Equilibrium Constant Formula

The equilibrium constant provides information about the connection between the products and reactants when a chemical process reaches equilibrium. It is commonly indicated by the symbol K. In this article, we will understand the concept and formula of equilibrium constant.

Equilibrium Constant Formula

According to the equilibrium constant formula, the ratio of the concentration of products to the concentration of reactants, each raised to their respective stoichiometric coefficients, can be defined as the equilibrium constant of concentration. It is indicated by Kc in a chemical reaction at equilibrium.

You can find that there are different types of equilibrium constants. These constants give relationships in terms of different units between the products and reactants of equilibrium reactions.

Thus, when the reaction reaches equilibrium:

aA + bB ↔ cC + dD

Rate of the Forward Reaction = Rate of the Backward Reaction

That is, Rf = Rb 

or

Kf × α × [A]a[B]b =  Kb × α × [C]c [D]d

Thus, for a reversible reaction:

aA + bB ↔ cC + dD

The equilibrium constant K will be as follows: 

K= [C]c  [D]d [A]a [B]b

where

[A] = Equilibrium Concentration of A 

 [B] = Equilibrium Concentration of B

[C] = Equilibrium Concentration of C

[D] = Equilibrium Concentration of D

Similarly, when the reaction involves gases, the formula will be:

K = kfkb

Kp = [PC]c [PD]d / [PA]a [PB]b

If we follow the equilibrium constant formula, then the equilibrium constant is depicted in terms of the partial pressure of the gases. Therefore, in the above formula, Kp defines the equilibrium constant in terms of partial pressures. Furthermore, the result of the values denote the following:

• Higher product formation and higher conversion percentages are indicated by the greater values of KcKp
• Lower product formation and lower conversion percentages are indicated by Lower KcKp values.

• There is optimum product formation when the values of KcKpare medium.

Unit of equilibrium constant

The unit of the equilibrium constant is equal to:

t = [Mole L-1]△n.

Here, ∆n = The summation of stoichiometric coefficients of products – Summation of stoichiometric coefficients of reactants. This equation is the outcome because the equilibrium constant can be defined as the ratio of the concentrations raised to the stoichiometric coefficients.

Relation between reaction quotient and Gibbs Free Energy 

The process is related to the free energy change. At equilibrium, K is the relative number of products to reactants. In contrast, Q represents the ratio at any point during the reaction. The direction of the reaction can be determined by comparing the Q value to the K value.

Thus, where △G refers to Gibbs Free Energy, K refers to equilibrium constant and Q relates to reaction quotient, 

The relation between reaction quotient and Gibbs free energy can be iterated as follows:

1. When at the beginning of the reaction, △G < 0 and Qc ˂ Kc or Kp, then the reaction will result in the formation of products.

1. When △G = 0 and Qc = Kc or Kp, the reaction is at equilibrium, and there are subsequent changes in the concentration of the mixture.

1. When after the equilibrium,  △G > 0 and Qc > Kc or Kp, then the reaction will result in the formation of reactants.

Factors affecting equilibrium constant

The equilibrium constant is affected by the factors mentioned below:

• The reaction releases the concentration of removed reactants or products in the direction of replenishment of the substance removed. In chemical equilibrium, the composition changes when the amount of the reactant or product is altered. 
• The change in volume causes the change in pressure. The total amount of gaseous reactants and products changes when pressure changes, transforming the gaseous process.
• Temperature variations have an impact on reaction rates. As the temperature rises, the equilibrium constant of an exothermic reaction drops.

Calculation

If the values are given, the equilibrium constant can be easily calculated. The steps given below should be used while calculating the equilibrium constant:

• The first step is to change the values in the equilibrium constant formula.
• The molar concentrations or partial pressures of the reactants and products must then be determined.
• Using the chart, calculate all equilibrium constant concentrations or partial pressures.
• Finally, solve for K by substituting into the equilibrium formula.

Characteristics of equilibrium constant

• The value of the equilibrium constant is unaffected by the starting concentration of reactants.
• The reciprocal of the initial equilibrium constant is the reverse equilibrium constant. This can be reflected as:

            Krev = 1keq

• The equilibrium constant is unaffected by the presence of a catalyst. This is because the catalyst affects the pace of both forward and backward reactions equally.
• The value of the equilibrium constant fluctuates as the temperature changes for the same process.
• Any change in the reaction’s stoichiometry causes a corresponding change in the power of the equilibrium constant.

• Lastly, equilibrium reactions take place at the same time and have the same result. The reaction’s equilibrium constant remains constant. Because of the larger concentration of the common product, product concentrations will be reduced.

Conclusion

The ratio of concentrations of products and reactants in a chemical reaction at equilibrium can be termed as equilibrium constant. The equilibrium constant is unaffected by the presence of a catalyst. This is because the catalyst affects the pace of both forward and backward reactions equally. The value of the equilibrium constant fluctuates as the temperature changes for the same process.