Introduction

In chemistry, reactions don't always proceed to the end. Sometimes, they get stuck in the middle. This is called equilibrium, and it happens for reactions that occur in both directions. When a reaction is in equilibrium, the concentrations of the compounds remain the same. This is because the rate of the forward reaction equals the rate of the reverse reaction, so there is no net change in concentration.

The rate at which a reaction occurs depends on the concentration of the reactants, the temperature of the reaction, the physical state of the reactants, and the presence of a catalyst. For the one-step reaction nA + mB ⇄ pC + qD where A, B, C, and D are all gases or solutions, the forward rate can be written as k₁[A]ⁿ[B]^m and the reverse rate as k₂[C]^p[D]^q Since the forward rate and the reverse rate are equal at equilibrium, the ratio of the reverse rate to the forward rate is one to one. From this, we can rearrange to find k₂[C]^p[D]^q k₁[A]ⁿ[B]^m = 1

[C]^p[D]^q [A]ⁿ[B]^m = k₁ k₂ The expression on the left is called the equilibrium expression, and the value on the right, k₁k₂ is a constant, which we call the equilibrium constant, or K_eq. The equilibrium constant does not depend on the concentration of any species in the reaction; it does change with temperature, however. Also, it is important to note that the equilibrium expression is only equal to the equilibrium constant when the reaction has reached equilibrium.

In general, to find the equilibrium expression for a reaction, take the concentration of each of the products raised to the power of its coefficient and multiply them together, then divide by the concentrations of the reactants raised to the power of their coefficients. However, solids and pure liquids are not included in the equilibrium expression. If you wouldn't include something in the rate law, then don't include it in the equilibrium expression. If none of the products or none of the reactants are included, then use 1 for the numerator or denominator of the expression.

Common uses for K_eq

Ok, we've seen that equilibrium reactions have equilibrium constants associated with them, but what are they good for?

One use for K_eq is to see which way a reaction will proceed. Given a reaction and the concentration of all its products and reactants, we can plug them in to the equilibrium expression. The result is not K_eq, because the reaction is not at equilibrium. Instead, we call this value Q, the reaction quotient. We can compare Q to K_eq to determine which way the reaction will go.

Q < Keq	Q = Keq	Q > Keq
Form products	At equilibrium	Form reactants

The reaction will always proceed in the way that makes Q approach K_eq.

Another use for K_eq is to calculate the amount of product formed by an equilibrium reaction. Given the initial concentrations of all species and the value of K_eq, we can create a system of equations to solve for the final concentrations. For example, consider the following reaction: H₂(g) + I₂(g) ⇄ 2HI(g),   K_eq = 2.9 × 10^-1 at 300K If we start with [H₂] = 0.100M, [I₂] = 0.100M, and [HI] = 0.000M, we can create a RICE table.

Reaction	H2(g)	+	I2(g)	⇄	2HI(g)
Initial	0.100M		0.100M		0.000M
Change	-x		-x		+2x
Equilibrium	0.100M - x		0.100M - x		2x

Because we don't know how much of the reactants will be used, we use the variable x to represent the change in concentration. We do know the ratio of the changes from the balanced equation, so we can write all the changes in terms of x. To fill in the equilibrium row, we simply add the changes to the initial concentrations. Then, we can plug these values in to the equilibrium expression and solve for x. K_eq = [HI]² [H₂][I₂]

2.9 × 10^-1 = (2x)² (0.100M - x)(0.100M - x)

5.4 × 10^-1 = 2x 0.100M - x

x = 2.7 × 10^-2 In this case, the final concentration of HI is 2x, or 5.4 × 10^-2 M.

Le Chatelier's principle

Systems at equilibrium are cool and all, but what happens when we alter them? Le Chatelier's principle can tell us the answer. It states that if a system at equilibrium is disturbed, the system will shift its equilibrium position so as to counter the effect of the disturbance. This can be explained in terms of kinetic molecular theory by examining the effect that each disturbance has on the collisions taking place in the reaction, and how that affects the forwards and backwards reaction rates of the equilibrium reaction. Le Chatelier's principle can be applied to the following four factors.

