Chapter 6Equilibria

Since the reaction does not cease at equilibrium, rather it keeps on going in both directions, it is called dynamic equilibrium.

The decomposition of water is endothermic (it absorbs the 571.6 kJ that is released when 2 mol of water form). Heating favours the endothermic direction, so increasing the temperature drives the reaction forward: more water decomposes into hydrogen and oxygen. (Water decomposes noticeably only at very high temperatures, above about 2000 °C.)

A reversible reaction may be forced to go to completion if one or all of the products are withdrawn from the reaction mixture as soon as they are formed.

Use a catalyst: a catalyst increases both the rates of forward and backward reactions, so it decreases the time taken by the reaction to attain the state of equilibrium. Raising the temperature also speeds up both reactions (though it may shift the equilibrium position).

No effect. There are 2 moles of gas on the left (1 N₂ + 1 O₂) and 2 moles on the right (2 NO). Change of pressure disturbs only those gaseous reactions in which the number of moles of the reacting gases is different from the number of moles of the gases produced.

In the water cycle (and in any closed container), water evaporates from seas, lakes and ice, and vapour condenses back as clouds, rain and dew; ice melts and water freezes. In a closed bottle the rates of evaporation and condensation become equal: H₂O(l) ⇌ H₂O(g). In a glass of ice-water at 0 °C, melting and freezing go on at equal rates: H₂O(s) ⇌ H₂O(l). The amounts stay the same although molecules keep changing state.

At first the gas is colourless. As some N₂O₄ changes to NO₂, a brown colour appears and deepens. NO₂ also combines back into N₂O₄; once the two rates become equal, the amount of NO₂ stops changing, and the colour stays a constant light brown. It never becomes dark brown, because N₂O₄ is never used up.

Compressing raises the pressure. The equilibrium moves to the side with fewer moles of gas: 1 mole (PCl₅) against 2 moles (PCl₃ + Cl₂). So the backward reaction is favoured and more PCl₅ forms.

Adding a product increases its concentration. To restore equilibrium, Cl₂ reacts with PCl₃ to form more PCl₅: the backward reaction is favoured, until a new equilibrium is reached.

The forward reaction is endothermic, so heating favours it: more PCl₅ decomposes into PCl₃ and Cl₂.

A reaction which goes to completion and moves in the forward direction only is called an irreversible reaction. If stoichiometric amounts are used, no reactant is left. Example: NaCl(aq) + AgNO₃(aq) → AgCl(s) + NaNO₃(aq).

A reaction which moves in both the forward and backward directions under the same conditions is called a reversible reaction. It is shown by ⇌. Example: N₂ + 3H₂ ⇌ 2NH₃.

As soon as products form, they react to give back the reactants. At any time all the species are simultaneously present in the reaction mixture, so the reactants are never used up completely (in a closed system).

If either one of the products is withdrawn from the reaction mixture or, being a gas, it escapes into the atmosphere. CaCO₃ heated in an open vessel decomposes completely, because CO₂ escapes.

Open: CO₂ escapes as soon as it forms, and the reaction goes to completion. Closed: CO₂ reacts with CaO to give back CaCO₃, and equilibrium is set up.

Yes, physical changes may also be reversible in nature. Water ⇌ ice and water ⇌ steam; the book gives the heating of blue copper sulphate (CuSO₄·5H₂O ⇌ CuSO₄ + 5H₂O).

It loses its five water molecules and becomes white anhydrous copper sulphate. When white anhydrous copper sulphate absorbs moisture from the atmosphere, it turns blue again.

With limited moisture it is first converted into a dihydrate which is purple. The dihydrate then absorbs four more water molecules to become the hexahydrate, which is pink.

White anhydrous copper sulphate turns blue, and blue cobalt chloride (paper) turns pink, when water is added. These changes show that a liquid contains water.

The fixed number of water molecules that are part of the crystal of a hydrated salt: five in CuSO₄·5H₂O, six in CoCl₂·6H₂O. It gives the crystals their shape and colour and is driven off by heating.

The state of a reversible reaction at which the rate of the forward reaction becomes equal to the rate of the backward reaction. The number of reactant molecules disappearing in the forward reaction equals the number formed in the reverse reaction.

Because the reaction does not cease at the state of equilibrium; rather it keeps on going in both directions. It only appears as if nothing is happening.

The concentrations of the reacting species (reactants and products) remain constant at equilibrium. They are not necessarily equal.

The forward rate is greatest at the start and decreases as reactants are used up; the backward rate is zero at the start and increases as products build up. At equilibrium they are equal.

