9.5.B - Quantitative Equilibrium


The position of equilibrium or yield of a system can be described qualitatively by making statements about the relative concentrations of reactants and products at equilibrium. Le Chatelier's Principle can also be used to qualitatively predict what happens to the position of equilibrium when changes are made to the concentration of species, the temperature or the pressure of a system.

The equilibrium constant, K, can be calculated using the equilibrium concentrations of reactants and products and provides a numerical measurement of the position of equilibrium for the system. Those systems with constants in the hundreds are said to favour the products and have higher yields. Those with constants in the order of 10-2 are said to favour the reactants and have a low yield. The equilibrium constant provides a way of quantitatively comparing the yield of different reactions.

While the value for the equilibrium constant for any system is independent of the initial concentrations of reactants and products, it is dependant on temperature. The constant will change in response to temperature, depending on whether the reaction is endothermic or exothermic.

In this topic students:

  • Calculate the equilibrium constant for different equilibrium systems
  • Use the equilibrium quotient analyse equilibrium systems and determine how they are approaching equilibrium
  • Analyse the dependance of the equilibrium constant on changing temperatures


Calculating the Equilibrium Constant

There is a relationship between the concentrations of reactants and products, called the equilibrium constant, K, that is independent of the initial concentration of reactants and products. This means that it does not matter how much reactant or product are placed in a flask, when the system comes to equilibirum the numerical value of K will always be the same. The expression of K was determined experimentally by measuring the concentrations of reactants and products for many different equilibrium systems and then trying to find a common expression.

Writing the equilibrium constant expression using an equilibrium equation, the reactant and
product species and the coefficients of the balanced equation.

In the equilibrium constant expression shown on the right, the square brackets mean 'concentration of' whatever is inside them. Concentrations should be expressed in mol L-1. For this course you need not worry about the units of the equilibrium constant.

You should also note that only those concentrations that can be varied are included in the equilibrium constant. Those substance (such as solids and liquids) that have fixed concentrations are given a concentration of 1 in the expression. Be careful with aqueous solutions. You cannot change the concentration of an ion in solution by adding more of the solution. You must add a more concentrated solution of the ion to increase its overall concentration in the system.

It does not matter what the initial concentrations of reactant and product were. For the same temperature and reaction, any number of trials will give the same numerical value for K.

The equilibrium constant gives industrial chemists a quantitative measuring of the equilibrium position. Large values of K (>102) means that the equilibrium favours the products. Small values of K (>10-3) means that the equilibrium favours the reactants. Where 10-2 < K <102, there is an appreciable amount of products and reactants present at equilibrium.

 

Reaction Quotient

The reaction quotient has exactly the same expression as the equilibrium constant; however, it is used for systems that have ot yet come to equilibrium. It is a useful way to determine whether the equilibrium is being approached from the reactant or product side of the equation.

Consider the reaction of sulfur dioxide with oxygen below.

2SO2 (g) + O2 (g) ⇔ 2SO3 (g)

Graphs showing how the concentrations of reactants and products
varies as the system approaches equilibirum and the relationship
to the reaction quotient.

If the initial concentration of sulfur trioxide was zero, Q will start at zero and as the reaction proceeds it will increase gradually until Q = K as shown in the graph below. AS the reaction proceeds, the concentration of products increases and the concentration of reactants decreases. If you were to write an expression for the quotient, this would mean that Q would be increasing over time.

On the other hand, if you put only sulfur trioxide into the reaction flask, Q would start at a very large value and steadily decrease until it was equal to K (use the reaction quotient expression again to verify this relationship). This is summarised in the diagram below.

If Q < K then the system is moving towards equilibrium from the reactants or the rate of the forward reaction is greater than the rate of the reverse reaction.

If Q > K then the system is moving towards equilibrium from the products or the rate of the reverse reaction is greater than the rate of the forward reaction.

If Q = K then the ssytem is at equilibrium and both the forward and reverse rates of reaction are equal.

 

Dependance on Temperature

The value of K for a particular reaction does not depend on pressure or the initial concentration of reactants or products (or the presence of a catalyst either). The equilibrium constant only changes for the same reaction when the temperature changes. This is why equilibrium constants should always be quoted with a temperature.

It is easy to see how the equilibrium constant changes with temperature.

N2O2 (g) ⇔ 2NO2 (g)
ΔH = 59 kJ mol-1
endothermic
3H2 (g) + N 2 (g) ⇔ 2NH3 (g)
ΔH = -92 kJ mol-1
exothermic
Temperature (K)
K
Temperature (K)
K
273
5.7 x 10-4
298
4.0 x 108
298
4.7 x 10-3
500
60
373
0.48
700
0.26
500
41.4
900
5.4 x 10-3


If you were to write an equilibirum expression for each reaction, the products would be in the numerator and the reactants in the denominator. For the endothermic reaction, an increase in temperature would favour the products and the value of K would increase. For the exothermic reaction, an increase in temperature favours the reactants and since the reactants are in the denominator, an increase in their concentration would decrease the value of K.

In summary:

  • For exothermic reactions, as the temperature increases, K decreases (and vice versa).

  • For endothermic reactions, as the temperature increases, K increases (and vice versa).