# What does it mean for chemical reaction network to be in equilibrium?

What does being in "equilibrium" mean for a set of chemical reactions? If we have some number $$n$$ of $$\ce{A}$$ molecules and $$m$$ of $$\ce{B},$$ and the following reaction where $$\ce{A}$$ and $$\ce{B}$$ can reversibly bind:

\begin{align} \ce{A + B &->[k_\mathrm{f}] AB} \\ \ce{AB &->[k_\mathrm{r}] A + B} \end{align}

Suppose $$k_\mathrm{f} = 2,$$ $$k_\mathrm{r} = 1.$$ Can this system be "in equilibrium" and what would it mean? Does it mean all reactions have to be reversible and that as $$t \to \infty$$ go on at the same rate? In that case it seems that this system cannot be in equilibrium, since $$k_\mathrm{f} \neq k_\mathrm{r}.$$

• k$_f$ and k$_r$ are rate constants. You have to multiply them by concentrations to get rates. So the rates can be equal at equilibrium even if the rate constants are not. – Karsten Theis Jun 15 '19 at 14:17
• and so at equilibrium $\ce{ k_r [AB]=k_f[A][B] }$ making $\ce{K_e=k_f/k_r=[AB]/[A][B]}$ which means that species A, B and AB all exist. – porphyrin Jun 15 '19 at 16:06
• @porphyrin is it correct to say that any set of such chemical reactions will always have at least one equilibrium? if not what is an intuitive example of one without it, if we assume conservation of mass? – bal Jun 15 '19 at 19:52
• No it is not a rule, reactions do not need to have an equilibrium step, $A \to B$ or $A\to B \to C$ type reactions are common. – porphyrin Jun 16 '19 at 8:27

## 1 Answer

Ignoring the math, "in equilibrium" means the forward and reverse reactions are proceeding at the same rate, so there is no gross change in the amount of reactants. In a closed system, if initially one reaction was faster, then it's product will start to dominate, and, by the law of mass action, the reverse action will "catch up" because there is now a larger supply of those reactants.

A simple physical analog:

• Balance a ruler on two fingers, one finger near the end of the ruler, the other finger inset from the end towards the middle.
• Gradually move your fingers together.

No matter where you start, the fingers will come to rest near the middle of the ruler.