The ratio $$\frac{K_P}{K_C}$$ for the reaction : $$CO_{(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons CO_{2(g)}$$ is :

We need to find the ratio $$K_P/K_C$$ for the reaction $$CO_{(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons CO_{2(g)}$$. The relationship between $$K_P$$ and $$K_C$$ is given by $$K_P = K_C(RT)^{\Delta n_g}$$ where $$\Delta n_g$$ is the change in the number of moles of gaseous species (moles of gaseous products minus moles of gaseous reactants).

Moles of gaseous products = 1 (CO$$_2$$) and moles of gaseous reactants = 1 (CO) + 1/2 (O$$_2$$) = 3/2, so $$\Delta n_g = 1 - \frac{3}{2} = -\frac{1}{2}$$.

Substituting into the formula gives $$\frac{K_P}{K_C} = (RT)^{\Delta n_g} = (RT)^{-1/2} = \frac{1}{\sqrt{RT}}$$, therefore the correct answer is Option (1): $$\frac{1}{\sqrt{RT}}$$.