### The Equilibrium Constant

In 1864, Peter Waage and Cato Maxmilian Guldberg (both of Norway) published the modern meaning of the equilibrium constant. A reaction they used was the one between acetic acid and ethyl alcohol:

CH3COOH + C2H5OH ---> CH3COC2H5 + H2O

This reaction, studied in 1862 by others, was carried out many times with different starting concentrations. The reaction was allowed to go to equilibrium and the concentrations of the reactants and products determined.

From the published data (as well as their own experiments), they were able to determine a general principle which applies to all chemical equilibria. They called it the "Law of Mass Action" and in modern terms, here it is:

When a system is at equilbrium, a constant value is established by the multiplicative product of the concentrations of the products' concentrations (each raised first to the power of its coefficient), then divided by the multiplicative product of the reactants' concentrations (each raised first to the power of its coefficient).

Now that may be somewhat wordy, so here it is using a generic chemical equation:

wA + xB ⇌ yC + zD

Following the word definition above, we have this:

$\mathrm{Keq}=\frac{\mathrm{\left[C\right]y}\mathrm{\left[D\right]z}}{\mathrm{\left[A\right]w}\mathrm{\left[B\right]x}}$

A, B, C, and D are the chemical substances. x, y, w and z are the coefficients.

I'll do it again, this time using a specific chemical equation:

2SO2(g) + O2(g) ⇌ 2SO3(g)

$\mathrm{Keq}=\frac{\mathrm{\left[SO3\right]2}}{\mathrm{\left[SO2\right]2}\mathrm{\left[O2\right]}}$

The above is called an equilibrium expression and it is different from the way Waage and Guldberg wrote it. Please trust the ChemTeam when I say that the above, modern way of writing an equilibrium expression says exactly the same thing as the way they wrote it.

By the way, you may notice that the terms products and reactants are somewhat blurred in an equilibrium situation. The agreed upon convention is to use the reaction AS WRITTEN and call the left side "reactants" and the right side "products."

Practice Problems

Write an equilibrium expression for each of the following reactions.

1) 3O2 ⇌ 2O3

2) N2 + 3H2 ⇌ 2NH3

3) H2 + I2 ⇌ 2HI

4) PCl5 ⇌ PCl3 + Cl2

5) SO2 + (1/2)O2 ⇌ SO3

Here is what Guldberg and Waage wrote in 1864:

If we maintain that for a given chemical process two opposing forces are in effect, one which strives to form new substances and one which strives to restore the original compounds from the new, it is enlightening that, when in the chemical process these forces become equally large, the system is in equilibrium. That the same equilibrium state occurs under the same conditions, whether one goes one way or the other in the process, lies in the nature of the matter.

Notice that an equilibrium condition requires a reaction which can run in two opposing directions. These types of reactions are called reversible. Also, notice the criterion for equilibrium: the reaction rates (using the modern term) of the two reactions (forward and reverse) ARE THE SAME.