• Concentration:

  Adding or removing a reactant or product. If a chemical system is already at equilibrium and the concentration of any substance in the mixture is increased (either reactant or product), the system reacts to consume some of that substance. Conversely, if the concentration of a substance is decreased, the system reacts to produce some of that substance.

  By adding more reactants or products to the reaction, the frequency of collisions between reactant or product molecules increases. This gives more opportunities for the forwards or backwards reaction to occur, speeding up the respective rate and shifting equilibrium the other way. Similarly, reducing the concentration reduces the number of collisions and slows down the rate in one direction causing the equilibrium to shift towards the slower rate.

• Pressure:

  Changing the pressure by changing the volume. Reducing the volume of a gaseous equilibrium mixture causes the system to shift in the direction that reduces the number of moles of gas. Increasing the volume of a gaseous equilibrium mixture causes the sytem to shift in the direction that increases the number of moles of gas. Note that changing the total pressure by adding a non-reacting gas to the system does not affect equilibrium. This is because the partial pressure of the reactants and products remain unchanged.

  When the partial pressures of the reacting gases are increased, the number of collisions for both products and reactants increases, but it increases more for the side with more moles of gas. This increases the reaction rate for the side with more moles of gas and causes the equilibrium to shift to the other side. Decreasing the pressure has the opposite effect. Adding a non-reacting gas has no effect because it changes the rate of collisions between both the reactants and the products by the same amount, leading to no net shift.

• Temperature:

  Increasing or decreasing the reaction temperature. When the temperature of a system at equilibrium is increased, the system reacts as if we added a reactant to an endothermic reaction or a product to an exothermic reaction. The equilibrium shifts in the direction that consumes the excess reactant (or product), namely heat.

  When the temperature increases, the average kinetic energy of all particles is higher, so the number of collisions in which the particles have enough energy to react is higher. This speeds up the rate in both directions, but the increase is greater for endothermic reactions than exothermic reactions so the equilibrium shifts to consume heat. The opposite is true for decreasing the temperature.

• Catalyst:

  Adding or removing a catalyst. A catalyst increases the rate at which equilibrium is achieved but does not change the composition of the equilibrium mixture.

  A catalyst works by lowering the activation energy of a reaction so that more collisions are energetic enough to react, but it does so equally in both directions. Both rates increase the same amount, so there is no net shift in equilibrium.

You can explore these factors yourself in the reaction simulator below.

Industrial applications

For industrial processes, it is important to maximize the concentration of the desired products and minimise the 'leftover' reactants. Le Chatelier's Principle and the principles of reaction kinetics can both be used to design the best reaction conditions to give the highest possible yield of product in an economic way.

Ideas on 'economic production' are described in most detail for the Haber Synthesis of ammonia, but equilibrium and kinetic factors are continually mentioned in the other examples too.

The Haber process, developed by Fritz Haber and Carl Bosch, is an artificial nitrogen fixation process and is the main industrial procedure for the production of ammonia today. The process converts atmospheric nitrogen (N₂) to ammonia (NH₃) by a reaction with hydrogen (H₂) using a metal catalyst under high temperatures and pressures. Although the Haber process is mainly used to produce fertilizer today, during World War I it provided Germany with a source of ammonia for the production of explosives, compensating for the Allied trade blockade on Chilean saltpeter.

N₂(g) + 3H₂(g) ⇄ 2NH₃(g),   ΔH = -92 kJ/mol The Haber process incorporates

• a high temperature — about 450℃
• a high pressure — about 200 atmospheres (200 times normal pressure)
• an iron catalyst

The pressure and catalyst make sense in order to maximize ammonia output rate, just like what the le Chatelier's Principle states. However, the high temperature may seem odd because the reaction is exothermic. While a lower temperature would result in a higher concentration of ammonia at equilibrium, it would also dramatically slow down the rate at which equilibrium is reached. The temperature 450℃ happens to be a compromise between increasing the equilibrium concentration of ammonia while keeping the reaction rate fast enough to be practical.

Reaction simulator