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

Notes on Chemical Equilibrium for BSc

  Based on 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 do not 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 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: The rate at which a substance reacts is directly proportional to its active mass (or concentration of the substance in a dilute solution) and the rate of a reaction is directly proportional to the active masses of reacting species raised to the power equal to stoichiometric coefficients.

    For normal calculations and for dilute solutions, active masses of solutes in solutions are considered to be equal to molar concentrations. Active masses of gaseous species are equal to their 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] 

thus, the rate of the chemical reaction α [A]²

Equilibrium State: 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 state the observable properties such as concentration, colour, pressure, temperature remains almost constant.

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

The following 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.

Derivation for the Equilibrium Constant of a reversible reaction:

    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 concentration (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 coefficient in the balanced chemical equation.

    From Law of Mass action we have derived the formula of equilibrium constant in terms of concentration (Kc). When we take partial pressure in place of concentration that becomes equilibrium constant in terms of partial pressure (Kp),

Kc = [C]^c [D]^d / [A]^a [B]^b ………. eq. 1.              

and       

Kp = P_C ^c . P_D ^d / P_A ^a . P_B ^b …….. eq. 2

Reaction Quotient:

    Consider a reversible reaction, A ⇌ B

Kc = [B]eq / [A]eq, ......... eq. 3

Where [B]eq and [A]eq are the concentrations of B and A at equilibrium 

When the concentrations of B and A at any instant other than equilibrium are put into the eq. 3, then it gives reaction quotient in terms of concentration (Q _c) as follows.

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. 4

If at this condition we increase the volume to double of 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. 4) 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). is not equal to 0.

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

Le Chatelier’s Principle

Statement: Whenever a reversible reaction at equilibrium is subjected to change in any condition like change in pressure, temperature or concentration etc. then the equilibrium shifts itself in such a direction to cancel out the effect and accordingly a new equilibrium state is established.

We will discuss, what happens when we increase or decrease the pressure or temperature of the reaction vessel or we add more reactant or when we add inert gas? Let us discuss one by one.

Preparation of ammonia in Haber's Process:

 N₂ + 3H₂ ⇌ 2NH₃

As a conclusion, in increasing the pressure, the equilibrium shifts in the direction in which lesser number of moles is prepared. 

    And there will be no effect of changing the pressure for a reaction in which Dn is not equal to 0. For example, H₂ + I₂ ⇌ 2HI

⇌ 2NH₃ , DH = — 92.4 kJ 

or we can write,

⇌ 2NH₃ +  92.4 kJ 

a.When temperature is increased: If we increase the temperature of the reaction vessel by heating it, then the equilibrium tries to decrease the temperature by absorbing the heat. Thus the equilibrium prefers the direction which is endothermic. The reaction of ammonia is exothermic in forward and endothermic in the backward direction. Hence the equilibrium shifts in the backward direction when we increase the temperature.

As a conclusion, in increasing the temperature the equilibrium shifts in a direction which is endothermic and vice versa.

As a conclusion, addition of inert gas at constant volume has no effect on the equilibrium whereas at constant pressure the equilibrium shifts towards larger number of moles.

5.Effect of catalyst: A catalyst increases both the rate of forward and backward reaction to the same extent. Thus it does not alter the position of the equilibrium nor does it changes the concentrations of any reactant or product rather it brings the equilibrium in earlier time than when it is not added.

Application of Le Chatelier's Principle to physical change:

    Le Chatelier's principle says that when a reversible process in equilibrium is subjected to any change in pressure temperature or concentration then the equilibrium shifts in such direction that the effect of change is compensated.

Let us apply the principle to a solid liquid equilibrium of water. 

                        Solid Ice  ⇌  Liquid Water

    As we know when a definite volume of water is converted into ice, the volume of ice becomes greater than that of liquid water. This is because of the cage like structure in ice due to inter molecular hydrogen bonds between water molecules.

 For your particular interest, we will discuss why the ice in Himalayan mountains becomes harder and harder as we go higher and higher in the mountain.

    According to Le Chatelier's principle, if we change (increase/decreases) the pressure or temperature or concentration of reactants or products of the system at equilibrium then the equilibrium tries to relieve the stress caused due to the change and shifts either in forward or backward direction accordingly. 

    Now, let us focus on the main concept, the ice water equilibrium. As we go higher, the pressure decreases. The equilibrium shifts in a direction in which the effect of decreasing pressure is relieved. Hence the shift takes place in the direction of increased volume. Clearly the equilibrium prefers ice side because the volume of ice is greater than water. This is why ice on the mountain becomes harder and harder as we go higher and higher.

    The reverse case also holds good. That means if pressure is increased the ice water equilibrium shifts towards the liquid water side. 

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