Chemical Equilibrium

The reactions can occur both in forward and backward directions. When the rates of the forward and reverse reactions become equal, the concentrations of the reactants and the products remain constant. This is the stage of chemical equilibrium. This equilibrium is dynamic in nature as it consists of a forward reaction in which the reactants give products and reverse reaction in which products gives the original reactants.

 For a better comprehension, let us consider a general case of a reversible reaction.

A+B    ⇋   C+D

The products C and D increases and the reactants A and B decreases. At same point there is decreases in rate of forward reaction and increase in rate of forward reaction and increases in rate of reverse reaction. If both the reactions occur at the same rate, the system reaches to equilibrium state.

Suppose if we start by taking products C and D in the above reaction. Even then equilibrium can be obtained. This means that even if the reaction occurs from any direction equilibrium can be obtained.

Ø Dynamic nature of chemical equilibrium:

The dynamic nature of chemical equilibrium can be demonstrated in the synthesis of ammonia by Haber’s process. In a series of experiments, Haber started with known amounts of dinitrogen and dihydrogen maintained at high temperature and pressure and at regular intervals determined the amount of ammonia present. He was successful in determining also the concentration of unreacted dihydrogen and dinitrogen. The composition of the mixture remains the same even though some of the reactants are still present.

 The dynamic nature of the reaction, synthesis of ammonia is carried out with exactly the same starting conditions but using D2 (deuterium) in place of H2. The reaction mixtures starting either with H2 or D2 reach equilibrium with the same composition, except that D and ND3 are present instead of H2 and NH3. After equilibrium is attained, these two mixtures are mixed together and left for a while. When this mixture is analysed, the concentration of ammonia is just the same as before.

N2(g) + 3H2(g)  ⇋  2NH3(g)

  When this mixture is analysed by a mass spectrometer, that ammonia and all deuterium containing forms of ammonia (NH3, NH2D, NHD2 and ND3) and dihydrogen and its deutrated forms (H2, HD and D2) are present. Thus one can conclude that scrambling of H and D atoms in the molecules must result from a continuation of the forward and reverse reactions in the mixture. If the reaction had simply stopped when they reached equilibrium, then there would have been no mixing of isotopes in this way.

Equilibrium can be attained from both sides, whether we start reaction by taking, H2(g) and N2(g) and get NH3(g) or by taking NH3(g) and decomposing it into N2(g) and H2(g).

N2(g) + 3H2(g)  ⇋  2NH3(g)

2NH3(g)  ⇋ N2(g) + 3H2(g)

Similarly, the reaction, H2(g) + I2(g) 2HI(g). With equal initial concentration of H2 and I2, the reaction proceeds in the forward direction and the concentration of H2 and I2 decreases of HI increases, until all of these become constant at equilibrium. We can also start with HI alone and make the reaction to proceed in the reverse direction, the concentration of HI will decrease and concentration of H2 and I2 will increases until they all become constant when equilibrium is reached. If total number of H and I atoms are same in a given volume, the same equilibrium mixture is obtained whether we start it from pure reactants or pure product.

Ø Law of chemical equilibrium and equilibrium constant:

The mixture of reactants and products at equilibrium is called equilibrium mixture. We shall study the relation between concentrations of reactants and products at equilibrium state.

Let us take a simple reversible reaction follows as   

A + B ⇋ C + D

In this reaction A and B are reactants and C and D are products. This means that in this reaction moles of reactants and products are one each but in all reactions this may not happen. Hence, it is necessary that their moles are expressed. Balanced reaction determines their moles.

N2(g)  +  3H2(g) ⇋  2NH3(g)

KC   =    = 

Where K is equilibrium constant and [ ] bracket expresses concentration of reactant or product in mollit-1 or M. The equilibrium equation is also known as law of active masses because in the early years of chemistry, concentration was said to be 'active mass'.

Now, we shall derive the equation for equilibrium constant of a general reaction. Suppose, if a reaction takes place, as given below in which the reactants and products are shown in balanced form with their proper moles (a, b, c or d).

Aa + Bb ⇋ Cc + Dd           ------ (1)

On the basis of Guldberg and Wage’s law the rate of forward reaction

     Vf  ∝  [A]a [B]b                           ------ (2)

or                         Vf  = Kf [A]a [B]b                        ------ (3)

where Kf  is directly proportionality constant for forward reaction.

The rate of reverse reaction is

      Vr ∝ [C]c [D]d                            ------ (4)

or                         Vr  = Kr [C]c [D]d                       ------ (5)

where Kr is directly proportionality constant for reverse reaction.

At equilibrium the rates of forward and reverse reaction will be equal and so Vf  =  Vr

i.e.,     Kf  [A]a [B]b  =  Kr [C]c [D]d

∴                             =    = Kc                 ------ (6)

where                  Kc =

Thus, when equilibrium is attained if we determine the concentration of the reactants and the products in any reaction and their stoichiometric multiples, the equilibrium constant K can be obtained.

Equation of chemical reaction

Equilibrium constant

Aa + Bb ⇋ Cc + Dd         

Kc

Cc + Dd   ⇋ Aa + Bb

K’c  =

(n) Aa +(n) Bb ⇋  (n) Cc +(n) Dd         

Knc  =  (KC)n