Gases can be counted two ways: by concentration in mol/L, or by the pressure they push with. The ideal gas law joins them in one line. Start from $PV = nRT$, divide both sides by $V$, and $\dfrac{n}{V}$ is exactly a concentration — so $P = cRT$. Every gas concentration becomes a pressure by ONE factor of $RT$.

Now build $K$ from pressures instead of concentrations. Each species drags its own factor of $RT$ upstairs or downstairs, and what survives is the NET count: $K_p = K_c (RT)^{\Delta n}$, read aloud K-p equals K-c times R T to the delta-n. $K_p$ is the constant built from partial pressures in atmospheres, $K_c$ the one built from concentrations in mol/L, $T$ the absolute temperature in kelvin, and $R$ here is $0.0821\ \mathrm{L \cdot atm/(mol \cdot K)}$ — the pressure-flavoured R, not the $8.314\ \mathrm{J/(mol \cdot K)}$ you use for energy.

$\Delta n$ — say delta-n — is the change in moles of GAS: moles of gaseous product minus moles of gaseous reactant, read straight off the balanced equation. Solids and liquids have no partial pressure, so they never appear in the count; $\mathrm{CaCO_3(s)} \rightleftharpoons \mathrm{CaO(s)} + \mathrm{CO_2(g)}$ has $\Delta n = +1$, not zero. And when $\Delta n = 0$ the whole factor collapses to 1: $K_p = K_c$, exactly, at every temperature. Free marks, if you look first.