For the reaction $2 \mathrm{NO}_{2(\mathrm{g})} \rightleftharpoons 2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{g})}$, ( $\mathrm{K}_{\mathrm{c}}=1.8 \times 10^{-6}$ at $184^{\circ}$ C ) ( $\mathrm{R}=0.0831$ kJ/(mol.K) ) When $\mathrm{K}_{\mathrm{p}}$ and $\mathrm{K}_{\mathrm{c}}$ are compared at $184^{\circ}$ C, it is found that

(A) $\mathrm{K}_{\mathrm{p}}$ is greater than $\mathrm{K}_{\mathrm{c}}$

(B) $\mathrm{K}_{\mathrm{p}}$ is less than $\mathrm{K}_{\mathrm{c}}$

(C) $\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{c}}$

(D) Whether $\mathrm{K}_{\mathrm{p}}$ is greater than, less than or equal to $\mathrm{K}_{\mathrm{c}}$ depends upon the total gas pressure

JEE Main · 2005 · 08 May 2005 · Offline · Equilibrium

For the reaction

2 NO_{2 (g)} ⇌ 2 NO_{(g)} + O_{2 (g)}

,
(

K_{c} = 1.8 \times 1 0^{- 6}

18 4^{\circ}

C )
(

R = 0.0831

kJ/(mol.K) )
When

K_{p}

and

K_{c}

are compared at

18 4^{\circ}

C, it is found that

(A) $K_{p}$ is greater than $K_{c}$ ✓ Correct
(B) $K_{p}$ is less than $K_{c}$
(C) $K_{p} = K_{c}$
(D)Whether $K_{p}$ is greater than, less than or equal to $K_{c}$ depends upon the total gas pressure

Answer: (A)

The two constants are tied by

K_{p} = K_{c} (R T)^{Δ n}

, with

Δ n

the change in gas moles. For

2 NO X_{2} 2 NO + O X_{2}

the count goes from two moles to three, so

Δ n = 3 - 2 = + 1

. With a positive

Δ n

and

R T

larger than one at

18 4^{\circ}

C (that is

457

K), the factor

(R T)^{1}

exceeds one, which makes

K_{p}

larger than

K_{c}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option