Industrial Equilibria: Finding the Balance Revision Notes | A Level AQA Chemistry

1. The Industrial Dilemma: Why You Can't Have Everything

Here is the central tension in industrial chemistry: the conditions that give you the highest yield are often the conditions that give you the slowest rate. A chemical engineer cannot choose the conditions that maximise equilibrium yield and walk away — they have to find a workable balance between yield, speed, and cost.

This is the concept of compromise conditions. For any reversible reaction used industrially, the chosen temperature and pressure are rarely the thermodynamically ideal values. They are the values that make the process economically viable and practically safe.

To understand why, you need to hold two ideas in tension simultaneously: what Le Chatelier's principle predicts about equilibrium position, and what kinetics tells you about how fast that position is reached. These two considerations pull in opposite directions, and the compromise sits between them.

2. Temperature: The Rate–Yield Conflict

Start with temperature, because this is where the conflict is sharpest. Consider a reaction that is exothermic in the forward direction — the synthesis of ammonia in the Haber process is the classic example: $\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)$, $\Delta H = -92 \text{ kJ mol}^{-1}$.

Le Chatelier's principle tells you that increasing temperature shifts the equilibrium position to the left — towards the endothermic direction — reducing the yield of ammonia. Conversely, lowering the temperature shifts the equilibrium to the right, increasing the proportion of ammonia at equilibrium. So far, so straightforward: low temperature favours yield.

The problem is kinetics. At low temperatures, the activation energy barrier is harder to overcome. Reaction rate drops dramatically, and the system takes an impractically long time to reach equilibrium. In a continuous industrial process, slow rate means low throughput — you produce very little product per unit time, which is economically disastrous.

The resolution is a compromise temperature. For the Haber process, approximately 450 °C is used. This temperature is high enough to give a reaction rate that produces ammonia at a commercially useful rate, yet low enough that the equilibrium position has not shifted so far to the left that yield becomes negligible. The equilibrium yield at 450 °C is only around 15–20%, but because unreacted nitrogen and hydrogen are recycled continuously, the overall efficiency of the process remains acceptable.

A catalyst such as finely divided iron with promoters increases the rate at which equilibrium is reached without changing the equilibrium position or Kc. In practice, that faster rate means industry can choose a lower compromise temperature than would otherwise be commercially acceptable, but the catalyst itself does not nudge equilibrium towards products.

For an endothermic forward reaction, increasing temperature increases both the rate and the equilibrium yield of products. That makes the conflict between rate and yield less severe than in an exothermic process, although energy cost, catalyst lifetime, and plant design still limit how high the operating temperature can be.

3. Pressure: Yield Versus Cost

Now consider pressure. Le Chatelier's principle states that increasing pressure shifts the equilibrium position towards the side with fewer moles of gas. For the Haber process, the left side has $1 + 3 = 4$ moles of gas and the right side has $2$ moles, so increasing pressure shifts equilibrium to the right, increasing ammonia yield. On this basis alone, you would want the highest possible pressure.

The constraint here is not kinetics but economics and engineering safety. Very high pressures require enormously thick-walled reaction vessels, specialised compressors, and extensive safety systems. The capital cost of building and maintaining such equipment is substantial, and the energy cost of compressing gases to extreme pressures is significant. There is also a safety risk: high-pressure vessels carrying flammable hydrogen and nitrogen require rigorous containment.

The Haber process typically operates at 150–200 atm. This is high enough to give a meaningful improvement in yield over atmospheric pressure, but far below the theoretical optimum of several hundred atmospheres. The compromise pressure is the point at which the additional yield gained by increasing pressure further no longer justifies the additional cost and engineering complexity.

4. The Role of Kc: What Changes and What Does Not

A critical distinction that examiners test repeatedly: changing temperature changes the value of $K_c$, but changing concentration or pressure does not. When you increase pressure or change concentrations, the equilibrium position shifts — but $K_c$ remains constant at constant temperature. The system adjusts the concentrations of reactants and products until the ratio defined by $K_c$ is restored.

For an exothermic forward reaction, increasing temperature shifts equilibrium to the left. This means the numerator of $K_c$ decreases and the denominator increases — so $K_c$ decreases. For an endothermic forward reaction, increasing temperature increases $K_c$. This is why temperature is the only variable that changes $K_c$: it is the only variable that changes the relative energies of reactants and products.

5. Putting It Together: The Haber Process as a Case Study

The Haber process brings every element of this lesson into sharp focus. The reaction $\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)$ is exothermic and involves a decrease in moles of gas. Thermodynamically, the ideal conditions for maximum yield would be very low temperature and very high pressure. Neither extreme is industrially practical.

