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Equilibria
Written by Tim Sheppard MBBS BSc. Last updated 9/11/10

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What is an equilibrium?

An equilibrium is basically a system where a reaction occurs both forwards and backwards, so the product and the reactants are formed at the same rate. This means that neither amounts change. It is often referred to as a dynamic equilibrium, because both reactions are still happening, it's just they replace each other. It may seem like quite a complicated concept but it's important to understand for many other aspects of science, especially chemistry, and once you get it, you get it! The example often used to demonstrate this is the Haber Process.

Ammonia (NH3) is formed from nitrogen and hydrogen in their gaseous forms (N2 and H2 respectively). This is given by the equation:

3H2(g) + N2(g) → 2NH3(g)

The reaction is exothermic, and is speeded up by an iron catalyst.

However, in this reaction, ammonia will spontaneously, automatically, split up again into its components nitrogen and hydrogen, given by the equation:

2NH3(g) → 3H2(g) + N2(g)

The reaction is endothermic, and again will be speeded up by an iron catalyst.

When both of these are put together, an essentially very simple system is set up, where nitrogen and hydrogen combine to form ammonia, and ammonia is then split up to form nitrogen and hydrogen. But how, then, is ammonia produced?

The position of an equilibrium is affected by many things. This means that the relative concentrations of reactant and products can differ. Although the rate of the forward reaction is the same as the rate of the reverse reaction, you can still start off with more ammonia. You might start off with a system which is ram-packed full of ammonia, with 90% of the volume taken up by it, and only 10% contains nitrogen and hydrogen. Equilibria are affected by concentration, however. If there is more ammonia, the equilibrium will shift to try and make things equal again. This means the reverse reaction will speed up a bit, until the concentrations are where they want to be, and then it will return to a constant dynamic equilibrium - forward and reverse reactions being the same.

However, equilibria are also affected by temperature. In the above reaction, the reverse reaction was endothermic. This means that it requires energy for the reaction to work - it needs energy to make up the deficit. For all the bonds to be broken, it requires a certain amount of energy, which is not supplied by the formation of the products' bonds, therefore if the system has a greater temperature (i.e. is hotter), it is supplied with more energy and therefore will enable the reaction to occur. The forward reaction was exothermic, which means it supplies energy - it has no need for the higher temperature. Therefore, if the temperature is increased, the equilibrium will shift to try and make things cooler again, to keep everything back to normal, so the reverse reaction, which requires energy, will speed up a bit to 'use up' the energy in the form of breaking some bonds, until conditions are considered back to normal, and then it will return to a constant dynamic equilibrium - forward and reverse reactions being the same. However, since the reverse reaction speeded up, the concentration of the reactants (nitrogen and hydrogen) will have increased. Although at the end the forward and backward reactions are the same, the relative amounts have changed.

Similarly equilibria are affected by pressure. In the above reaction, the forward reaction starts with four molecules of gas (3 hydrogen, 1 nitrogen) and finishes with only two. The reverse reaction obviously starts with two and ends with four. This means that if the system wanted to reduce the pressure, it simply needs to speed up the forward reaction a bit until there are fewer molecules of gas in total. This is what happens if the pressure wre increased; then it returns to its dynamic equilibrium, only once again the relative concentrations will have changed; there will be more ammonia. Even though the forward and reverse reactions occur at the same rate, the concentration of ammonia will have increased in an effort to decrease the pressure in the system.

The position of an equilibrium is not affected by a catalyst. A cataylst will increase both the forward reaction and the reverse, and therefore make no difference to the relative concentrations; however, if a change is made to the pressure, temperature or concentrations, a catalyst will make sure that it sorts itself out quickly, and gets to its dynamic equilibrium.

In practice, if a factor such as pressure, temperature or concentration is changed, the equilibrium will automatically shift to oppose that change - if the temperature is increased, the endothermic reaction is favoured to 'use up' the energy; if the concentration of, say, nitrogen is increased, the forward reaction is favoured to use up the nitrogen and return everything to normal. Although the rate may not differ, the relative concentrations of the reactants can be changed by altering the conditions. The shifting of an equilibrium to oppose any change in conditions is known as Le Chatelier's Principle. In each case, doing the opposite will have the opposite effect (i.e. decreasing pressure will cause an increase in nitrogen and hydrogen as the equilibrium favours the reverse reaction in an attempt to raise the pressure again).

In industry, companies want to produce as much ammonia for as little cost as possible. Reactions generally happen quicker at higher temperatures, but this will favour the reverse reaction, so a compromise of about 450?C is used. A high pressure will favour ammonia production, but will cost a lot, so 200 atmospheres - not terrible high - is used. To help matters more, the products of the reaction are cooled so that the ammonia can be tapped off while nitrogen and hydrogen are still gases; the equilibrium will shift to oppose the reduction in ammonia concentration, and give a greater yield or 'value for money' for the manufacturer.


