Dynamic equilibrium, Le Chatelier's principle and industrial compromise

Both directions at once

A reaction that appears to have stopped may still be running, in both directions at once and at the same rate. An unopened bottle of sparkling water shows it. Nothing fizzes, the pressure inside holds steady, and it would look the same after a year on a shelf. Inside, carbon dioxide molecules are leaving the water for the gas above it all the time, and molecules from that gas are dissolving back into the water at the same rate. Unscrew the cap and the gas above escapes into the room. Dissolving can no longer keep pace with escaping, and the drink fizzes until it is flat.

CO₂(g) ⇌ CO₂(aq)The ⇌ arrow shows a change that runs in both directions at once.

A reversible reaction is one that can go in either direction under the same conditions. Hydrogen and iodine show it well. Hydrogen sealed with purple iodine vapour in a flask at 490 °C loses the purple as colourless hydrogen iodide forms, but it never fades completely: after a few minutes the colour stops changing. Twice that amount of pure hydrogen iodide, sealed in an identical flask at the same temperature, turns purple: the colour deepens and stops at the same shade.

H₂(g) + I₂(g) ⇌ 2HI(g)The forward reaction runs left to right, the reverse reaction right to left.

Describe the drawing

Two graphs of concentration against time for hydrogen, iodine and hydrogen iodide at 490 degrees Celsius. On the left the run starts from hydrogen and iodine at 0.0100 mol dm⁻³ each: their shared amber curve falls and levels at 0.00228 while the cyan hydrogen iodide curve rises from zero and levels at 0.0154. On the right the run starts from hydrogen iodide alone at 0.0200: it falls to 0.0154 while hydrogen and iodine rise to 0.00228. In both, a dashed line at eight minutes marks equilibrium, after which the shaded region shows constant, unequal concentrations at the same heights in both panels.

Describe the drawing

Rate against time for the hydrogen and iodine equilibrium at 490 degrees Celsius, drawn in four stages from a start of hydrogen and iodine only. The amber forward rate starts at 1 and falls as the reactants are used up; the cyan reverse rate starts at zero and rises as hydrogen iodide builds up. Printed values at half a minute, 2, 4 and 10 minutes show the gap closing until both rates level at the same value, about 0.05, at equilibrium, where neither is zero.

The rates explain the levelling. At the start of the first run only the forward reaction can happen, and it is fast because hydrogen and iodine are at their highest concentrations. As they are used up the forward rate falls. Hydrogen iodide builds up, so the reverse reaction, which started from nothing, speeds up. When the two rates are equal, every molecule of hydrogen iodide made is matched by one broken down somewhere else in the flask, and no concentration changes any more.

That state is a dynamic equilibrium. Dynamic means both reactions carry on. The evidence comes from an isotope: add a little iodine made from radioactive iodine-131 to a mixture already at equilibrium, and within minutes the radioactivity turns up in the hydrogen iodide too, although the concentrations of all three substances have not changed. Iodine atoms are still crossing from one side of the equation to the other.

Equal rates do not mean equal amounts. At 490 °C the hydrogen and iodine mixture settles with about three-quarters of the iodine turned into hydrogen iodide; other reactions settle with almost all product or almost all reactant. The position of equilibrium describes those proportions. An equilibrium that lies to the right has mostly products in it; one that lies to the left has mostly reactants.

An equilibrium needs a closed system, one that no substance can enter or leave. Limestone heated in a sealed container decomposes only until the carbon dioxide reaches a fixed pressure, and from then on calcium oxide and carbon dioxide recombine as fast as calcium carbonate breaks down. A lime kiln is open at the top. The carbon dioxide is carried off with the hot gases, the reverse reaction has nothing to work with, and all the limestone decomposes.

CaCO₃(s) ⇌ CaO(s) + CO₂(g)In a sealed container. In an open kiln the arrow becomes →.

Reversible reaction

A reaction that can proceed in both the forward and the reverse direction under the same conditions.

Dynamic equilibrium

The state of a reversible reaction in a closed system in which the forward and reverse reactions proceed at equal rates, so the concentrations of reactants and products remain constant.

Closed system

A system that no substance can enter or leave, although energy may be transferred to or from it.

Open system

A system that substances can enter or leave, so a reversible reaction in it cannot reach equilibrium.

Position of equilibrium

The relative proportions of reactants and products in a mixture at equilibrium.

Le Chatelier's principle

One rule predicts which way the position of an equilibrium moves when the conditions change. It gives the direction of the shift; the reason for the shift comes from the equilibrium constant. The rule carries the name of Henri Le Chatelier, who stated it in 1884.

Le Chatelier's principle

If a system at equilibrium is subjected to a change in conditions, the position of equilibrium shifts in the direction that opposes the change.

Adding a substance shifts the position away from it, and removing one shifts the position towards it. Yellow chromate(VI) ions and orange dichromate(VI) ions are in equilibrium in water. A few drops of dilute sulfuric acid turn the solution orange: the forward reaction uses up the extra hydrogen ions, so the position shifts to the right. Sodium hydroxide removes hydrogen ions as water, and the solution goes back to yellow as the position shifts left to replace them.

