Question

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

• A. 4.5 atm
• B. 0.45 atm
• C. 0.6 atm
• D. None of these

Answer 1

Answer: (B)

Let $x$ be partial pressure of $A$ and $y$ be partial pressure of $C$ when
both equilibrium are simultaneously established in a vessel


$\frac{K_{P_1}}{K_{P_2}}=\frac{x}{y}$
$\Rightarrow x=2y$
$K{P}_1=x(2x+2y{)}^2$
$\Rightarrow x=0.1$ atm ;
$\therefore y=0.05$ atm ;
Total pressure of gases $=P_A+P_B+P_C$
$=3(x+y)=0.45$ atm.