THE EQUILIBRIUM CONSTANT

Now consider we have a mixture of reactants and products that is not yet at equilibrium, or one that is at equilibrium. 

 

Which way will the reaction go in order to reach equilibrium?

How far will the reaction go, that is, what will be the amounts of reactants and products at equilibrium?

If we make changes to the system, such as to its volume, or add more of a reactant, how will the equilibrium composition be affected? 

To be able to answer these questions we have to know about the Equilibrium Constant. Now back to the equilibrium involving H₂(g), I₂(g) and HI(g) at 720K.

H₂(g) + I₂(g)        2HI(g)

In four separate experiments at 720 K, chemical equilibrium was allowed to establish. Two were started with different concentrations of H₂(g) and I₂(g) only in each, and two with differing initial concentrations of HI(g) only. In each of the four experiments, the equilibrium concentration of H₂(g), I₂(g) and HI(g) were measured. These are given in the table below:

Equilibrium concentrations (mol dm-3)
[H2(g)]eqm	[I2(g)]eqm	[HI(g)]eqm
1.14 x 10-2	0.12 x 10-2	2.52 x 10-2
0.92 x 10-2	0.20 x 10-2	2.96 x 10-2
0.34 x 10-2	0.34 x 10-2	2.35 x 10-2
0.86 x 10-2	0.86 x 10-2	5.86 x 10-2

If we substitute these equilbrium concentrations into the expression below:

then a constant value, within experimental error, is obtained. The square brackets represent concentrations in mol dm^-3.

The value of this ratio of equilibrium concentrations (in mol dm^-3) is known as the equilibrium constant, represented by the symbol K_c.

Many other chemical equilibrium reactions have been studied and in each case an equilibrium constant relating to the stoichiometric chemical equation has been calculated. This observation can be universally applied, in what is sometimes called the Law of Chemical Equilibrium, as illustrated by the general chemical equilibrium:

aA_(g) + bB_(g)        cC_(g) + dD_(g)

Can the equilbrium constant be expressed in other terms?

The Ideal Gas Equation shows that the pressure of a gas is proprtional to its concentration.

pV = nRT

where p is pressure of a particular gas (its partial pressure) in an equilibrium mixture, V is the total volume, n is the number of moles of the particular gas, R is the general gas constant, and T is the absolute temperature.

In the above equation where the temperature is also constant,

P a n / V

The equilibrium constant can therefore also be expressed in terms of partial pressures, and is denoted as K_p:

Does the equilbrium constant have units?

The equilibrium constant (K_c or K_p) may or may not have units; this depends precisely upon the equilibrium expression. 

Does the equilibrium constant depend on temperature?

Yes. An equilibrium constant is constant only at a constant temperature. Changing the temperature of a chemical system at equilibrium will change the value of the equilibrium constant, and also the position of the equilibrium. 

Are K_c and K_p related?

Yes. The relationship depends on the reaction and how it is written. Specifically, it depends on the number of moles of gaseous reactants and products.

The equation is:

K_p = K_c(RT)^Dn

where Dn is the number of moles of gaseous products minus the number of moles of gaseous reactants, R is the gas constant, and T is the absolute temperature at which the equilibrium exists.

Which way will the reaction go in order to reach equilibrium?

We have a mixture of SO₂(g), O₂(g), and SO₃(g) at 1000K which has still to reach equilibrium. The partial pressures are p_SO2 = 0.48 atm, p_O2 = 0.18 atm, and p_SO3 = 0.72 atm. K_p = 3.40 atm^-1. The reaction is:

2SO₂(g) + O₂(g)      2SO₃(g)

Which way must the reaction go to reach equiilibrium? 

Answer:

                    Calculate a value (Q) for the reaction which can be compared with the equilibrium constant, K_p. This is given by the expression:

                                                                       

     The value of Q calculated is 12.50 atm^-1. Since Q is greater than K_p, to reach equilibrium, the equilibrium must go from right to left.

     If we make changes to the system, such as to its volume, or add more of a reactant, how will the equilibrium composition be affected?


     This question is really an extension of the first, except that a reactant or product may be added or removed, the volume or pressure changed, or the temperature of the system increased or decreased. We consider that these changes are made to a chemical system already at equilibrium.

     At the instant when such a change is made, we consider that the system is no longer at equilibrium. We are going to consider, in qualitative terms, what the new equilibrium composition will be. Calculating the new amounts of reactants and products at equilibrium might be possible but the working is often tricky, so we'll give this a miss. We will discuss an approach in the next section with reference to Le Chatelier's Principle.