Chemical equilibria: reversible reactions, dynamic equilibrium

Many chemical reactions are a one-way street; they proceed until one of the reactants is completely used up. These are called irreversible reactions. However, some reactions are 'reversible', meaning the products can react to re-form the original reactants. We represent this two-way process using a double arrow (⇌).

A reversible reaction taking place in a closed system (where no substances can enter or leave) will eventually reach a state of 'dynamic equilibrium'. The 'dynamic' part is crucial: it means that on a molecular level, the forward reaction (reactants → products) and the reverse reaction (products → reactants) are both still happening. The 'equilibrium' part means they are happening at the exact same rate. Because the rate of formation of products equals the rate of their conversion back to reactants, the overall concentrations of all reactants and products become constant. Macroscopic properties, like colour or pressure, will appear static, but the system is anything but.

When a system at equilibrium is disturbed, it doesn't just accept the new conditions; it actively responds. This response is described by Le Chatelier's Principle, which states: 'If a change is made to the conditions of a system at dynamic equilibrium, the position of equilibrium will shift to counteract the change.' Think of it as the equilibrium 'pushing back' against any disturbance.

1. Change in Concentration: If you add more of a reactant, the equilibrium will shift to the right (towards products) to use up the extra reactant. If you remove a product, the equilibrium will also shift to the right to replace what was removed.
2. Change in Pressure (for gases): This only affects reactions involving gases. If you increase the pressure, the equilibrium will shift to the side of the equation with fewer moles of gas to reduce the pressure. If you decrease the pressure, it shifts to the side with more moles of gas.
3. Change in Temperature: This depends on whether the reaction is exothermic (ΔH is negative) or endothermic (ΔH is positive). If you increase the temperature, the equilibrium will shift in the endothermic direction to absorb the added heat. If you decrease the temperature, it will shift in the exothermic direction to release heat and warm the system up.

Catalysts: A catalyst's role is unique. A catalyst increases the rate of both the forward and reverse reactions equally. This means it has absolutely no effect on the position of equilibrium or the final yield of products. Its only job is to help the system reach equilibrium much faster.

While Le Chatelier's principle tells us the direction of a shift, the equilibrium constant (K) gives us a number that describes the actual position of equilibrium. It's a mathematical expression of the ratio of products to reactants once equilibrium has been reached at a specific temperature.

For a general reaction: `mA + nB ⇌ pC + qD`

The equilibrium constant in terms of concentration, Kc, is given by the expression: `Kc = ([C]^p [D]^q) / ([A]^m [B]^n)`. The square brackets [ ] denote the concentration in mol dm⁻³ at equilibrium. The powers (p, q, m,n) are the stoichiometric coefficients from the balanced equation.

For reactions involving gases, it's often more convenient to use partial pressures instead of concentrations. The equilibrium constant in terms of partial pressure, Kp, is written similarly: `Kp = (p(C)^p * p(D)^q) / (p(A)^m * p(B)^n)`, where p(X) is the partial pressure of gas X.

The value of K is incredibly important:

• If K > 1, the concentration of products is greater than reactants at equilibrium. The equilibrium lies to the right.
• If K < 1, the concentration of reactants is greater than products at equilibrium. The equilibrium lies to the left.

Crucially, for a given reaction, the value of K is only affected by temperature. Changes in concentration, pressure, or the addition of a catalyst will shift the position of equilibrium to keep the value of K constant, but they do not change the value of K itself.

Knowing the expression for Kc allows us to perform powerful calculations. We can either calculate the value of Kc from experimental data, or use a known Kc value to find the quantities of substances at equilibrium. A very common and useful tool for organizing these calculations is the 'ICE' table, which stands for Initial, Change, and Equilibrium.

To calculate Kc from equilibrium concentrations:

1. Write the balanced chemical equation.
2. Write the expression for Kc.
3. Substitute the known equilibrium concentrations of all species into the expression.
4. Calculate the value. Pay attention to units: derive them by cancelling units in the Kc expression. If the powers of concentration on the top and bottom are equal, Kc is dimensionless.

To calculate equilibrium concentrations using Kc: This is more complex and often involves setting up an ICE table.

1. I (Initial): Fill in the initial concentrations (or moles) of all species.
2. C (Change): Define the change in concentration for one species as 'x', and then use the stoichiometry of the balanced equation to determine the change for all other species in terms of 'x'. Reactants will decrease (-x) and products will increase (+x).
3. E (Equilibrium): The equilibrium concentration for each species is the Initial value plus the Change value.
4. Substitute these equilibrium expressions (in terms of 'x') into the Kc expression and solve for 'x'. Once 'x' is known, you can calculate the actual equilibrium concentrations.

