For the given reaction: $2\text{NOCl}(g) \rightleftharpoons 2\text{NO}(g) + \text{Cl}_2(g)$

The relationship between the equilibrium constants $K_p$ and $K_c$ is given by the equation: $K_p = K_c(RT)^{\Delta n}$

where $\Delta n$ is the difference between the sum of moles of gaseous products and the sum of moles of gaseous reactants. $\Delta n = \text{moles of gaseous products} - \text{moles of gaseous reactants}$ $\Delta n = (2 + 1) - 2 = 1$

Given data: $K_c = 3.0 \times 10^{-6}$ $R = 8.314\text{ J K}^{-1}\text{mol}^{-1}$ $T = 1000\text{ K}$

Substitute these values into the relationship (as directed by the explicitly given value of $R$): $K_p = (3.0 \times 10^{-6}) \times (8.314 \times 1000)^1$ $K_p = 3.0 \times 10^{-6} \times 8314$ $K_p = 24942 \times 10^{-6}$ $K_p = 2.4942 \times 10^{-2}$

Thus, the value of $K_p$ is $2.494 \times 10^{-2}$.