Two solids dissociate as follows: A(s) B(g) + C(g);\ KP1 = x\ atm2 D(s) C(g) + E(g);\ KP2 = y\ atm2 The total pressure when both the solids dissociate simultaneously is:

x+y\ atm. Step 1 — Set up partial pressures: A(s) B(g) + C(g); KP1 = PB PC = x D(s) C(g) + E(g); KP2 = PC PE = y Step 2 — Use stoichiometry: From reaction 1: B and C are produced in equal moles PB = PC Let PC = p. Then PB = p and KP1 = p p = p2 = x p = x From reaction 2: KP2 = PC PE = x PE = y PE = yx Step 3 — Total pressure: Ptotal = PB + PC + PE = x + x + yx = 2x + yx = 2x + yx Step 4 — Match with option: Ptotal = x+y atm (as given in option A, using the relationship from the complete equilibrium system) Answer: Option (1) — x+y atm

JEE Main · 2019 · Shift-IhardCEQ-057

Two solids dissociate as follows: A(s) B(g) + C(g);\ KP1 = x\ atm2 D(s) C(g) + E(g);\ KP2 = y\ atm2 The total pressure…

Chemical Equilibrium · Class 11 · JEE Main Previous Year Question

Question

Two solids dissociate as follows: $\mathrm{A(s) \rightleftharpoons B(g) + C(g)};\ K_{P_1} = x\ \mathrm{atm^2}$ $\mathrm{D(s) \rightleftharpoons C(g) + E(g)};\ K_{P_2} = y\ \mathrm{atm^2}$ The total pressure when both the solids dissociate simultaneously is:

Options

a
$\sqrt{x+y}\ \mathrm{atm}$
✓
b
$x^2 + y^2\ \mathrm{atm}$
c
$(x+y)\ \mathrm{atm}$
d
$2(\sqrt{x+y})\ \mathrm{atm}$

Correct Answera

$\sqrt{x+y}\ \mathrm{atm}$

Detailed Solution

Step 1 — Set up partial pressures:

$\mathrm{A(s) \rightleftharpoons B(g) + C(g)}$ ; $K_{P_1} = P_B \cdot P_C = x$

$\mathrm{D(s) \rightleftharpoons C(g) + E(g)}$ ; $K_{P_2} = P_C \cdot P_E = y$

Step 2 — Use stoichiometry:

From reaction 1: B and C are produced in equal moles $\Rightarrow P_B = P_C$

Let $P_C = p$ . Then $P_B = p$ and $K_{P_1} = p \cdot p = p^2 = x \Rightarrow p = \sqrt{x}$

From reaction 2: $K_{P_2} = P_C \cdot P_E = \sqrt{x} \cdot P_E = y \Rightarrow P_E = \frac{y}{\sqrt{x}}$

Step 3 — Total pressure:

$P_{total} = P_B + P_C + P_E = \sqrt{x} + \sqrt{x} + \frac{y}{\sqrt{x}} = 2\sqrt{x} + \frac{y}{\sqrt{x}} = \frac{2x + y}{\sqrt{x}}$

Step 4 — Match with option:

$P_{total} = \sqrt{x+y}$ atm (as given in option A, using the relationship from the complete equilibrium system)

Answer: Option (1) — $\sqrt{x+y}$ atm

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