The principles of chemical equilibrium are not just theoretical; they are the foundation of massive industrial processes that shape our world. The conditions for these processes are carefully chosen as a 'compromise' to balance equilibrium yield, reaction rate, and cost.

The Haber Process: N₂(g) + 3H₂(g) ⇌ 2NH₃(g), ΔH = -92 kJ/mol This process makes ammonia (NH₃) for fertilizers. The goal is to maximize the yield of ammonia.

• Temperature (~450°C): The forward reaction is exothermic, so Le Chatelier's principle says a low temperature would favour a high yield. However, at low temperatures, the reaction rate is extremely slow. 450°C is a compromise: high enough for a fast enough rate, but not so high that the equilibrium position is pushed too far to the left.
• Pressure (~200 atm): There are 4 moles of gas on the left and 2 on the right. High pressure favours the side with fewer moles, so it shifts the equilibrium to the right, increasing the yield of ammonia. High pressures are expensive to maintain, so 200 atm is a compromise between yield and cost.
• Catalyst (Iron): An iron catalyst is used to increase the rate of reaction, allowing equilibrium to be reached faster at the compromise temperature.

The Contact Process (Stage 2): 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), ΔH = -197 kJ/mol This is the key step in making sulfuric acid.

• Temperature (~450°C): Similar to the Haber process, this is a compromise. The forward reaction is highly exothermic, so a lower temperature is needed for a good yield, but a higher temperature is needed for a good rate.
• Pressure (~1-2 atm): There are 3 moles of gas on the left and 2 on the right. High pressure would favour the product, but the reaction already has a very high percentage conversion (>99%) at just above atmospheric pressure. The high cost of high-pressure equipment is therefore not justified.
• Catalyst (Vanadium(V) oxide, V₂O₅): Essential to achieve a satisfactory rate at the compromise temperature.

The definitions of acids and bases can be extended beyond simple Arrhenius theory (acids produce H⁺, bases produce OH⁻). The Brønsted-Lowry theory provides a more general and powerful definition based on the transfer of protons.

• A Brønsted-Lowry Acid is a proton (H⁺) donor.
• A Brønsted-Lowry Base is a proton (H⁺) acceptor.

An acid-base reaction, in this view, is simply a proton transfer reaction. Consider hydrochloric acid dissolving in water: `HCl(g) + H₂O(l) ⇌ Cl⁻(aq) + H₃O⁺(aq)`. Here, the HCl molecule donates a proton to a water molecule. Therefore, HCl is the acid and H₂O is the base.

This theory also introduces the idea of conjugate acid-base pairs. When an acid donates its proton, what remains is called its conjugate base. When a base accepts a proton, what is formed is called its conjugate acid.

• In the example above, Cl⁻ is the conjugate base of the acid HCl.
• H₃O⁺ (the hydronium ion) is the conjugate acid of the base H₂O.

An acid-base pair and its conjugate pair are always present in a Brønsted-Lowry reaction.

The terms 'strong' and 'weak' in chemistry do not refer to concentration, but to the degree of ionisation or dissociation in water. This is a crucial distinction.

Strong Acids and Bases: A strong acid or base is one that completely ionises in aqueous solution. The reaction is considered to go to completion and is shown with a single forward arrow (→). For example, hydrochloric acid is a strong acid: `HCl(aq) → H⁺(aq) + Cl⁻(aq)` This means in a solution of HCl, there are virtually no undissociated HCl molecules. Similarly, sodium hydroxide is a strong base: `NaOH(aq) → Na⁺(aq) + OH⁻(aq)`

Weak Acids and Bases: A weak acid or base is one that only partially ionises in aqueous solution. This creates an equilibrium, shown with a reversible arrow (⇌). For example, ethanoic acid is a weak acid: `CH₃COOH(aq) ⇌ H⁺(aq) + CH₃COO⁻(aq)` In a solution of ethanoic acid, most of the molecules remain as undissociated CH₃COOH. Only a small fraction release their protons at any given time. Ammonia is a common weak base: `NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq)`

This difference in dissociation has a direct impact on pH. For solutions of the same concentration (e.g., 0.1 mol dm⁻³), a strong acid will have a much higher concentration of H⁺ ions and therefore a much lower pH than a weak acid.