The mass action expression is an equation that shows the ratio of the product activities raised to the power of their coefficients to that of the reactant activities raised to the power of their coefficients. The expression itself is very easy to correctly write as long as you have a balanced chemical equation to reference. So let's consider the following generic reaction in aqueous solution. Each of the lowercase letters represents the coefficient for that species.

\[a\,{\rm A(aq)} + b\,{\rm B(aq)} \rightleftharpoons c\,{\rm C(aq)} + d\,{\rm D(aq)}\]

the true mass action expression : \( \displaystyle{ {a_{\rm C}^c \cdot a_{\rm D}^d} \over {a_{\rm A}^a \cdot a_{\rm B}^b} }\)

Of course activities can be approximated by using the numeric values of the concentrations (M) for solutions species, and the pressures (atm) for gas species.

The reaction quotient is symbolized with the capital letter Q. Q is simply the numerical value for the mass action expression under any stated set of conditions (concentrations and/or pressures). So Q can essentially be any number between \(0\) and \(\infty\). There is no such thing as a negative concentration or pressure which is why you cannot have negative values of Q.

Take all the concentrations and pressures of all the species in the system and put them into the mass action expression. Then calculate the number - that is Q! It will range from infinitely small (zero, or approaching zero) OR infinitely large (approaching \(\infty\)). Students should THINK of the pivot point within this range as a 1 (one). Generally, when the mass action express calculates to greater than one, then this is a situation where the system is more product favored. Values smaller than one generally mean that the system is more reactant favored.

The value of Q is what is important because you will use that value to determine in which way the system will respond so as to reach the equilibrium state.

IMPORTANT! Q can be all possible values

Q can be every possible value between zero and infinity because you can pick any value you want to go into the mass action expression. You will usually pick the real concentrations and/or pressures that are given in a problem though.

Q is a single number that represents
the current state of the system.

(yes, it IS a state function)

The equilibrium constant is symbolized with the capital letter K. Unlike Q, K is a very specific value for a specific reaction under specific conditions. K is a recasting of ΔG° for the reaction.

K is also equal to the mass action expression just like Q, except that all the concentrations and pressures must be their equilibrium values! So think of K as a subset of Q at which equilibrium occurs. There will be lots and lots of possible equilibrium values for a given reaction - just like there are lots of solutions to calculating various points that lie on a straight line. If you know the formula for the straight line (\(y=mx+b\)), then you can generate an infinite number of matched (x,y) coordinates that fall on that line.

A given reaction under specific conditions (lets say standard conditions for reference purposes) will have a very specific value for \(\Delta G^\circ_{\rm rxn}\). The magnitude and the sign of that standard free energy change tells us about the reaction being either strongly or weakly (big kJ or little kJ) spontaneous or non-spontaneous (positive or negative) as written. The equilibrium constant is a recasting of standard free energy. And by recasting I mean that there is an equation that relates the two values. What is that equation?

\[\Delta G^\circ = -RT\ln K\]

now flip that equation

\[K = e^{-\Delta G^\circ\over RT}\]

So the secret is out... K is just a mathematical conversion of ΔG°.