To solve this problem, we need to understand the relationship between the equilibrium constant in terms of pressure, $$K_P$$, and the equilibrium constant in terms of concentration, $$K_C$$. The relationship between these two constants for a general reaction is given by:

$$ K_P = K_C (RT)^{\Delta n} $$

where:

$$\Delta n$$ is the change in the number of moles of gas (moles of gaseous products minus moles of gaseous reactants),

$$R$$ is the ideal gas constant, and

$$T$$ is the temperature in Kelvin.

For the given reaction:

$$ \mathrm{CO}_{(\mathrm{g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{CO}_{2(\mathrm{~g})} $$

we need to calculate $$\Delta n$$.

On the reactants side, we have:

• 1 mole of $$\mathrm{CO}$$ (g)
• 0.5 moles of $$\mathrm{O}_2$$ (g)

So, the total number of moles of reactants is:

$$ 1 + \frac{1}{2} = \frac{3}{2} = 1.5 $$

On the products side, we have:

• 1 mole of $$\mathrm{CO}_2$$ (g)

The total number of moles of products is:

$$ 1 $$

Therefore, $$\Delta n$$ is:

$$ \Delta n = \text{moles of products} - \text{moles of reactants} = 1 - 1.5 = -0.5 $$

Now, we can use the relationship between $$K_P$$ and $$K_C$$:

$$ K_P = K_C (RT)^{\Delta n} $$

Substituting $$\Delta n = -0.5$$, we get:

$$ K_P = K_C (RT)^{-0.5} $$

or equivalently:

$$ \frac{K_P}{K_C} = (RT)^{-0.5} $$

Therefore, the correct option is:

Option D: $$\frac{1}{\sqrt{R T}}$$