The time a reaction takes to attain dynamic equilibrium depends upon the nature of the reaction and the conditions at which it is performed. For very slow reactions it may take years; ammonia formation at 400 °C with a catalyst takes minutes.

Not if a product is a gas: it escapes, so the backward reaction cannot occur and the reaction goes to completion. A dynamic equilibrium needs a closed system, where nothing enters or leaves.

The concentration of N₂ increases and the reaction no longer maintains equilibrium. Nitrogen reacts with hydrogen to produce more ammonia until a new equilibrium is reached, with concentrations different from before.

Its concentration decreases. To restore equilibrium, more nitrogen and hydrogen react to produce ammonia.

The formation of ammonia is exothermic (ΔH negative); the reverse reaction is endothermic. Increasing the temperature pushes the reaction in the backward direction. Decreasing the temperature drives it forward.

4 moles of reacting gases produce 2 moles of product gas. When the pressure is increased, the reaction moves to the side with fewer moles, i.e. forward.

Gas reactions with the same number of moles of gas on both sides, such as N₂ + O₂ ⇌ 2NO and H₂ + I₂(g) ⇌ 2HI(g), and reactions with no gases at all.

CO₂ is dissolved under pressure: CO₂(g) ⇌ CO₂(aq). Opening the can lowers the pressure, the equilibrium moves towards the gas, and bubbles of CO₂ come out.

A catalyst increases both the rates of forward and backward reactions. So it decreases the time taken by the reaction to attain the state of equilibrium. It does not change the amounts present at equilibrium.

The ability of ammonia gas to be converted into its liquid form easily is used to drive the reaction to completion. Ammonia is liquefied and removed, and the unreacted N₂ and H₂ are recycled through the catalyst.

It is used as a thinner in the paint industry. C₂H₅OH + CH₃COOH ⇌ CH₃COOC₂H₅ + H₂O; the yield is improved by removing water from the reaction mixture as soon as it is formed.

Coal reacted with steam gives water gas: C + H₂O → CO + H₂. These products then react by a reversible reaction called catalytic methanation to yield methane: CO + 3H₂ ⇌ CH₄ + H₂O. Pakistan's Thar coal could be used this way.

Irreversible

A reaction is irreversible when its products cannot easily turn back: a product leaves the mixture (a precipitate such as AgCl, or a gas that escapes), or the reaction gives out so much energy that the products sit far below the reactants and the backward reaction would need a huge activation energy (combustion).

Reversible

A reaction is reversible when the products stay in contact with each other (a closed system) and the activation energy of the backward reaction is comparable to that of the forward reaction, so both reactions take place under the same conditions (N₂ + 3H₂ ⇌ 2NH₃).

So CH₄ + 2O₂ → CO₂ + 2H₂O goes only one way; plants reverse it only by using sunlight energy in photosynthesis.

Reversible → irreversible: yes

A reversible reaction goes to completion if one of the products is withdrawn from the reaction mixture or, being a gas, it escapes. Heating CaCO₃ in an open vessel; liquefying NH₃ in the Haber process.

Irreversible → reversible: generally no

Not under the same conditions: burnt fuel cannot be turned back into fuel and oxygen just by changing pressure or temperature. Some reactions that are one-way at one temperature become reversible at another (water starts to split into H₂ and O₂ only above about 2000 °C), and a precipitation can be reversed by redissolving the solid, but these need very different conditions.

In equations a reversible reaction is shown by ⇌ and an irreversible one by →.

Reversible. Ice melts to water when heat is supplied and water freezes back when heat is removed; water evaporates to vapour and vapour condenses back to water. No new substance is formed and the same water is recovered.

In a closed container they set up a dynamic equilibrium: at 0 °C melting and freezing happen at the same rate; in a closed bottle evaporation and condensation happen at the same rate.

The example reaction

If a reversible reaction has attained dynamic equilibrium, it will remain in this state for infinite time unless it is somehow disturbed. We can disturb it on purpose to push it the way we want.

(a) Forward direction

(b) Backward direction

What a catalyst does

A catalyst increases both rates equally: it does not drive the reaction either way; it only makes equilibrium come sooner.

At the start

If a reversible reaction is started by mixing the reactants, the reaction moves in the forward direction only. The concentration of reactants is greatest, so the forward rate is at its highest; there are no products yet, so the backward rate is zero.

As the reaction goes on

Reactants are used up, so the forward rate falls. When enough concentrations of the products are built up, they react to give back the reactants: the backward rate rises from zero.

At equilibrium

The reaction keeps on going in both directions until the rate of the forward reaction becomes equal to the rate of the backward reaction. The number of reactant molecules which disappear in the forward reaction becomes equal to the number formed in the reverse reaction; the same is true for product molecules. From then on the rates stay equal and the concentrations constant.

