Question

Which of the options is correct if the degree of dissociation of A and A' are $\alpha$ and ${\alpha }^{{}^{\prime }}$ respectively ($P^{{}^{\prime }}$=partial pressure at equilibrium) ?
$A\left(s\right)\rightleftharpoons 2B\left(g\right)+C\left(g\right)$; $K_{P_1}=8\times {10}^{-2}$
$A^{{}^{\prime }}\left(s\right)\rightleftharpoons 2B\left(g\right)+D\left(g\right)$; $K_{P_2}=2\times {10}^{-2}$

• A. $\frac{K_{P_2}}{K_{P_1}}=\left(\frac{3{\alpha }^{{}^{\prime }}+2\alpha }{3\alpha +2{\alpha }^{{}^{\prime }}}\right).\frac{\alpha }{{\alpha }^{{}^{\prime }}}$
• B. $\frac{P_C^{{}^{\prime }}}{P_D^{{}^{\prime }}}=4$
• C. $P_B^{{}^{\prime }}=P_C^{{}^{\prime }}+P_P^{{}^{\prime }}$
• D. $\alpha +{\alpha }^{{}^{\prime }}$

Answer 1

The correct option is B $\frac{P_C^{{}^{\prime }}}{P_D^{{}^{\prime }}}=4$

For the given two equilibria,
$\begin{array}{ccccc}A\left(s\right)& \rightleftharpoons & 2B\left(g\right)& +& C\left(g\right)\\ & & (2P_1+2P_2)& & P_1\end{array}$

$\therefore K_{P_1}=2^2(P_1+P_2{)}^2.P_1$

$\begin{array}{ccccc}{A}^{{}^{\prime }}\left(s\right)& \rightleftharpoons & 2B\left(g\right)& +& D\left(g\right)\\ & & (2P_1+2P_2)& & P_2\end{array}$

$\therefore K_{P_2}=2^2(P_1+P_2{)}^2.P_2$

$\therefore \frac{K_{P_1}}{K_{P_2}}=\frac{P_1}{P_2}=4$