The relationship between $K_p$ and $K_c$ is given by $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ is the difference between the number of moles of gaseous products and gaseous reactants ($\Delta n = n_p - n_r$). For $K_p$ to be equal to $K_c$, $\Delta n$ must be zero. Let's calculate $\Delta n$ for the given reactions:

1. $2NO(g) \rightleftharpoons N_2(g) + O_2(g)$; $\Delta n = (1 + 1) - 2 = 0$
2. $SO_2(g) + NO_2(g) \rightleftharpoons SO_3(g) + NO(g)$; $\Delta n = (1 + 1) - (1 + 1) = 0$
3. $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$; $\Delta n = 2 - (1 + 1) = 0$
4. $2C(s) + O_2(g) \rightleftharpoons 2CO_2(g)$; $\Delta n = 2 - 1 = 1$ (Carbon is in the solid state, so it is not considered in calculating $\Delta n$). Since $\Delta n \neq 0$ for reaction 4, its $K_p$ and $K_c$ values are not equal.