Two solids dissociate as follows $\begin{array}{l} A_{(s)} ⇌ B_{(g)} + C_{(g)}; K p_{1} =' x' {atm}^{2} \\ D_{(s)} ⇌ C_{(g)} + E_{(g)}; K p_{2} =' y' {atm}^{2} \end{array}$
The total pressure when the solids dissociate simultaneously is?

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${(x + y)}^{\frac{1}{2}} atm$

$(x^{2} + y^{2}) atm$

$2 {(x + y)}^{\frac{1}{2}} atm$

$(x + y) atm$

answer is C.

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Detailed Solution

$\begin{array}{l} A (s) ⇌ \underset{P_{1}}{B (g)} + \underset{P_{1} + P_{2}}{C (g)} K_{P_{1}} = x a t m^{2} \\ D (s) ⇌ \underset{P_{1} + P_{2}}{C (g)} + \underset{P_{2}}{E (g)} K_{P_{2}} = y a t m^{2} \\ k_{P_{1}} = x = P_{B} . P_{C}, S i m i l a r y, k_{P_{2}} = y = P_{C} . P_{E} \\ x = P_{1} (P_{1} + P_{2}) .... (1) \\ y = P_{2} (P_{1} + P_{2}) ..... (2) \\ A d d i n g (1) a n d (2) \\ x + y = {(P_{1} + P_{2})}^{2} \\ o r P_{1} + P_{2} = \sqrt{x + y} .... (3) \\ T o t a l p r e s s u r e P_{t} = P_{B} + P_{C} + P_{E} = P_{1} + P_{1} + P_{2} + P_{2} = 2 (P_{1} + P_{2}) \\ P_{t} = 2 \sqrt{x + y} a t m (f r o m 3) \end{array}$