Advanced A level theoretical chemistry - chemical equilibrium

Part 3. Application of chemical equilibrium concepts (Le Chatelier's Principle) to industrial processes

[Author ©  Dr Phil Brown PhD: Doc Brown's exam revision notes suitable for students of advanced pre-university A level theoretical-physical chemistry courses: chemical equilibria [page updated April 28th 2026 *]

ALL my advanced A level theoretical chemistry revision study notes

Part 3 sub–index for this page: 

3.0 Introduction to the application of Le Chatelier's Principle to industrial process

3.1 Lime production

3.2 Haber Synthesis of ammonia

3.3 The Contact Process in H₂SO₄ production

3.4 Methanol production

Important prior study reading:

Part 2a. How to write equilibrium expressions and the effect of temperature on the equilibrium constant K

Part 2b. How to write K_c equilibrium expressions & units, exemplar K_c calculations including esterification

Part 2c. How to write K_p expressions, units, partial pressures and exemplar K_p equilibrium calculations

Examples of how to apply the principles of chemical equilibrium to industrial chemical processes.

The equation and equilibrium express is given and the predictions from Le Chatelier's Principle discussed for the production of lime, Haber synthesis of ammonia, the Contact process in the manufacture of sulfuric acid and the synthesis of methanol.

You need to be able to explain why, for a reversible reaction used in an industrial process, a compromise temperature and pressure may be used (e.g. ammonia synthesis).

For industrial processes, it is important to maximise 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.

• calcium carbonate (limestone) calcium oxide (lime) + carbon dioxide

• CaCO_3(s) CaO_(s) + CO_2(g) (ΔH = +178 kJ mol^–1)

• The concentration of the solids is constant, so the only effective equilibrium expression is:
  • K_p = p_CO2 atm or Pa
• From Le Chatelier's Principle, increase in temperature moves the equilibrium to the right, the heat absorbing endothermic direction to minimise temperature change, hence K_p will increase with increase in temperature
• The forward reaction is endothermic, 178kJ of heat energy is absorbed (taken in) for every mole of calcium oxide formed and so CaO formation is favoured by high temperature. In fact the reaction is not viable/feasible until at least 900^oC, and at 1000^oC in a limekiln the equilibrium position is very much on the RHS.
• One mole of gas is formed in the process, so there is a net increase in the moles of gas in lime formation, since there are no gaseous reactants. Therefore decreasing the pressure will favour the formation of more gas molecules if possible, so more carbon dioxide formed, and hence more lime.
• However, the reaction is carried out at normal atmospheric pressure in a lime kiln that that is well ventilated. This reduces the partial pressure of carbon dioxide and so reduces the un–desired backward reaction. It means that a true equilibrium is never established because the reaction is not in a closed system and so as CO₂ is vented, the forward reaction is promoted.
• Old kilns essentially worked on a batch process i.e. coal fuelled furnace heating adjacent limestone, but modern tilted rotary kilns run continually with limestone fed in at one end and lime extracted at the other end.

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• Ammonia gas is synthesised in the chemical industry by reacting nitrogen gas with hydrogen gas.
• The three raw principal materials are (i) air, (ii) coal–coke/methane or higher hydrocarbons and (iii) water.
• The nitrogen is obtained from air (80% N₂) by two principal methods:
  1. Air is cooled and compressed under high pressure to form liquid air (liquefaction). The liquid air is fractionally distilled at low temperature to separate oxygen (used in welding, hospitals etc.), nitrogen (for making ammonia), Noble Gases e.g. argon for light bulbs, helium for balloons).
  2. By burning natural gas in air and separating the nitrogen from the water and carbon dioxide combustion products.
• Synthesis gas is the primary source of hydrogen, though 'syn–gas' or 'syngas' is a mixture of hydrogen and carbon monoxide and is made by three main methods. (Hydrogen can also be obtained as a by–product from oil–cracking and the electrolysis of brine.)
  1. Historically synthesis gas was made by passing steam over white hot coke at 800–1200^oC. Coke is made by heating coal at high temperature and is mainly carbon. This process is still used in many parts of the world and if coal is available in a country without oil, then it will be cheaper than using hydrocarbons from oil.
     • C_(s) + H₂O_(g) CO_(g) +  H_2(g) (ΔH = +131 kJ mol^–1)

