The Law of Chemical Equilibrium and Equilibrium Constant

The state in a reversible reaction at which the concentration of both the reactants and the products does not change with time is called chemical equilibrium. It can be described as a condition of rechargeable reactions, where two contradictory reactions advance simultaneously. However, in the process, the reactant concentrations and products remain constant and do not change as time passes. This article will study the law of chemical equilibrium and equilibrium constant and explain how to determine the actual value of constants and concentrations of the substances within the equilibrium.

Characteristics of chemical equilibrium

The characteristic features of the law of chemical equilibrium and equilibrium constant are as follows.

• At a given temperature, chemical equilibrium is characterised by constant specific properties such as pressure, concentration, density, and colour.
• It is possible to attain chemical equilibrium from either direction (forward or backwards).
• As the rates are equal without any change in the concentration of products and reactants, we can say that chemical equilibrium is dynamic.
• A catalyst can either hasten or delay the approach of this equilibrium state. However, it cannot change the state. In other words, the relative concentrations of both reactants and products are not altered due to the presence or absence of catalysts.

Chemical equilibrium is considered dynamic equilibrium

Now, suppose we consider a reaction, say: A + B ⇌ C + D. In this reaction, as you can see, if we combine both the substances, A and B, in a closed container, then forward reaction occurs, and it produces C and D. In this process, the concentration of A and B constantly decreases, whereas the concentration of C and D simultaneously increases. Hence, the forward reaction rate decreases when the pace of the reverse reaction increases, and then a point comes when both the reactors equalise, achieving the state of equilibrium.

When A + B ⇌ C + D achieve equilibrium, the concentration of all the four components remains constant over the period. Although it may look like the balance is lost at that point, in actuality, it has reached the state of dynamic equilibrium. Therefore, the reverse and forward processes reach equilibrium; however, the concentration remains unaffected.       

If we see the above kinetic molecular model, we can easily understand that when A and B collide with each other, then C and D are formed; on the other hand, the same process continues as C and D return to the state of A and B, although in the process, the equilibrium remains the same.   

Law of chemical equilibrium

Consider a reversible homogeneous reaction at equilibrium at a particular temperature, such as:

A+B ⇌ C+D

Let’s assume the active masses of A, B, C, and D are [A], [B], [C], and [D], respectively.

As we know, according to the law of mass action, 

The rate of the forward reaction shall be ∝ [A] [B]

Thus, the rate of the forward reaction = kf [A] [B]

Where kf is the velocity for the forward reaction.

Similarly,

The rate of the backward reaction shall be ∝ [C] [D]

Thus, the rate of the backward reaction = kb [C] [D]

Where kb is the velocity for the backward reaction.

Now, at equilibrium constant, 

K= Rate of the forward reaction = Rate of the backward reaction.

i.e. kf [A] [B]= kb [C] [D]

Kf / kb= [C] [D] / [A] [B]

Let’s suppose kf  / kb as a new constant, i.e. K.

Kf / kb= K = [C] [D] / [A] [B]

This K is the equilibrium constant. 

Equilibrium constant for molar concentration Kc

Consider a reaction             aA+bB ⇌ cC+dD

Where a,b,c and d are moles of A, B,C and D respectively.

                                                                                 Kc = [ C ]c·[ D ]d / [ A ]a·[ B ]b

Equilibrium constant for gaseous Kp 

                                                Kp= (PCcPDd)/(PAaPBb)

Relation between Kc and Kp

Deriving the ideal gas equation, 

PV = nRT

And, P = (n/V)RT 

P = CRT, where C is the number of moles per litre (molar concentration).

By inserting PA=CART, PB=CBRT, PC=CCRT, and PD=CDRT in the equation of equilibrium constant for gaseous Kp, we get,

Kp = Kc (RT)Δn   

WhereΔn=(c+d)-(a+b),the difference in the sums of the coefficients for the gaseous products and reactants.   

Gibbs free energy and chemical equilibrium 

ΔG = ΔH -TΔS,

Thus, Gibbs free energy is the enthalpy minus the product of absolute temperature with its entropy. The relation of Gibbs free energy with the equilibrium constant is as follows:

G° = -RT ln Keq

Where, T= temperature

R= universal gas constant, and 

Keq= equilibrium constant.

Le Chatelier’s Principle

As the name suggests, this principle was devised by a French scientist named Le Chatelier. The principle has great importance in the law of chemical equilibrium and equilibrium constant.

This principle dealt with the effect of change in the concentration, pressure, or temperature within an equilibrium state. 

Le Chatelier’s principle states that if an equilibrium system is subjected to a change of temperature, pressure, or concentration of products or reactants, the equilibrium gets disturbed and shifts in the direction of the effect of change.

What happens when different properties of a chemical reaction are changed?

• Change of concentration: If we increase the concentration of reactants, the equilibrium shifts towards the product. Similarly, on increasing the concentration of the product, the equilibrium shifts towards the reactants. Thus, we can say the change in concentration will be inversely proportional to its change. 
• Change of pressure: If we increase the pressure to the system at equilibrium, the reaction will favour the direction that produces a lower number of moles of gases. Similarly, if the pressure decreases, it will favour the direction with a higher number of moles of gas.
• Change in temperature: In a reversible reaction in chemical equilibrium, one (either forward or backwards) will be endothermic, and the other will be exothermic. So, suppose heat energy increases with the temperature rising. In that case, the system can relieve itself from the stress if the reaction which absorbs heat moves faster, i.e. endothermic reaction is always favoured with the increasing temperature. 
• Changes due to catalyst: The catalyst does not affect the equilibrium concentration of a reaction as the catalyst increases both forward and backward rates. 

Conclusion

The law of chemical equilibrium and equilibrium constant states that there is no change in the concentration of reactants or products after achieving a certain state, i.e. the equilibrium. It is possible to attain chemical equilibrium from either direction (forward or backwards). It is dynamic, which means the rates are equal without any change in the concentration of products and reactants. A catalyst can only increase or decrease the time of attaining the equilibrium state without any change in its concentration. Moreover, if the concentration is decreased, the reactants change the balance and go backwards. On the other hand, if the product concentration increases, then the equilibrium shifts towards the backward position, and if it decreases, it goes towards the forward path.