Dynamic, not stopped

It appears as if nothing is going on, but the reaction has not ceased; it keeps on going in both directions, so this state is called dynamic equilibrium.

Catalyst

A catalyst is a substance that increases the rate of a reaction without itself undergoing any permanent chemical change. It provides a path of lower activation energy.

Effect on the two rates

At dynamic equilibrium the rates of both forward and backward reactions are equal. A catalyst increases both the rates of forward and back reactions of a reversible reaction. It lowers the hump on the energy profile, and the hump is the same hill crossed from either side, so both directions speed up by the same factor.

Effect on time

So if a reversible reaction is carried out in the presence of a catalyst, it will decrease the time taken by the reaction to attain the state of equilibrium. With an iron catalyst at about 400 °C, ammonia formation reaches equilibrium within minutes.

No effect on the position

Why it normally does not

A reversible reaction never goes to completion: the products keep reacting to give back the reactants, and at any time all species are present.

The method

However, it may be forced to go to completion if one or all of the products are withdrawn from the reaction mixture as soon as they are formed, or, being a gas, a product escapes into the atmosphere. With no product to react back, only the forward reaction continues.

Example 1: heating limestone

In an open container, carbon dioxide escapes into the atmosphere as soon as it is formed and the reaction is forced to go to completion. In a closed container, CO₂ reacts with CaO to give back the reactants.

Example 2: Haber process

The ability of ammonia to be converted into its liquid form easily is used to drive the reaction to completion. In this way practically 100 % conversion of N₂ and H₂ to NH₃ is achieved.

Example 3: ethyl acetate

Removing water from C₂H₅OH + CH₃COOH ⇌ CH₃COOC₂H₅ + H₂O as soon as it forms gives a better yield of the ester.

Rule

Every reversible reaction is exothermic in one direction and endothermic, by the same amount, in the other. Raising the temperature favours the endothermic direction; lowering it favours the exothermic direction.

Example 1: ammonia (exothermic forward)

The formation of ammonia is exothermic in the forward direction and endothermic in the reverse direction. The total energy of N₂ and H₂ is higher than that of ammonia. Increasing the temperature at equilibrium pushes the reaction in the backward direction, i.e. to the reactants side. Decreasing the temperature drives the equilibrium forward.

Example 2: PCl₅ (endothermic forward)

Increasing the temperature favours the forward reaction: more PCl₅ decomposes.

Example 3: hydrated salts

Heating blue CuSO₄·5H₂O drives off water (endothermic) to give white CuSO₄; on cooling with moisture, the exothermic reverse change gives the blue salt back.

Speed versus yield

A higher temperature always makes both reactions faster, so equilibrium comes sooner, even when it lowers the yield. That is why ammonia is made at a compromise temperature of about 400 °C with a catalyst.

Observation

When blue copper sulphate pentahydrate is heated strongly, its colour changes to white. When white anhydrous copper sulphate absorbs moisture from the atmosphere, it turns blue again.

Why it is coloured

In the hydrated salt, water molecules are bonded around each Cu²⁺ ion (water of crystallisation). These water molecules change the energies of the copper ion's electrons so that it absorbs red-orange light; the light that is left looks blue.

Why it loses colour

Heating drives off the water molecules. Without them, the Cu²⁺ ion no longer absorbs visible light in the same way, so anhydrous copper sulphate looks white. The crystals also crumble into a powder, because the water held the crystal shape.

Reversibility

Adding water puts the water molecules back around Cu²⁺: the blue colour returns and heat is given out. The same idea explains pink CoCl₂·6H₂O, purple CoCl₂·2H₂O and blue CoCl₂.

The reaction

1. High pressure

4 moles of reacting gases produce 2 moles of product gas. When the pressure is increased, the reaction moves to the side with fewer moles, i.e. forward. The formation of ammonia is thus favoured at high pressure. About 200 atm is used; higher pressure gives more NH₃ but the plant becomes very costly and dangerous.

2. Temperature

The forward reaction is exothermic, so a lower temperature gives a higher yield. But at low temperature the reaction is too slow. About 400 °C is chosen as a compromise between yield and rate.

3. Catalyst

An iron catalyst increases both rates, so equilibrium is reached quickly at this temperature; it does not change the yield.

4. Remove ammonia

The ability of ammonia gas to be converted into its liquid form easily is used to drive the reaction to completion. The mixture is cooled, NH₃ liquefies and is removed, and the unreacted N₂ and H₂ are recycled. In this way practically 100 % conversion of N₂ and H₂ to NH₃ is achieved.