Worked example: Reasoning Through Compromise Conditions for the Haber Process

Justify the choice of approximately 450 °C and 150–200 atm for the Haber process, referring to both rate and equilibrium yield. [6 marks]

1. $\Delta H = -92 \text{ kJ mol}^{-1}$ (exothermic forward reaction) — Because the forward reaction is exothermic, Le Chatelier's principle predicts that increasing temperature shifts equilibrium to the left, reducing ammonia yield. Low temperature favours yield thermodynamically. [B1]
2. Rate $\propto$ fraction of particles with $E \geq E_a$; this fraction increases with temperature. — At low temperatures, very few particles have sufficient energy to overcome the activation energy barrier. The rate of reaching equilibrium becomes impractically slow. A higher temperature is needed for an acceptable rate. [B1]
3. Compromise temperature $\approx 450$ °C; a catalyst (iron) is also used. — 450 °C gives a rate fast enough for commercial throughput. The iron catalyst increases the rate of attainment of equilibrium without changing the equilibrium position, allowing a lower temperature to be viable. [B1]
4. Left: $1 + 3 = 4$ mol gas; Right: $2$ mol gas. Increasing pressure shifts equilibrium right. — Higher pressure increases yield because the system shifts towards the side with fewer moles of gas. On this basis alone, very high pressure would be ideal. [B1]
5. Very high pressure requires thick-walled vessels, high-energy compressors, and extensive safety systems. — The engineering and energy costs of pressures above ~200 atm are not justified by the marginal gain in yield. Equipment failure risk also increases. [B1]
6. Compromise pressure $\approx 150$–$200$ atm; unreacted gases are recycled. — 150–200 atm gives a meaningful yield improvement over atmospheric pressure at manageable cost. Recycling unreacted $\text{N}_2$ and $\text{H}_2$ compensates for the relatively low single-pass conversion of ~15–20%. [B1]

Answer: A temperature of ~450 °C balances the need for acceptable rate (kinetics) against the thermodynamic preference for lower temperature (yield). A pressure of ~150–200 atm balances improved yield against the prohibitive cost and safety risks of higher pressures. A catalyst is used to increase rate without altering equilibrium position.

Notice how the argument always has two parts: what Le Chatelier's principle predicts, and why the ideal prediction is not used in practice. Examiners award marks for both halves — a response that only discusses equilibrium position without addressing rate or cost will not reach the top mark band.

6. Generalising: Beyond the Haber Process

The Haber process is the most examined example, but the same reasoning framework applies to any industrial reversible reaction. The Contact process ($2\text{SO}_2 + \text{O}_2 \rightleftharpoons 2\text{SO}_3$) uses around 450 °C and approximately 1–2 atm. Here, $K_c$ is so large at this temperature that conversion is already around 99.5%, so the economic case for higher pressure is weak — the marginal yield gain does not justify the cost.

When you encounter an unfamiliar industrial process in an exam, apply the same four-question framework: Is the forward reaction exothermic or endothermic? Does the reaction involve a change in moles of gas? What does Le Chatelier's principle predict for ideal conditions? Why are those ideal conditions not used in practice?

7. Exam Technique: Writing High-Mark Answers

Questions on compromise conditions almost always carry 4–6 marks and use the command words explain or evaluate. The mark scheme rewards a structured argument, not a list of facts. You need to state the Le Chatelier prediction, explain the opposing constraint, and then state the compromise — for both temperature and pressure if the question asks about both.

A common error is to say that a catalyst "increases the yield" or "shifts the equilibrium position". It does neither. A catalyst increases the rate at which equilibrium is reached, which means the process can operate at a lower temperature than would otherwise be needed — and that lower temperature may itself give a slightly better yield. But the catalyst is not the direct cause of any yield change.

The core principle of this lesson — that industrial conditions are always a compromise between thermodynamic ideal and practical reality — is one of the most transferable ideas in A-level chemistry. Whenever you see a reversible reaction in an industrial context, ask yourself what the ideal conditions would be and then ask why they are not used. That two-step reasoning is what separates a top-band answer from a mid-band one.

Worked example: How to Choose Industrial Compromise Conditions

1. Use Le Chatelier’s principle to decide which conditions favour equilibrium yield.
2. Use collision theory / activation-energy ideas to decide which conditions give a commercially viable rate.
3. Add engineering and cost constraints, then justify the compromise rather than the theoretical optimum.