1. The problem involves the reaction: 2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g). 2. We are asked to relate the equilibrium constants $K_c$ and $K_p$ for this reaction at temperature $T$. 3. The general relationship between $K_p$ and $K_c$ is given by: $$K_p = K_c (RT)^{\Delta n}$$ where $R$ is the gas constant, $T$ is the temperature in Kelvin, and $\Delta n$ is the change in moles of gas. 4. Calculate $\Delta n$ for the reaction: $$\Delta n = \text{moles of gaseous products} - \text{moles of gaseous reactants} = 2 - (2 + 1) = 2 - 3 = -1$$ 5. Substitute $\Delta n = -1$ into the formula: $$K_p = K_c (RT)^{-1} = \frac{K_c}{RT}$$ 6. Therefore, the relationship between $K_p$ and $K_c$ for this reaction is: $$\boxed{K_p = \frac{K_c}{RT}}$$ This means that to find $K_p$ from $K_c$, divide $K_c$ by the product of the gas constant and temperature.