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JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Equilibrium

For reaction :

SO_{2} (g) + \frac{1}{2} O_{2} (g) ⇌ SO_{3} (g)

K_{P} = 2 \times 1 0^{12}

at

2 7^{\circ} C

and 1 atm pressure. The

K_{c}

for the same reaction is ______

\times 1 0^{13}

. (Nearest integer)
(Given

R = 0.082 L atm K^{- 1} mol^{- 1}

)

Answer: 1

Solution

Using

K_{P} = K_{C} (R T)^{Δ n_{g}}

with

Δ n_{g} = 1 - \frac{3}{2} = - \frac{1}{2}

and

R T = 0.082 \times 300 = 24.6

,

K_{C} = K_{P} (R T)^{1/2} = 2 \times 1 0^{12} \times 24.6 = 2 \times 1 0^{12} \times 4.96 \approx 9.9 \times 1 0^{12}

. Written as a multiple of

1 0^{13}

this is

0.99 \times 1 0^{13}

, so the required integer is

1

.

JEE Main · 2023 · 31 Jan 2023 · Shift 1 · Integer answer

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