The Concept of Equilibrium

Sometimes you can visually observe a certain chemical reaction.

• A reaction may produce a gas or a color change and you can follow the progress of the reaction by noting the volume of gas, or the intensity of the color.
• Often a reaction may appear to stop even though some reactants remains in the sample

What is actually going on?

• At chemical equilibrium, the forward rate of the reaction, that produces product(s), and the backwards rate of reaction, that produces reactant(s) are equal
• One condition for reaching equilibrium is that there is no process by which the reactant(s) or product(s) are removed from the system

You have already seen several examples of physical processes in equilibrium:

• Establishment of a vapor pressure results from equilibrium of molecular movement between the liquid and gas phase. The rate of molecules leaving the liquid phase is equal to the rate of molecules entering the gas phase.
• In a saturated aqueous solution containing an ionic solid a crystal of the ionic solid may neither dissolve or grow, but stay the same size. The rate of ions leaving the crystal is equal to the rate of ions colliding with the crystal and entering the crystal lattice.

Chemical equilibrium is similar, but deals with rates of chemical reactions

Consider the unimolecular elementary reaction process:

A -> B

• Since this reaction as written has been defined as an elementary process, we now know something about the rate of the (forward) reaction:

Reaction rate = k [A]

• What about the reverse reaction? The reverse reaction is also a unimolecular elementary process and, therefore, the reaction rate is equal to some rate constant times the concentration of B. But it is a potentially different rate constant
• Recall that the rate is proportional to the activation energy, E_a, and the activation energy for the reverse reaction will be equal to (E_a + DE_rxn)
• The forward rate constant (k_f) will therefore be different from the reverse reaction rate constant (k_r)

Forward reaction rate = k_f [A]

Reverse reaction rate = k_r [B]

Consider how this reaction would look at the molecular level if we started with pure A:

• At the beginning there is no B, therefore, the reverse reaction rate is 0 (since [B] = 0). At the beginning there is a lot of A, so the forward reaction rate is high (since [A] = large)
• As time goes by (as it always does) the concentration of A decreases (as it is used up). Therefore the forward reaction rate slows down. Also, the concentration of B starts to build up. Therefore, the reverse reaction rate starts to increase.
• At some point, the forward and reverse reaction rates will balance out and equal each other. Note that this does not necessarily mean the concentrations of A and B equal each other. For the rates to be equal, the product of (k_f * [A]) must equal( k_r *[B]). Therefore, the concentrations of A and B will be equal at equilibrium only if k_f = k_r.

Forward Rate = Reverse Rate

k_f [A] = k_r [B]

• This equation can be rearranged to relate the concentration of A to B at equilibrium:

What this means is that at equilibrium the ratio of the concentration of B to A will always have the same value

• Once equilibrium is established, the concentrations of A and B do not change
• This does not mean that all reactions have stopped. Rather it means that the rates of the forward and backward reactions are equal to each other, and therefore, there is no net change in the concentration of reactant and product
• This is known as a dynamic equilibrium. The forward and reverse reactions are represented by a double arrow in the chemical equation:

At dynamic equilibrium:

• The concentrations of A and B are constant
• The forward and reverse reaction rates are equal