     • Kp =	pCO pH2
       	–––––––– (units atm or Pa)
       	pH2O

     • Note that carbon solid is not included in the equilibrium expression, its concentration is considered constant.
     • From Le Chatelier's Principle, increase in temperature moves the equilibrium to the right, the heat absorbing endothermic direction to minimise temperature change, hence K_p will increase with increase in temperature
     • The very high temperature favours the endothermic production of hydrogen and of course considerably increases the rate of reaction. Water and carbon show little reaction at lower temperatures.
     • The reaction can be carried out at normal pressure since higher pressures favour the reverse reaction (1 gas mol <== 2 gas mol).
  2. Methane can be partially oxidised by reaction with the oxygen in air.
     • CH_4(g) + ¹/₂O_2(g) ==> CO_(g) + 2H_2(g) (ΔH = –36 kJ mol^–1)
     • Low pressure (1.5 gas mol ==> 3.0 gas mol) and low temperatures (exothermic) favour this reaction.
     • This reaction can be carried out with nearly 100% conversion at atmospheric pressure (so low pressure) at 800–1000^oC using cobalt/nickel based catalysts e.g. Ni–ThO₂ or Ni–SiO₂. Very little water or carbon dioxide is formed if the reaction conditions are carefully controlled.
     • Although the 'unfavourable' high temperature is needed (plus catalyst) to break the strong C–H or O=O bonds in the reactant molecules and get an effective rate of reaction, there is quite an entropy increase via the doubling of moles of gas, and quite clearly the RHS is favoured (its probably irreversible?).
     • The reaction also produces the required 1:2 ratio of CO:H₂ for methanol production.
  3. These days hydrogen is primarily made by reacting methane (natural gas) and water (steam), and the process is called a catalytic steam–methane reforming.
     • CH_4(g) + H₂O_(g) 3H_2(g) + CO_(g) (ΔH = +206 kJ mol^–1)

     • Kp =	pH23 pCO
       	––––––––––
       	pCH4 pH2O

     • The reaction is carried out at 700–1000^oC, over a nickel catalyst, at a pressure of 1–2 x 10⁶ Pa (1–2MPa, 10–20 atm).
  • From Le Chatelier's Principle, increase in temperature moves the equilibrium to the right, the heat absorbing endothermic direction to minimise temperature change, hence K_p will increase with increase in temperature

  • This reaction is favoured by high temperature (endothermic, heat absorbing) and low pressure (2 gas moles ==> 4 gas moles).

  • In practice a high temperature is indeed used, and combined with a catalyst,  both factors will increase the rate of reaction to ensure the process is economic.

  • However, although a low pressure is advantageous, in practice a moderately high pressure is used, which effectively increases the concentration of the reactants, increasing the rate of reaction, and allows a greater bulk of material to pass through the reactor in a given time.

  • The yield of hydrogen can be further increased by using the 'shift' reaction.

    • CO_(g) + H₂O_(g) CO_2(g) + H_2(g) (ΔH = –41 kJ mol^–1)

    • Since 2 gas mol ==> 2 gas mol, changing pressure offers no advantage.

    • From Le Chatelier's Principle, an increase in temperature moves the equilibrium to the left, the heat absorbing endothermic direction to minimise temperature change, hence K_p will decrease with increase in temperature

    • However, although the lower the temperature, the greater the yield of this exothermic reaction, too low a temperature leads to an uneconomic low rate of reaction, so research continues into low temperature catalysts, usually based on transition metals and their oxides e.g. Cr–Fe oxides (e.g. Fe₃O₄) are effective at 400–500^oC, Cu–ZnO–Al₂O₃ at 200–400^oC and CuO–ZnO at 175–325^oC.

    • The carbon dioxide can be absorbed under pressure into water or potassium carbonate solution.

