Consider the two gaseous equilibria, SO2(g) + (1/2)O2(g) SO3(g)...?

Question

Consider the two gaseous equilibria
SO2(g) + (1/2)O2(g) SO3(g) K1
2SO3(g) SO2(g) + O2(g) K2
The values of the equilibrium constants K1 and K2 are related by

a) K2 = K1^2
b) K2^2 = K1
c) K2 = 1/K1^2
d) K2 = 1/K1
e) none of these.

These are probably a little hard to read, but I think its none, because the SO2 is the same in both reactions where the others are different, if it was 2SO2 then it whould be 1/k^2 because the reaction is flipped...am I right? I just hope the professor didnt do a typo and forget the 2..

Answer 1

balance the eqn first.....

SO2(g) + (1/2)O2(g) -----> SO3(g) K1
2SO3(g) -----> 2SO2(g) + O2(g) K2

K1 = [SO3]/[SO2][O2]^1/2 eqn 1
[SO3] = K1[SO2][O2]^1/2 eqn 2
K2 = [O2][SO2]^2/[SO3]^2 eqn 3
substituting eqn 2 to eqn 3
we got
K2 = [O2][SO2]^2 / (K1[SO2][O2]^1/2)^2
K2 = 1/K1^2

best answer?

Answer 2

if the equations were balanced, then the answer is d.
if they aren't balanced, then the question is irrelevant because the two wouldn't be related enough to find an equation.

odds are the professor did forget the 2, because k2 isn't balanced, and therefore can't even happen. i'd just assume it's a typo and answer d. happens all the time. most professors aren't that lame to ask a trick question as trivial as that.