Question

Two solids dissociate as follows ${A(s) <=> B(g) + C(g) ; K_{p_1} = x \; atm^2}$ ${D(s) <=> C(g) + E(g) ; K_{p_2} = y \; atm^2}$ The total pressure when both the solids dissociate simultaneously is :

• A. $x^2 + y^2 \; atm$
• B. $2 x^2 + y^2 \; atm$
• C. $2 (\sqrt{x + y} ) atm$
• D. $\sqrt{x + y} \,atm$

Answer 1

Answer: (C)

$2 (\sqrt{x + y} ) atm$

Answer 2

{A(s) <=>\underset{{ P_1}}{ { B(g)}}$+$\underset{{ P_1}}{ { C(g)}}$\; \;$\underset{{ x = P_1 (P_1 + P_2) }}{ { K_{P_1} = x = P_{B} . P_{C}}} } ....(1) {D(s) <=>\underset{{ P_2}}{ { C(g)}}$+$\underset{{ P_2}}{ { E(g)}}$\; \;$\underset{{ y = (P_1 + P_2) (P_2)}}{ { K_{P_2} = y = P_{C} . P_{E}}} } ...(2) Adding (1) and (2) $x +y = (P_1 + P_2)^2$ Now total pressure $P_T = P_C + P_B + P_E$ $= (P_1 + P_2) + P_1 + P_2 = 2 (P_1 + P_2)$ $P_{T} = 2 (\sqrt{x+y})$