Equilibrium Constant Explained I'm not interested in a simple telling of what the properties of the equilibrium constant are and how to use them. I'm more hoping for an explanation of where it came from/how it might be possible to derive it. 

My current guess is that it is a probability equation: 

The numerator in the equation is proportional to the probability reactants meet and form products in the volume and the denominator is proportional to the probability products meet and form reactants in the volume. This ratio clearly must stay constant (unless the proportionality constants are changed via temperature or such).

Would anyone help?
Equilibrium is the state at which the rates of the forward and reverse reactions are equal. 

$$\mathrm{rate_{forward}=rate_{reverse}}$$

Let's take a generic reaction:

$$\ce{A + B &lt;=&gt; C + D}$$

For simplicity's sake let's have both the forward and reverse reactions be concerts fundamental reactions. Then we can write the rate laws for the forward and reverse reactions:

$$\begin{aligned}
\mathrm{rate_{forward}}&amp;=k_1 [\ce{A}][\ce{B}]\\
\mathrm{rate_{reverse}}&amp;=k_{-1} [\ce{C}][\ce{D}]
\end{aligned}$$

If we set them equal to each other, we can rearrange the equation to get the rate constants on one side and the concentrations on the other. 

$$\begin{aligned}
k_1 [\ce{A}][\ce{B}]&amp;=k_{-1} [\ce{C}][\ce{D}]\\
\dfrac{k_1}{k_{-1}}&amp;=\dfrac{[\ce{C}][\ce{D}]}{ [\ce{A}][\ce{B}]}
\end{aligned}$$

The ratio of rate constants is the equilibrium constant. Thus is derived the law of mass action.