Chemical Equilibrium, Equilibrium Constant, Reaction Quotient and Shifting of Equilibrium

    Based on the fact that whether a chemical reaction would go for completion or not, the chemical reaction can be divided into two categories.

1. Irreversible reaction: In these reactions the reactants are completely converted into products and the products formed donot react to give back the reactants. Precipitation or ionic, neutralisation, redox, combustion and decomposition reactions come under this category.

2. Reversible reaction: These reactions take place in both the directions under similar conditions of temperature and pressure.

Example: 1. N2 (g) + 3H2 (g)   ⇌  2NH3 (g)

2. 3Fe (s) + 4 H2O (g) ⇌ Fe3O4 (s) + 4 H2 (g)

Characteristics of reversible reaction:

1. Proceed in both directions, the forward and backward.

2. Take place in closed vessel.

3. Reactants and products are separated by double arrow (⇌)

4. Never proceed to completion

5. An equilibrium is established at the end of the reaction.

6. At a given equilibrium the temperature, pressure and concentrations of reactants and products remains constant.

Rate of reaction: The amount of reactant consumed or the amount of product formed per unit time is called the rate of reaction. In other words, the change in concentration of reactant or product per unit time is called the rate of reaction.

       Mathematically, Rate of reaction = change in concentration / change in time

     Consider a reaction, A → B in which the concentrations of A and B changes with time as follows:

Thus if we consider the concentrations at time 5 minutes and 10 minutes, we have,

Rate of reaction = Dx / Dt  = – (1.25 – 1.35) mol L^-1  / (10 –5) sec     

        = (0.25 – 0.15) mol L^-1 / (10 –5) sec       

        = 0.02 mol L^-1 S ^–1

Note: 1. Unit of rate of reaction is mol L^-1 S ^–1

Note: 2. A negative sign is multiplied while calculating rate of reaction w.r.t. the reactant to get a positive value because rate of reaction can’t be negative.

Law of mass action: Rate of a reaction is directly proportional to the active masses of reacting species raised to the power equal to stoichiometric coeeficients.

    For normal calculations and in general for dilute solutions, active masses of solutes in solutions are considered to be equal molar concentrations. Active masses of gaseous species is equal to its partial pressure. Active masses of pure liquids and solids are taken as unity.

    Consider a reaction A ------> product

    According to Law of mass action, rate at which A reacts α [A] 

    (where [A] = concentration of A )

    If we consider a reaction, A + B --------> Product

    Then, According to Law of mass action, rate at which A reacts α [A]

    Rate at which B reacts α [B]

    And the rate of the chemical reaction α  [A] . [B]

    If we consider 2A --------> Product Or A + A ---------> Product

    According to Law of mass action, 

    rate at which A reacts = the rate of the chemical reaction α  [A] . [A] = [A]²

Equilibrium State, Equilibrium Constant and law of chemical equilibrium: It is defined as the state of a reversible process at which the rate of forward reaction becomes equal to the rate of backward reaction. At this atete the observable properties such as concentration, colour, pressure, tepmperature remains almost constant.

The equilibrium state may be observed both in physical process and chemical reaction.

The follwing graphs indicate the variation of concentrations of reactants and products in different reactions as the equilibrium is reached.

    From the above figures, it becomes clear that concentrations of reactants and products may vary in different reactions.

Fig. 1. Initially only A was present, finally the concentration of B couldn't exceed the concentration of A at equilibrium. We can say the reaction could not proceed much in the forwared direction. 

Fig. 2. Initially only A was present, finally the concentration of B became greater the concentration of A at equilibrium. The reaction proceeded in the forward direction.

Fig. 3. Initially both A and B were present (concentration of A was greater than B), finally the concentration of B couldn't exceed the concentration of A at equilibrium.

Fig. 4. Initially both A and B were present (concentration of A was smaller than B), finally the concentration of A couldn't exceed the concentration of B at equilibrium.

Fig. 5. Initially only B was present, finally the concentration of A became greater the concentration of B at equilibrium. In this case we consider the B as reactant and the reaction proceeded in the forward direction.

Fig. 6. Initially only B was present, finally the concentration of A couldn't exceed the concentration of B at equilibrium. In this case we consider the B as reactant and the reaction proceeded in the backward direction.

    Consider a reversible reaction aA + bB ⇌ cC + dD. 

    Initially A and B are consumed at a fast rate and the products reproduce the reactants in a slower rate. But with progress of time rate of forward reaction decreases and rate of backward reaction increases due to concentration change and finally both the rate of forward and backward reaction become equal and the state is called the chemical equilibrium.

   

    The above mathematical expression is known as Law of chemical equilibrium. The equilibrium constant of a reversible reaction is defined as the ratio of the product of concetration (active mass) of products to the product of concentration (active mass) of reactants, each concentration (active mass) term is raised to the power equal to the coeeficient in the balanced chemical equation.

Reaction Quotient:  When we alter any of the concentration, temperature or pressure then the reaction no longer exists in equilibrium. 

    From Law of Mass action we have derived the formula of equilibrium constant,

Kc  (Eq. Const. in terms of  concentration) = [C]^c [D]^d / [A]^a [B]^b ………. eq. 1.              Or       

Kp = (Eq. Const. in terms of  partial pressure)  = P_C ^c . P_D ^d / P_A ^a . P_B ^b …….. eq. 2

The concentrations or partial pressures of C, D, A and B here are the concentrations or partial pressures when the reversible reaction is at equilibrium. But if the concentrations or partial pressures at any other instant are put into the same expression as eq. 1 or eq. 2, then it gives reaction quotient (Q _c or Q _P).

Now if Q _c = Kc  or  Q _P = K _p , then the reversible reaction is at equilibrium.

If Q _c > Kc or  Q _P > K _p , then the reversible reaction proceeds in the backward direction forming more reactants.

Similarly, if Q _c < Kc  or  Q _P < K _p , then the reversible reaction proceeds in the forward direction forming more products.

This concept can be applied to any reversible reaction to predict how far the equilibrium is.

Let us consider the preparation of ammonia in Haber’s Process. 

N₂ + 3H₂ ⇌ 2NH₃. 

Suppose the reaction is at equilibrium. 

We can write, 

Kp = (P NH₃)² / (P N₂) . (P H₂)³ ……… eq. 3

If at this condition if we increase the volume to double its equilibrium volume, then partial pressure of each component becomes halved, and the reaction no longer exists in equilibrium. The same expression (as mentioned in eq. 3) gives us the reaction quotient, Qp.

Thus Qp = (P NH₃ / 2)² / (P N₂ / 2) . (P H₂ / 2)³ 

= 4 . (P NH₃)² / (P N₂) . (P H₂)³ 

= 4 . Kp

=> Q _P > K _p , then the reversible reaction proceeds in the backward direction forming more reactants. Thus if we increase the volume a reversible reaction at equilibrium, then the reaction proceeds in a direction (forward or backward) in which more number of molecules (or moles) are formed. This can easily be seen in the above reaction. The total number of moles of reactants is four where as the number of moles of product is two.

We can consider other examples also and can find that changing the volume shifts the equilibrium in any direction only when the change in gaseous moles (Dn = n_p — n_r ¹ 0).

This concept has been established theoretically or logically in Le-Chatelier’s principle.

Click here to find application of Le chatelier's principle to physical and chemical equilibrium.

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