• The Bosch–Haber synthesis equation for ammonia is

• N_2(g) + 3H_2(g) 2NH_3(g) (ΔH = –92 kJ mol^–1

• (see also Le Chatelier's example 1.4.2 and K_p calculations)

• Kp =	pNH32
  	–––––––––
  	pN2 pH23

• From Le Chatelier's Principle, an increase in temperature moves the equilibrium to the left, the heat absorbing endothermic direction to minimise temperature change, hence K_p will decrease with increase in temperature
• Since a dynamic equilibrium will form, there is no chance of 100% yield even if you use, as you actually do, the theoretical stoichiometric reactant volume/mole ratio of N₂ :H₂ of 1 : 3 !
• In forming ammonia, heat energy is given out to the surroundings i.e. exothermic, 46kJ of heat released per mole of ammonia formed.
• Four moles of 'reactant' gas form two moles of 'product' gas, so there is net decrease in gas molecules on forming ammonia.
• So applying the Le Chatelier's Principle equilibrium rules, the formation of ammonia is favoured by  ...
  • (a) Using high pressure because you are going from 4 to 2 gas molecules (the high pressure also speeds up the reaction because it effectively increases the concentration of the gas molecules) and allows a greater bulk flow rate material through the reactor, but very high pressure means more dangerous and more costly engineering to address the health and safety issues involved.
  • (b) Carrying out the reaction at a low temperature, because it is an exothermic reaction favoured by low temperature, but this may produce too slow a rate of reaction,
  • So, the idea is to use a set of optimum conditions to get the most efficient yield of ammonia and this may well, as in this case, be a low % yield (e.g. 8% conversion) but fast. Described below are the conditions to give the most economic production of ammonia.
  • these arguments make the point that the yield* of an equilibrium reaction depends on the conditions used.
    • * The word 'yield' means how much product you get compared to the theoretical maximum possible if the reaction goes to 100% completion.
    • For more basic ideas on chemical economics see GCSE notes on economics of the chemical industry (3 linked pages)
• 
• The above chart completely illustrates and vindicates the predictions from Le Chatelier's Principle.
• In industry moderate–high pressures of 2.5–25 x 10⁶ Pa (2.5–5MPa, 25–250 atm) in line with the theory but to high to raise H&S engineering costs.
• Theoretically a low temperature would give a high yield of ammonia BUT ...
  • Nitrogen is very stable molecule and not very reactive i.e. chemically inert and the rate of reaction at high % yield low temperatures is much to slow to be economic.
  • To speed up the reaction an iron oxide catalyst (Fe₃O₄?) is used as well as a higher temperature (e.g. 400 – 450^oC).
  • The higher temperature is an economic compromise, i.e. it is more economic to get a low yield very fast, than a high yield very slowly!
  • Note: a catalyst does NOT affect the yield of a reaction, i.e. the equilibrium position BUT you do get there faster!

• The above chart illustrates the dilemma caused by the % ammonia formed at equilibrium at different temperatures compared to the relative rate of reaction at four different activation energies. It also illustrates the very positive effect of using a catalyst to lower the activation energy, Ea, to give a faster rate of production at a lower temperature, and the added benefit of a higher % ammonia formed at equilibrium at this lower temperature.
• At the end of the process, when the gases emerge from the iron catalyst reaction chamber, the gas mixture is cooled under high pressure, when only the ammonia liquefies and is so can be removed and stored in cylinders.
• Any unreacted nitrogen or hydrogen (NOT liquified), is recycled back through the reactor chamber, nothing is wasted!
  • Nitrogen (bpt –196^oC) and hydrogen (bpt –252^oC) have much lower boiling points than ammonia (bpt –33^oC). Boiling points increase with increase in pressure but these normal atmospheric pressure bpt values offer a fair comparison.
• To sum up: A low % yield of ammonia is produced quickly at moderate high temperatures and pressures, and is more economic than getting a higher % equilibrium yield of ammonia at a more costly high pressure or slower lower temperature reaction.
• Mathematical computer modelling of the Haber Synthesis of Ammonia (used to produce the two charts)
• Detailed AS–A2 notes on "Kinetics – rates of reaction" for further reading.
• AND there are some more general notes on the GCSE level Chemical Economics section pages.

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3.3 The Contact Process in the manufacture of sulphuric acid

• The basics of sulphuric acid uses and its manufacture via the Contact Process is covered on the GCSE level Extra Industrial Chemistry Notes.

