# Equilibrium constant in a reaction with stoichiometric coefficient 1/2

I calculated the equilibrium constant for the follow reaction at 298 K.

$$\ce{CH4(g) + 1/2 S8 (s) <=> CS2 (l) + 2 H2S(g)}$$

I got $1.65 \times 10^{-9}$. However my professor wrote the answer as $2.66 \times 10^{-18}$ (so the square vale of my value). And I wonder why? I checked my answer 3 times already and I get to the same result. Is it because of the coefficient 1/2? Do we need to treat our equation with integer coefficients?

• We need more information! What are the partial pressures of the gases at equilibrium? You can ignore solids and liquids as they have activities of 1. $K= (\ce{H2S})^2/(\ce{CH4})$ Does this tally with your result? May 12 '16 at 20:59
• There is no more information. Except a table of thermodynamics standard values. $K_p$ is calculated using $K_p = e^{\frac{-\Delta G^0}{RT}}$ May 12 '16 at 21:14
• There is that method too! But yes in general you would use lowest integer ratios to calculate this and that would lead to a doubling of $\Delta_rG^O$ and hence the square of the $K_p$ value. Although I would say in the above case you were asked for the $K$ value for the given reaction with that stoichiometry and I would award you the marks in an exam situation. If the question is ambiguous or not precisely stated then the professor is at fault. Now, however you probably have learned more from this exercise than if you got it right first time! May 12 '16 at 21:53
• Check this question for further clarification...chemistry.stackexchange.com/questions/9034/… May 13 '16 at 9:05