Equilibria

An equilibrium reaction is one in which the reactants, say A + B, collide successfully and react together to form the products, C + D. The 'reverse' also occurs simultaneously, in which C + D react to form A + B once again. When this system reaches a point in which the concentrations of A, B, C & D are constant, the reaction is said to be in Dynamic Equilibrium. At this point, the reaction appears to have stopped, but both the forward and backward reactions are still occurring at equal rates. However, it is very rare for this equilibrium position to be at the half-way point.

The above equilibrium reaction can be represented by the equation:

A + B ⇌ C + D

In general, the rate of the reaction between A and B (v_AB) can usually be predicted with the equation:

v_AB = k_AB[A][B]

k_AB is the "rate constant"
[A] is the concentration of A
[B] is the concentration of B.

The rate of the reverse reaction between C and D (v_CD) can usually be predicted with the equation:

v_CD = k_CD[C][D]

At equilibrium, the two rates are equal:

v_AB = v_CD

k_AB[A][B]= k_CD[C][D]

k_AB / k_CD = [C][D]/[A][B]

We call the ratio of the two rate constants "the equilibrium constant" (K_c)

K_c = [C][D]/([A][B])

K_c is > 1 if the equilibrium has more products than reactants.

K_c is not affected by concentration, pressure or catalysts, but it is affected by temperature.

K_c is directly related to the chemical equation:

p A + q B ⇌ r C + s D

K_c = [C]^r[D]^s/([A]^p[B]^q)

Examples:

For the reaction 2 NO₂ ⇌ N₂O₄

K_c = [N₂O₄]/[NO₂]²

K_c has the units mol^-1 dm³

For the reaction 3 H₂ + N₂ ⇌ 2 NH₃

K_c = [NH₃]²/([N₂][H₂]³)

K_c has the units mol^-2 dm⁶

For the reaction {Cu(H₂O)₆}²⁺ + 4 Cl^– ⇌ {CuCl₄}^2– + 6 H₂O

K_c = [{CuCl₄}^2–][H₂O]⁶/([{Cu(H₂O)₆}²⁺][Cl^–]⁴)

K_c has the units mol² dm^-6

Le Chatelier's Principle

Le Chatelier's principle can be used to predict the changes that will occur if the conditions are changed in a chemical equilibrium reaction. His principle states that:

"If a system at equilibrium is subject to a change in either pressure, temperature or concentration, then the system will move to oppose that change."

Using this principle is relatively straightforward; whatever you change in the reaction conditions, the system will move in the opposite direction as if to "try" to restore the equilibrium condition.

Sometimes the equilibrium will actually manage to change the conditions part-way back to the original conditions. In other cases, the change in the equilibrium has no observable effect on the conditions.

For example, let us consider the reaction in which nitrogen dioxide forms dinitrogen tetroxide

2 NO₂(g) ⇌ N₂O₄(g) ΔH = -57.2 kJ mol^-1

Temperature

It can be seen that the reaction here is exothermic (takes in heat from the surroundings). If the reaction conditions are changed, such that the temperature is increased, the equilibrium will "attempt" to oppose the change by decreasing the temperature and thereby shifting in the endothermic direction, to the left. Conversely, if the temperature is decreased, then the equilibrium will oppose the change by moving in the exothermic direction to raise the temperature once again, and hence the system will move to the right.

Think about the rates of the forward and reverse reactions. The endothermic reaction (in this case, the reverse reaction) is more sensitive to changes in temperature. Increasing temperature will increase the rates of both forward and reverse reactions, but the rate of the endothermic reverse reaction will increase by a bigger factor.

Pressure

To determine the way an equilibrium reaction will shift when the overall pressure is changed, one must look at the number of moles of each gas species present in the reaction. In the above reaction concerning Nitrogen Dioxide it can be seen from the equation that the side with the greatest number of moles of gas is the left. Therefore, increasing the pressure on this reaction will cause the equilibrium to move right, as this is the side with fewer moles of gas, which thereby reduces the pressure once again.

Again, you can think about the rates of the forward and reverse reactions. In this case, the forward reaction has two gas molecules (2 NO₂(g)) reacting but the reverse reaction has only only gas molecule reacting (N₂O₄(g)). Increasing pressure will increase the rates of both forward and reverse reactions, but the rate of the forward reaction will increase by a bigger factor.

Concentration

If the concentration of one of the chemicals in an equilibrium reaction is changed, then the system will "oppose" the change by moving to restore the original concentration. Again, consider the reaction:

2 NO₂(g) ⇌ N₂O₄(g)

If you were to add lots of N₂O₄ to the above equilibrium, the system will move left to remove the excess N₂O₄ concentration added. Likewise, if a large excess of NO₂(g) were added, then the system would move to the right to reduce the concentration.

Again, you can think about the rates of the forward and reverse reactions. Adding N₂O₄ will increase the rate of the reverse reaction. Adding NO₂(g) will increase the rate of the forward reaction.

Catalysts

Some reactions require the use of a catalyst in order to reach equilibrium in a feasible, efficient time. A catalyst does not affect the position of an equilibrium; it speeds up both the forward and backward reactions equally and therefore only increases the rate at which equilibrium is reached.

Catalysts work by providing an alternate reaction pathway of lower activation energy for both the reactants and products in an equilibrium reaction, and the overall reaction energy remains unchanged.

Equilibria & Industry

Ammonia

For many reactions, a compromise in reaction conditions must be met in order to achieve the best yield of product. Although, for example, a reaction may yield the greatest amount of product at extremely high temperatures, it is not feasible to generate such high temperatures in industry.

