Question

$X\left(s\right)\rightleftharpoons A\left(g\right)+2B\left(g\right)$
$Y\left(s\right)\rightleftharpoons 2B\left(g\right)+C\left(g\right)$
$K_{P_1}=9\times {10}^{-3}at{m}^3$
If the ratio, $K_{P_1}$ : $K_{P_2}=2$, then the total pressure of gases over a mixture of excess of $X$ and $Y$ is :

• A. $4.5atm$
• B. $0.45atm$
• C. $0.6atm$
• D. $noneofthese$

Answer 1

The correct option is B $0.45atm$

Let, the partial pressures of A and B from X are x atm and 2x atm respectively.
$K_{P_1}=9\times {10}^{-3}at{m}^3=x(2x{)}^2=4x^3$
$x=0.131atm$
The total pressure is $x+2x=3x=3\left(0.131\right)=0.393atm$.
Let, the partial pressure of C is y atm .
$K_{P_2}=0.5\times 9\times {10}^{-3}at{m}^3=4.5\times {10}^{-3}at{m}^3=y(0.262{)}^2$
$y=0.0655$
Total pressure of gases from X and Y is $0.393+0.00655=0.45atm$