1. Use the relation between $K_p$ and $K_c$

For a gaseous equilibrium,

$K_p = K_c (RT)^{\Delta n}$

where

$\Delta n = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$

2. Find $\Delta n$ for the reaction

Given:

$2NO_2(g) \rightleftharpoons 2NO(g) + O_2(g)$

Reactant moles of gas $= 2$

Product moles of gas $= 2 + 1 = 3$

So,

$\Delta n = 3 - 2 = 1$

3. Write the expression for $K_p$

Since $\Delta n = 1$,

$K_p = K_c (RT)^1 = K_c RT$

At $184^\circ C$,

$T = 184 + 273 = 457\,K$

Given,

$R = 0.0831\, \text{L·bar mol}^{-1}\text{K}^{-1}$

So,

$RT = 0.0831 \times 457 \approx 37.98$

Thus,

$K_p = K_c \times 37.98$

Since $37.98 > 1$,

$K_p > K_c$

(Indeed, numerically: $K_p \approx 1.8 \times 10^{-6} \times 37.98 \approx 6.8 \times 10^{-5}$.)

4. Check options

• A: $K_p$ is greater than $K_c$ ✅
• B: $K_p$ is less than $K_c$ ❌
• C: $K_p = K_c$ ❌
• D: Depends on total gas pressure ❌

$K_p/K_c = (RT)^{\Delta n}$ depends on temperature and $\Delta n$, not on total pressure.

5. Final answer

The correct option is:

$\boxed{A}$