2CrO₄²⁻(aq) + 2H⁺(aq) ⇌ Cr₂O₇²⁻(aq) + H₂O(l)Yellow chromate(VI) on the left, orange dichromate(VI) on the right.

A change of pressure moves only equilibria involving gases. The pressure of a gas mixture depends on how many molecules it holds in its volume. When the pressure is raised, the position shifts towards the side with fewer moles of gas, because forming fewer molecules lowers the pressure again. In the Haber equilibrium four moles of gas on the left become two on the right, so a higher pressure gives more ammonia. In the hydrogen iodide equilibrium there are two moles of gas on each side, and pressure has no effect on the position at all. Write 'fewer moles of gas' rather than 'fewer moles': a solid or liquid in the equation does not count.

Describe the drawing

A gas syringe of nitrogen dioxide and dinitrogen tetroxide animated in three stages. At equilibrium the box holds 20 linked pairs for dinitrogen tetroxide and 10 amber discs for nitrogen dioxide, with Q equal to Kc, 0.0100. The piston then halves the volume: the same molecules, every concentration doubled, the brown deeper and Q 0.0200, above Kc. Finally two nitrogen dioxide molecules pair up, leaving 21 pairs and 8 singles, concentrations 0.0854 and 0.0292, and Q back at Kc: the position has moved to the side with fewer moles of gas.

Temperature acts through the enthalpy change. A reversible reaction is exothermic in one direction and endothermic in the other, by the same amount. Raising the temperature shifts the position in the endothermic direction, which takes in heat and opposes the rise. Lowering it shifts the position in the exothermic direction. The sign of ΔH for the forward reaction settles it: if it is negative, heating moves the position to the left and lowers the yield of products. Name the direction, 'the endothermic direction', in an answer; 'the reaction uses up the heat' does not say which way the position moves.

Cobalt(II) chloride gives a clear laboratory test of the temperature rule. In water the cobalt(II) ions are pink [Co(H₂O)₆]²⁺; at a high chloride concentration they become blue [CoCl₄]²⁻, and a solution holding plenty of each looks purple.

[Co(H₂O)₆]²⁺(aq) + 4Cl⁻(aq) ⇌ [CoCl₄]²⁻(aq) + 6H₂O(l)Pink on the left, blue on the right.

Divide one purple solution between three boiling tubes. Stand one in water at about 80 °C, one in iced water, and leave the third in the rack. The hot tube turns blue and the iced one pink, and each goes back to purple as it returns to room temperature, which shows a shift in an equilibrium and not a decomposition. The third tube is the control: each colour is judged against it, because the eye judges a shade badly on its own.

Heating favours the blue side, so the forward reaction is endothermic. Concentration can be tested on the same solution. Concentrated hydrochloric acid added drop by drop turns it blue, as the extra chloride ions shift the position right; water turns it pink again by diluting the chloride. Questions set the same reasoning on coloured equilibria never met before: the colour that appears names the side the position has moved to. Cobalt(II) chloride is toxic and the acid corrosive, so gloves and eye protection are worn.

A catalyst provides an alternative route with a lower activation energy, lowering it by the same amount for the forward and the reverse reaction, so it speeds both up by the same factor. The position of equilibrium does not move. What changes is the time taken to get there, and in a factory a shorter time means more product from the same plant.

Catalyst

A substance that increases the rate of a reaction without being changed in chemical composition or amount, by providing an alternative reaction route with a lower activation energy.

The Haber process and the Contact process: yield against rate

About 180 million tonnes of ammonia are made each year by the Haber process, most of it for fertiliser. Nitrogen comes from the air and hydrogen from natural gas, and they react over an iron catalyst.

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)ΔH = −92 kJ mol⁻¹

Le Chatelier's principle gives a clear answer about yield. The forward reaction is exothermic, so a low temperature shifts the position to the right. Four moles of gas become two, so a high pressure shifts it to the right as well. At 200 °C and 1000 atm the equilibrium mixture would be almost all ammonia.

Describe the drawing

Percentage of ammonia in the equilibrium mixture plotted against pressure from 0 to 400 atmospheres, one rising curve for each of four temperatures. The 300 degree curve is highest, reaching 76 percent at 400 atmospheres; the 400, 450 and 500 degree curves lie successively lower, the 500 degree curve reaching only 32 percent. A ringed dot on the cyan 450 degree curve at 200 atmospheres marks the typical operating point, about 27 percent ammonia at equilibrium.

The plant runs at about 450 °C and 200 atm instead, and the gas leaving the converter is only about 15% ammonia. The temperature is a compromise between yield and rate. At 200 °C few collisions have the activation energy, even on the catalyst, and equilibrium would take far too long to reach. At 450 °C the equilibrium yield is lower, but the reaction is fast enough to make far more ammonia each hour.

