Question

Two solid compounds $X$ and $Y$ dissociates at a certain temperature as follows
$X\left(S\right)\rightleftharpoons A\left(g\right)+2B\left(g\right);K_{P1}=9\times {10}^{-3}at{m}^3$
$Y\left(s\right)\rightleftharpoons 2B\left(g\right)+C\left(g\right);K_{P2}=4.5\times {10}^{-3}at{m}^3$
The total pressure (in atm) of gases over a mixture of $X$ and $Y$ is :

Answer 1

Let $x$ is partial pressure of $A$ and $y$ is partial pressure of $C$ when both equilibrium simultaneously established in a vessel
$X\left(s\right)\rightleftharpoons A\left(g\right)+2B\left(g\right)$
$x(2x+2y)$;
$K_{P_1}=P_A\times P_{B\left(total\right)}^2$
$Y\left(s\right)\rightleftharpoons C\left(g\right)+2B\left(g\right)$
$y(2y+2x);$
$K_{P_2}=P_C\times P_{B\left(total\right)}^2$
$\frac{K_{P_1}}{K_{P_2}}=\frac{x}{y}\Rightarrow x=2y$
$K_{P_1}=x(2x+2y{)}^2$
$\Rightarrow x=0.1atm;$
$\therefore y=0.05atm$
Total pressure of gases =$P_A+P_B+P_C$
$=3(x+y)$
$=0.45atm$