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### Unit of Equilibrium Constant K

Posted: Mon Mar 13, 2017 12:20 am
Hello, I have a question regarding one of the questions in quiz 2.

The question is:
Consider the following reaction at equilibrium.
$A\rightleftharpoons B+C$
The equilibrium concentration were measured as follows:
[A] = 0.0100M, [B] = 0.500M, [C] = 2.50M
In a kinetic experiment, the rate constant of the forward reaction k is determined to be $200s^{-1}$. Calculate the rate constant of the reverse reaction.

I calculated K to be
$K = \frac{[products]}{[reactants]} = \frac{[B][C]}{[A]} = \frac{(0.500)(2.50)}{0.0100} = 125$

And since $K = \frac{k(forward)}{k(reverse)}$
$k(reverse) = \frac{k(forward)}{K} = \frac{200s^{-1}}{125} = 1.60s^{-1}$

However, the right answer was supposed to be $1.60s^{-1}M^{-1}$. Equilibrium constant K was supposed to have the unit M.

I am slightly confused by this. I've always thought that K is an expression of the "activities" of the species (as learned in Chem 14A), so it should be a unitless value?
Can someone please clarify when K should have a unit and when it shouldn't?