The pressure is a compromise between yield and cost. A higher pressure would raise both the yield and the rate, but compressing gas uses a great deal of electrical energy, and every pipe, valve and vessel needs thicker walls to hold it. A leak of hot hydrogen at very high pressure is a serious hazard. Above about 200 atm the extra ammonia no longer pays for the extra plant and energy.

Fifteen per cent per pass is acceptable because nothing is wasted. The hot mixture is cooled, the ammonia condenses to a liquid long before nitrogen or hydrogen would and is run off, and the unreacted gases are pumped back to the converter. Over many passes about 98% of the nitrogen and hydrogen ends up as ammonia.

Describe the drawing

A flow diagram of the Haber process. Nitrogen from air and hydrogen from natural gas join and pass, in a 1 to 3 ratio, into a compressor at 200 atmospheres, then a reactor with an iron catalyst at 450 degrees Celsius. Gas leaving the reactor, about 15 percent ammonia, goes to a cooled condenser, where liquid ammonia drains out downwards. A cyan return line runs from the condenser along the bottom and back up to rejoin the feed before the compressor, carrying the unreacted nitrogen and hydrogen round the loop again.

Energy is the largest running cost. Ammonia plants use about 1 to 2% of the world's energy supply, most of it to make the hydrogen and to compress the gases. The forward reaction gives out heat, and the plant uses it to raise steam rather than losing it to the air. A catalyst that worked fast at a lower temperature would give a higher yield on each pass at the same rate, so less gas would go round the loop to be recompressed, and a lower pressure might do. That is why new catalysts are still being sought for a process over a century old.

The Contact process for sulfuric acid makes the opposite decision about pressure. Its key step, the oxidation of sulfur dioxide, is also exothermic with fewer moles of gas on the right, so Le Chatelier's principle again asks for a low temperature and a high pressure.

2SO₂(g) + O₂(g) ⇌ 2SO₃(g)ΔH = −197 kJ mol⁻¹

The temperature is about 450 °C, the same compromise as in the Haber process: below about 400 °C the vanadium(V) oxide catalyst works too slowly to be useful. The pressure is only 1 to 2 atm, just enough to push the gas through the plant. The gas passes over three or four beds of catalyst and is cooled between them, because the heat released would otherwise warm the gas and shift the position left. Air supplies oxygen in excess, which shifts the position right. By the last bed more than 99% of the sulfur dioxide has been converted, so compression would buy almost nothing and would cost a great deal.

Equilibrium yield

The proportion of the reactants converted into products once the reaction mixture has reached equilibrium.

Compromise conditions

Conditions chosen to give an acceptable equilibrium yield at an acceptable rate and cost, where the conditions for the highest yield would make the reaction too slow or the plant too expensive.

Ethanol and methanol

Ethanol for industry is made by hydrating ethene with steam. The forward reaction is exothermic, and two moles of gas become one.

C₂H₄(g) + H₂O(g) ⇌ CH₃CH₂OH(g)ΔH = −45 kJ mol⁻¹, over a phosphoric acid catalyst on silica

The conditions are about 300 °C and 60 to 70 atm. The temperature is again a compromise between yield and rate. The pressure is held down for two reasons: the cost of compression, and the fact that at high pressure ethene polymerises to poly(ethene), which wastes the feedstock. Only about 5% of the ethene reacts on each pass, so the ethanol is condensed out and the ethene recycled, giving an overall conversion of about 95%.

Methanol, a fuel and the starting point for many plastics, is made from carbon monoxide and hydrogen, and the pattern is the Haber pattern again.

CO(g) + 2H₂(g) ⇌ CH₃OH(g)ΔH = −91 kJ mol⁻¹

It runs at about 250 °C and 50 to 100 atm over a catalyst of copper and zinc oxide. Three moles of gas become one, so pressure helps the yield. The reaction is exothermic, so a low temperature helps the yield and slows the rate. An active catalyst is what allows a lower temperature here than in the Haber process.

Four things settle the conditions for any of these plants: the number of moles of gas on each side, the sign of ΔH, the rate at the temperature the yield prefers, and the cost of each extra atmosphere. Le Chatelier's principle settles the first two. The catalyst, the price of energy and the strength of steel settle the rest.

Other boards: the practical investigation and the named processes

OCR lists the practical investigation of an equilibrium shift as a statement of its own, 3.2.3(d). The cobalt(II) chloride tubes and the chromate and dichromate colours are the usual choices, and an OCR question can ask for the method in full: the control tube kept at room temperature, the hot and iced water baths, the return to the starting colour that shows a reversible shift, and the hazards of cobalt(II) chloride and concentrated hydrochloric acid.

Cambridge names the Haber process and the Contact process in its specification and expects the conditions for each, the reason for each condition, and the reason a compromise is needed. The table of the two processes holds what a Cambridge answer needs, including the two catalysts and the cooling between the Contact process beds.

Edexcel teaches the principle, the effect of a catalyst and the industrial compromise in Topic 10, alongside Kc, so its questions often join a prediction of the shift to a statement about whether Kc changes. The answer is the one Kc teaches: only temperature changes the constant.