibrium coefficients) with the List II (New equilibrium constant).

Answer 1

Suppose the given reaction,

$aA+bB\rightleftharpoons cC+dD$

then, $K=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}\to \left(I\right)$

(I) If divided by $n$

$\frac{a}{n}A+\frac{b}{n}B\rightleftharpoons \frac{c}{n}C+\frac{d}{n}D$

then, $K^{{}^{\prime }}=\frac{{\left[C\right]}^{c/n}{\left[D\right]}^{d/n}}{{\left[A\right]}^{a/n}{\left[B\right]}^{b/n}}={\left(K\right)}^{1/n}$

(II) Multiplying by $n$

$naA+nbB\rightleftharpoons ncC+ndD$

then, $K^{{}^{\prime }}=\frac{{\left[C\right]}^{nc}{\left[D\right]}^{nd}}{{\left[A\right]}^{an}{B}^{bn}}={\left(K\right)}^n$

(III) Reaction is reversed

$cC+dD\rightleftharpoons aA+bB$

$\Rightarrow K^{{}^{\prime }}=\frac{{\left[A\right]}^a{\left[B\right]}^b}{{\left[C\right]}^c{\left[D\right]}^d}=\frac{1}{K}$

(IV) If $n$ equations are added, then,

$K=K_1\times K_2\times K_3\times ......\times K_n$