What is an equilibrium constant?

So an equilibrium is where the forward reaction is happening just as quick as the backward reaction. However, as explained above, there might be more of the reactants than the products, because of the position of the equilibrium. If you start off with a simple, established dynamic equilibrium (so everything's happy as it is): A + B → C + D.

Then add loads of A and B, the equilibrium will shift to oppose the change. You've tried to change it so that there's loads of A and B - so the equilibrium will try to shift to oppose the change that you've just put in. Once the shift has happened, the amounts will stop changing because the forward reaction is happening at the same rate as the backward reaction.

To understand the equilibrium constant, you need to understand the concept of the position of an equilibrium. Remembering that altering the conditions will cause the equilibrium to shift and oppose the change (Le Chatelier's Principle), then during that shift the amount of reactants and products will change. It's quite difficult to follow, but ultimately the system will still be in equilibrium after a change, it's just that the proportions of reactants may be different. Put simply, this difference in proportions indicates the position of the equilibrium.

To give a measure of the position of the equilibrium, we simply need to consider something that considers the relative proportions of the reactants and products. Therefore we have come up with something called the equilibrium constant. Let's imagine we have the following reaction:

aA + bB ↔ cC + dD

That is, 'a' molecules of substance 'A' react with 'b' molecules of substance 'B' to produce 'c' molecules of substance 'C' and 'd' molecules of substance 'D', where a, b, c and d could be any numbers. This system is in equilibrium (i.e. c molecules of C react with d molecules of D to produce a molecules of A and b molecules of B as well), and so the reaction doesn't just happen and then finish. If we want to know the position of the equilibrium (so that we have a good idea of which direction is more 'dominant') we can find out the concentrations of the reactants and products, and produce an equilibrium constant, Kc.

Although the image on the left shows the formula, the equilibrium constant when put into words is as follows: the product of the concentrations of each product, each expressed to the power of the number of molecules involved, divided by the product of the concentrations of each reactant, each expressed to the power of the number of molecules involved.

If there is lots of the product (i.e. the forward reaction is dominant) then the value of Kc will be large (in this case, even '2' could be considered large) and the equilibrium is said to lie to the right. If there is more of the product, then the backward reaction is more dominant - the value will be small (e.g. 0.05) and the equilibrium is said to lie to the left.

If this is applied to to the formation of ATP, we consider that 1 molecule of AMP and 2 phosphate groups react to produce 1 molecule of ATP; so, Kc is given by the concentration of ATP, divided by the product of the concentration of AMP and the concentration of phosphate squared. That is, using the concentration of AMP multiplied by the concentration of phosphate squared, to divide the concentration of AMP.

(Note that the concentrations of ATP and AMP are not raised to any power, as there is just one molecule of each involved - it is 'to the power of 1'.)

You can see that in the case of Kc - in, indeed in Kp to follow - the order that the reaction is expressed is important. It must be clear which way round you're working it out, because you'll get a different result if you write the reaction in reverse(!).

At the top, however, we quite clearly have a reaction that involves gases. The above equilibrium constant is perfectly fine when dealing with substances in solution (e.g. ATP(aq)), but in the case of gases, we use a slightly different measure. Let's take the following reaction:

aA(g) + bB(g) ↔ cC(g) + dD(g)

'a' molecules of substance 'A' react with 'b' molecules of substance 'B' to produce 'c' molecules of substance 'C' and 'd' molecules of substance 'D', where a, b, c and d could be any numbers, and all of the substances involved are gases. This system is in equilibrium (i.e. it happens in reverse too; c molecules of C react with d molecules of D to produce a molecules of A and b molecules of B as well), and so the reaction doesn't just happen and then finish. If we want to know the position of the equilibrium (so that we have a good idea of which direction is more 'dominant') we can find out the partial pressures of the reactants and products, and produce an equilibrium constant, Kp.

Although the image shows the formula, the equilibrium constant when put into words is as follows: the product of the partial pressures of each product, each expressed to the power of the number of molecules involved, divided by the product of the partial pressures of each reactant, each expressed to the power of the number of molecules involved.

If there is lots of the product (i.e. the forward reaction is dominant) then the value of Kp will be large and the equilibrium is said to lie to the right. If there is more of the product, then the backward reaction is more dominant - the value will be small and the equilibrium is said to lie to the left.

If this is applied to our Haber process equilibrium at the top of the page (as shown in the image), we consider that 3 molecules of hydrogen and 1 molecule of nitrogen react to produce 2 molecules of ammonia; so, Kp is given by the partial pressure of ammonia squared, divided by the product of the partial pressure of hydrogen cubed and the partial pressure of nitrogen.


Further Reading