What does equilibrium constant mean?

Question

I really don't understand equilibrium constants: they seem to change nonstop! Can someone clarify the definition of equilibrium constants and give me examples of them?

Also, I looked in my textbook and the explanation for heterogeneous equilibrium used an example of decomposing calcium carbonate.

$$\ce{CaCO3 (s) <=> CaO(s) + CO2(g)}$$

The textbook continued to explain that $K^{'}_{c} = \frac{[\text{CaO}][\text{CO}_{2}]}{[\text{CaCO}_3]}$

There is my first obstacle: What is the meaning of $K^{'}$ (I don't think they're talking about the reverse process equilibrium constant)? And the next part to me is even stranger...

I do get that the concentration of the two solids are basically constants, so we can treat those parts as constants.

But why would you do $K^{'} \times \frac{[\text{CaCO}_{3}]}{[\text{CaO}]}$, which equals $K$, according to the textbook, the actual equilibrium constant of this reaction?

Answer 1

I am sure the book, if it is any decent, should have said something like this already. $K'$ is not a measure of the forward reaction, nor is it a measure of the reverse reaction. It is a measure of the equilibrium position.

Equilibrium occurs when the rate of the forward reaction is equal to the rate of the backward reaction. By the laws of thermodynamics, this occurs at one special point where the instantaneous concentrations of all the compounds satisfy the equation

$$\frac{[\ce{CaO}][\ce{CO2}]}{[\ce{CaCO3}]} = K'$$

$K'$ for a reaction is a constant. Clearly, a large $K'$ indicates that when equilibrium is reached, there is a lot of $\ce{CaO}$ and $\ce{CO2}$, and only a little bit of $\ce{CaCO3}$. We say that the equilibrium position lies to the right. Conversely, a small $K'$ means that the equilibrium position lies to the left, i.e. reactants predominate.

---

The equilibrium constant is properly defined in terms of activities of the compounds, not concentrations. This means that for the reaction you gave,

$$K = \frac{(a_{\ce{CaO}})(a_{\ce{CO2}})}{a_{\ce{CaCO3}}}$$

The activity of a pure solid is defined to be equal to $1$, which means that you can simplify this by removing all the terms corresponding to pure solids:

$$K = a_{\ce{CO2}}$$

The "equilibrium constant" that you are learning that involves concentrations is a simplification.