5. Concentration

Keep feeding fresh N₂ and H₂ in the ratio 1 : 3; adding reactant drives the reaction forward.

Irreversible reactions

In a chemical reaction the reactants react to give the products. The reaction continues until all the reactants or one of the reactants is converted into product. NaCl + AgNO₃ → AgCl + NaNO₃ takes place immediately in aqueous solution. The reaction goes to completion, and if stoichiometric amounts are used then no reactant species are present at the end. Such a reaction is called an irreversible reaction. It moves in the forward direction only.

Reversible reactions

In the majority of chemical reactions, however, the reaction does not go to completion. The products react among themselves to give back the reactants under the same conditions. Such a reaction moves in both the forward and backward directions. It is called a reversible reaction and is denoted by ⇌.

One mole of nitrogen reacts with three moles of hydrogen in a closed container to give two moles of ammonia. After its formation, the ammonia decomposes to give the reactants back. The reaction never goes to completion. At any time all three species are present.

Forcing completion

A reversible reaction goes to completion if one of the products is withdrawn or, being a gas, escapes into the atmosphere (CaCO₃ heated in an open vessel).

Physical changes

Like chemical changes, physical changes may also be reversible: copper sulphate pentahydrate turns white on heating and blue again with moisture.

Copper sulphate

Copper sulphate pentahydrate (CuSO₄·5H₂O) is an important salt which is blue in colour. When it is heated strongly, its colour changes to white.

When white anhydrous copper sulphate absorbs moisture from the atmosphere, it turns blue again.

Cobalt chloride

When cobalt chloride hexahydrate (CoCl₂·6H₂O), which is pink, is heated, it is converted into anhydrous CoCl₂, which is blue.

Stepwise rehydration

In the reverse reaction, with limited moisture, anhydrous cobalt chloride is first converted into a dihydrate which is purple. This dihydrate then absorbs four more water molecules to become a hexahydrate, which is pink.

Uses

Both are tests for water: anhydrous CuSO₄ turns blue, cobalt chloride paper turns from blue to pink.

How it is reached

If a reversible reaction is started by mixing the reactants, the reaction moves forward only. After some time, when enough products are built up, they react to give back the reactants. The reaction keeps going in both directions until the rate of forward reaction equals the rate of backward reaction.

Example

N₂ + 3H₂ ⇌ 2NH₃ in a closed vessel at 400 °C with a catalyst: within minutes N₂, H₂ and NH₃ are all present in fixed amounts, while molecules of NH₃ keep forming and decomposing.

Characteristics

Time taken

It depends on the nature of the reaction and the conditions; for very slow reactions it may take years.

At equilibrium

The concentrations of all the participating chemicals are constant at the state of equilibrium.

Adding nitrogen

If we add more N₂ gas, its concentration will increase and the reaction will no longer maintain its state of equilibrium. To restore equilibrium, nitrogen will react with hydrogen to produce more ammonia. This change goes on until a new equilibrium is reached, at which the concentrations will again become constant but different from those of the earlier equilibrium.

Withdrawing ammonia

If some ammonia is withdrawn, its concentration decreases. To restore equilibrium, more nitrogen and hydrogen react to produce ammonia.

Pressure

Change of pressure disturbs the equilibrium of only those gaseous reactions in which the number of moles of reacting gases differs from that of the gases produced. In this reaction 4 moles of reacting gases produce 2 moles of product gas. If the pressure is increased, the reaction moves to the side with fewer moles, i.e. forward. The formation of ammonia is favoured at high pressure.

Why equilibrium matters

Most industrial reactions are reversible. If left alone they give only an equilibrium mixture; by changing the conditions on purpose, chemists push the reaction towards the product and get a high yield quickly.

Haber process (ammonia)

Industrial production of ammonia in the Haber process is a very useful application of chemical equilibrium. Ammonia leads to the important fertilizer urea. High pressure (fewer gas moles), a moderate temperature of about 400 °C, an iron catalyst and liquefying and removing the ammonia give practically 100 % conversion.

Ethyl acetate

Ethyl acetate is commercially very important because it is used as a thinner in the paint industry. One way to get a better yield is to remove water from the reaction mixture as soon as it is formed (concentrated H₂SO₄ or a drying agent).

Lime

CaCO₃ ⇌ CaO + CO₂: heating in an open kiln lets CO₂ escape, giving lime for the steel, glass and paper industries.

Methanation

Coal + steam → CO + H₂ (water gas); CO + 3H₂ ⇌ CH₄ + H₂O over a catalyst: a possible use for Thar coal.