Question

Two solids dissociated as follows
$A\left(s\right)\rightleftharpoons B\left(g\right)+C\left(g\right);K_{p_1}=xat{m}^2$
$D\left(s\right)\rightleftharpoons C\left(g\right)+E\left(g\right);K_{p_2}=yat{m}^2$
The total pressure when both the solids dissociate simultaneously is:

• A. $x^2+y^{2}atm$
• B. $\sqrt{x^2-y^2}atm$
• C. $2\left(\sqrt{x+y}\right)atm$
• D. $\sqrt{x+y}atm$

Answer 1

The correct option is C $2\left(\sqrt{x+y}\right)atm$

$A\left(s\right)\rightleftharpoons \underset{P_1}{B\left(g\right)}+\underset{P_1}{C\left(g\right)}$

$D\left(s\right)\rightleftharpoons \underset{P_2}{C\left(g\right)}+\underset{P_2}{E\left(g\right)}$

Total pressure of C, $P_C=P_1+P_2$

$K_{P_1}=x=P_B\cdot P_C.....\left(1\right)$

$x=P_1(P_1+P_2)$

$K_{P_2}=y=P_C\cdot P_E.....\left(2\right)$

$y=(P_1+P_2)\left(P_2\right)$

Adding $\left(1\right)$ and $\left(2\right)$
$x+y=(P_1+P_2{)}^2$

Now total pressure
$P_T=P_C+P_B+P_E$

$=(P_1+P_2)+P_1+P_2=2(P_1+P_2)$

$P_T=2\left(\sqrt{x+y}\right)$.