Consider the Haber Process, in which hydrogen and nitrogen react to form ammonia:

3 H₂ + N₂ ⇌ 2 NH₃ ΔH = -92.4 kJ mol^-1

The forward reaction is exothermic, and therefore the reaction is favoured by low temperatures. Even though this is the case, having temperatures that are too low will make the reaction too slow to be commercially useful. It is therefore necessary for a compromise temperature of approx 450 °C to be made, resulting in a mere 10-20 % yield of ammonia.

The Haber Process is also favoured by high pressures, since there are more moles of gas on the left (reactant) side of the equilibrium equation. Generating pressures that are extremely high is a difficult and costly process, since the energy required to generate such pressures can be high, as can the cost of the vessel used to withstand such high pressures. The compromise pressure here is 250 atm.

Ethanol

This is the alcohol in alcoholic drinks and therefore is unsurprising that it has been made for thousands of years by fermentation of sugars such as glucose while using the enzymes in yeast as a catalyst.

C₆H₁₂O₆ → 2 C₂H₅OH + 2 CO₂

Ethanol is also used in drugs, cosmetics, detergents and inks. At present the main source of ethanol is ethene, which is made from crude oil obtained by fractional distillation then cracking.

Ethanol is made by the reversible reaction of hydration (adding of water) to ethene and is speeded up by the catalyst of phosphoric acid absorbed on silica.

H₂C=CH₂(g) + H₂O(g) ⇌ CH₃CH₂OH(g) ΔH = -46 kJ mol⁻¹

The products and reactants are all gaseous at the temperature used. Applying Le Chatelier's principle to this equilibrium predicts that the maximum yield will be produced with:

a high pressure forcing the equilibrium to move to the right with fewer gas molecules
a low temperature forcing the equilibrium to the right to give out heat
excess steam to force equilibrium to the right again to reduce the steam concentration.

However the practical problems include;

the low temperature will reduce the reaction rate and thus how quickly the equilibrium is reached
the high pressure tends to cause ethene to polymerise (to polyethene)
the high pressure increases costs of building the plant and energy cost to run it
too much steam will simply dilute the catalyst.

In practice conditions of about 570 K and 6500 kPa (64 atm) pressure are used obtaining a yield of ethanol at around 5 %. The unreacted ethene is separated from the reaction mixture and recycled over the catalyst again until a 95 % conversion is obtained.

Acid-Base Reactions

Acids and Bases

An acid is a substance which in an aqueous solution will release H⁺ ions. Acids are also known as proton donors as they release a "proton" in the form of a H⁺ ion. Common laboratory acids include hydrochloric acid (HCl), sulfuric acid (H₂SO₄), nitric acid (HNO₃) and ethanoic acid (CH₃COOH).

A base is a proton receiver as it readily accepts H⁺ ions ("protons") from an acid. Examples:

OH^- + H⁺ → H₂O
O^2- + 2 H⁺ → H₂O
NH₃ + H⁺ → NH₄⁺

Common bases are metal oxides, metal hydroxides, and ammonia. An alkali is a soluble base, and will release OH^- ions in an aqueous solution. Common alkalis include sodium hydroxide (NaOH), potassium hydroxide (KOH), and aqueous ammonia (NH₃(aq)).

Weak Acids

A weak acid is an acid which does not fully dissociate in solution. Strong acids are completely dissociated.

A 1 mol dm^-3 solution of any strong acid (e.g. HCl) will have an H⁺ concentration of 1 mol dm^-3.

A 1 mol dm^-3 solution of a weak acid (e.g. CH₃COOH) will have an H⁺ concentration of less than 1 mol dm^-3. A 1 mol dm^-3 solution of CH₃COOH will have H⁺ of 0.0042 mol dm^-3.

Do not confuse "weak" with "dilute". Any acid can be diluted to reduce its concentration. For example, HCl and CH₃COOH can both have a concentration of 1 mol dm^-3. However, because HCl is a strong acid, its concentration will equal the H⁺ concentration. For a weak acid like CH₃COOH the H⁺ concentration is only a fraction of the acid concentration. If H⁺ is neutralised by an alkali, a weak acid will keep dissociating to replace the H⁺. At the same concentration, weak and strong acids will neutralise the same amount of alkali, but with a weak acid most of the H⁺ is released as the alkali is added and not before. An analogy would be different ways of managing money; A strong acid has all its money in a current account, ready to spend immediately. A weak acid has the same amount of money, but most is in a savings account, and only when the current account is empty is money transferred from the savings account to replenish the current account.

pH

The pH scale is a convenient way to measure H⁺ concentration.

pH = -log[H⁺] and [H⁺] = 10^-pH

Comparison of [H⁺] and pH
[H⁺] (mol dm^-3)	pH (no units)
1 x 10^-7	7.0
1 x 10^-11	11.0
10	-1.0
1 x 10^-5	5.0
2 x 10^-5	4.7
2 x 10^-7	6.7
5 x 10^-7	6.3
5 x 10^-9	8.3

Salts

A salt is produced during neutralisation: the reaction of an acid with a base, alkali or carbonate. The H⁺ ion of an acid is replaced by a metal ion or NH₄⁺.

Here are some common reactions:

Acid + Base → Salt + Water
Acid + Alkali → Salt + Water
Acid + Metal → Salt + Hydrogen
Acid + Carbonate → Salt + Carbon Dioxide + Water