• The mechanism of the Contact Process is discussed on the AS–A2 Transition Metals page but its the application of equilibrium and kinetic concepts which is important here.

• The Contact Process of sulphur trioxide production must be economically efficient for the manufacture of the important industrial chemical sulphuric acid.

• In the Contact Process reactor the sulphur dioxide is mixed with air (the required stoichiometric volume/mole SO₂:O₂ ratio is 2:1, in practice 1–2:1 is used) and the mixture passed over a catalyst of vanadium(V) oxide V₂0₅ at a relatively high temperature of about 450°C and at a pressure of between 1–2 atm. It is an exothermic oxidation and is known as the .

• (1) In the reactor the sulphur dioxide is oxidised in the reversible exothermic reaction ...

  •   2SO_2(g) + O_2(g) 2SO_3(g) (ΔH = –196 kJ mol^–1)

  • (see also Le Chatelier's example 1.4.8)

  • Kp =	pSO32
    	–––––––––––
    	pSO22 pO2

  • From Le Chatelier's Principle, an increase in temperature moves the equilibrium to the left, the heat absorbing endothermic direction to minimise temperature change, hence K_p will decrease with increase in temperature.

• The reaction forms sulphur trioxide and the equilibrium is very much to the right hand side because  

  • Despite the reaction being exothermic a relatively high temperature is used which favours the reverse reaction R to L, from the energy change equilibrium rule, i.e. increasing temperature shifts the equilibrium in the endothermic direction. However the value of K_p is high enough to give a 99% yield.

  • The reaction is favoured by high pressure (pressure equilibrium rule, 3 => 2 gas molecules), but only a small increase in pressure is used to give high yields of sulphur trioxide, because the right hand side is energetically very favourable (quite exothermic and high K_p)

  • The use of the V₂O₅ catalyst ensures a fast reaction without having to use too a higher temperature which would begin to favour the left hand side too much (energy change equilibrium rule), but remember a catalyst does not affect the % yield or equilibrium concentration of SO₃, you just get there more economically faster.

  • Multiple reactor beds are used to ensure the maximum % conversion and heat exchange systems are used to control the temperature, and pre–heat incoming reactant gases.

  • Good anti–pollution measures need to be in place since the sulphur oxides are harmful and would cause local acid rain! To help this situation AND help the economics of the process the residual SO₂ is kept to the minimum by the reaction conditions describe above.

• (2) The sulphur trioxide is dissolved in concentrated sulphuric acid to form fuming sulphuric acid (oleum).

  • SO_3(g) + H₂SO_4(l) ==> H₂S₂O_7(l)

• (3) Water is then carefully added to the oleum to produce concentrated sulphuric acid (98% H₂SO₄).

  • H₂S₂O_7(l) + H₂O_(l) ==>  2H₂SO_4(l) 

  • If the sulphur trioxide is added directly to water an acid mist forms which is difficult to contain because the reaction to form sulphuric acid solution is very exothermic with a big K value!

3.4 Methanol production

• Methanol is an important alcohol used in fuel mixtures, making methyl esters and oxidation to methanol (formaldehyde) to make urea–formaldehyde resin glues.

• It is manufactured directly from synthesis gas (CO + H₂, see section 3.2 above).

• CO_(g) + 2H_2(g) CH₃OH_(g) (ΔH = –90 kJ mol^–1)

•  

  Kp =	pCH3OH
  	––––––––––
  	pCO pH22

• From Le Chatelier's Principle, an increase in temperature moves the equilibrium to the left, the heat absorbing endothermic direction to minimise temperature change, hence K_p will decrease with increase in temperature.

• The reaction is carried out at 250^oC, over a Cu–ZnO–Al₂O_3(alumina) catalyst at a pressure of 5–10 x 10⁶ Pa (5–10MPa, 50–100 atm).

• Theoretically the reaction is favoured by high pressure (3 gas mol ==> 1 gas mol) and low temperature.

• In practice a high pressure is used to give an acceptable yield in accordance with Le Chatelier's Principle, but a moderately high temperature plus a catalyst, are employed to get an economic production rate.

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Chemical Equilibrium Notes Index