Contents
At the end of this section you will be able to
Equilibrium constant
Many chemical reactions are capable of proceeding in both directions and if contained in a closed system, will come to equilibrium. The equilibrium state for any reaction is a function of the concentrations of the reactants and products. For any equilibrium reaction, an equilibrium constant is defined. For the reaction
The equilibrium constant, Kc is defined as
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2.1 |
Where cA, cB, cC & cD are the concentrations of A, B, C & D at equilibrium and the exponents a, b, c & d are the stoichiometric proportions of the four components given by the reaction equation.
If the reaction is a gas reaction, the proportions of the components can be expressed by the partial pressures of the components and an alternative equilibrium constant, Kp may be defined
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2.2 |
Special Circumstances
If one of the reactants or products is a solid, then, providing some solid is present at equilibrium, the concentration of the solid is defined as 1.0
Similarly, if a reaction takes place in aqueous solution and water is one of the reactants or products, the concentration of the water is also treated as 1.0.
Disturbing Equilibrium – LeChatalier’s principle
If a system is in equilibrium and a disturbance is applied, the system will react to try and restore equilibrium. This is known as LeChatalier’s principle.
This means that the position of equilibrium can be affected by temperature, pressure, change in concentration, addition or removal of reactants or products. The effect is always to try to restore equilibrium so each case must be treated on its merits.
The significance of the equilibrium constant
The magnitude of the equilibrium constant can give information about a reaction. If the value of the equilibrium constant is very large, the equilibrium will be well over to the right and the reaction is sometimes referred to as "product favoured". Conversely, if the equilibrium constant is very small, the equilibrium is well over to the left and the reaction is "reactant favoured". The terms product and reactant favoured are in fact relative as it depends which way the reaction equation is written.
Relationship between equilibrium constant and rate constants
Chemical equilibrium is a dynamic equilibrium, that is both forward and reverse reactions are continually occurring. Equilibrium occurs, therefore, when the rate of the forward reaction is equal to the rate of the reverse reaction. This means that the equilibrium constant and the rate constant must be related in some way. This can most easily be shown for a simple first order system.
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2.3 |
Assuming a first order reaction, the rate equations for the forward and reverse reactions are.
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2.4 |
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2.5 |
At equilibrium, the rate of the forward reactions are the same, i.e.
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2.6 |
This means that
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2.7 |
Rearranging gives
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- the equilibrium constant |
2.8 |
Thus, for a simple reaction system, the equilibrium constant is equal to the ratio of the rate constants.
Equilibrium Constant and the Second Law of Thermodynamics
From the second law of thermodynamics, we can predict that a reaction will occur spontaneously if the free energy change for the reaction is negative. For a simple reversible reaction, for example
A ó B
If this reaction is to occur spontaneously, the free energy change for the reaction A à B must be negative, but so also must the free energy change B à A which appears to be a contradiction. However if we plot a graph of free energy vs concentrations of A and B we get a curve something like this (fig 1)
Fig. 1. Free energy at equilibrium
The free energy change between either pure A or pure B and the equilibrium condition is negative, so the reaction will proceed from either end towards equilibrium. However, at equilibrium, it can be seen that the slope of the line of free energy is zero, so that equilibrium occurs when the rate of free energy change is zero.
It can be shown that the relationship between the equilibrium constant and the free energy change for the overall reaction Aó B under standard conditions is
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2.13 |
If the reaction takes place under conditions other than standard conditions, the actual D G for the reaction is
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2.14 |
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Produced by Geoff Walker
Last modified 14 October 2002
