Consider the reaction $\mathrm{N}_{2}\mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2\mathrm{NO}_{2}(\mathrm{~g})$. The temperature at which $\mathrm{K}_{\mathrm{C}}=20.4$ and $\mathrm{K}_{\mathrm{p}}=600.1$, is ______ K. (Round off to the nearest integer). [Assume all gases are ideal and $\mathrm{R}=0.0831 \mathrm{~L}$ bar mol $^{-1} \mathrm{~K}^{-1}$]

JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Equilibrium

Consider the reaction

N_{2} O_{4} (g) ⇌ 2 NO_{2} (g)

. The temperature at which

K_{C} = 20.4

and

K_{p} = 600.1

, is ______ K. (Round off to the nearest integer).
[Assume all gases are ideal and

R = 0.0831 L

bar mol

^{- 1} K^{- 1}

]

Answer: 354

For a gaseous equilibrium the two constants are related by

K_{p} = K_{c} (R T)^{Δ n}

, where

Δ n

is the change in the number of moles of gas. Here one mole of

N_{2} O_{4}

gives two moles of

N O_{2}

, so

Δ n = 1

and the relation becomes

K_{p} = K_{c} R T

. Hence

T = \frac{K _{p}}{K _{c} R} = \frac{600.1}{20.4 \times 0.0831} = \frac{600.1}{1.6952}

The temperature at which the two constants take these values is

354 K

JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Integer answer