# Find Equilibrium Constant with only balanced equation?

Calculate the value of $$K_p$$ for the following equation:

$$\ce{PCl3 (g) + Cl2 (g) <=> PCl5 (g)} ,\qquad \mathrm{R = 0.0821 \frac{L\times atm}{mol\times K}}$$

This question appeared on my test. I know how to find $$K_p$$ if I was given $$K_c$$ $$(K_{\mathrm{p}} = K_\mathrm{c} \times (\mathrm{R} \times T)^{n})$$ or if I was given the partial pressures of all of the parts at equilibrium, but none of those values were given; only the equation. My professor marked the answer as $$0.041$$ (no units), but I have no idea how to calculate that if I wasn't given any values.

• Notice that I replaced \mathrm with \ce for your chemical equation. Just like that, it properly rendered the subscripts and reaction arrows! – airhuff Feb 21 '17 at 3:19
• Interesting that the answer is 1/2 of R, and that there 1/2 as many moles of gas on the right side of the equation. – airhuff Feb 21 '17 at 3:45
• Thanks for the help! Interesting observation. I wonder if my professor accidentally took the moles of each side and divided them (products/reactants) instead of using the partial pressures. – Eric Feb 21 '17 at 4:03
• Were you given any other information at all for the problem? I think the key is that the total pressure of the products is half of the total pressure of the reactants if the volume is constant. – airhuff Feb 21 '17 at 4:12
• Were you allowed to use tables of free energies of formation or enthalpies and entropies of formation? – Chet Miller Feb 21 '17 at 13:09