Calculating the Equilibrium Concentration

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 learn the concept and formula of the Equilibrium Constant along with solved examples. This article also elaborates on the steps for calculating equilibrium concentration. 

Equilibrium Constant Formula

To calculate the equilibrium concentration, we first need to know that the equilibrium constant is indicated by Kc in a chemical reaction at equilibrium. 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. 

Thus, when the reaction reaches equilibrium:

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

=[C]c  [D]d [A]a [B]b

= Kp 

The equilibrium constant is, thus, 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 denotes 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 KcKp are medium.

Unit of Equilibrium Constant

The unit of the equilibrium constant is:

t = [Mole L-1]△n

Here, ∆n = The summation of stoichiometric coefficients of products – The summation of stoichiometric coefficients of reactants.

This is because the equilibrium constant is the ratio of the concentrations raised to the stoichiometric coefficients. 

The ICE Table

Using the ICE table to find the equilibrium concentration equation is the easiest method. ICE table is a well-organised table that shows how much of each product and reactant is given and how much needs to be found. When we look at how to compute equilibrium concentration, the equilibrium constant and table will come in handy. The ICE table stands for:

1. Initial concentration
2. Change in concentrations
3. Equilibrium concentration

Calculating the Equilibrium Concentration

In cases where some values are given and some are not, the following steps should be used while calculating the equilibrium concentration:

Step 1: Write the balanced equation of the reaction.

The first step of calculating the equilibrium constant is to write the balanced equation of the chemical reaction in the form of aA +bB cC + dD.

Step 2: Convert the concentration units.

The second crucial step is to convert the concentration units. We must convert the concentration of the reactants and the products in terms of their molarity.

Step 3: Create the ICE table of a given reaction.

The third step to calculate the equilibrium constant is to create the ICE table of the given reaction by inputting the initial concentration, change in concentrations, and equilibrium concentration.

Step 4: Substitute the values.

Using the formula for calculating the equilibrium constant, i.e., K= [C]c  [D]d [A]a [B]b, we will form an equation where ‘x’ is the unknown variable.

Step 5: Solve for x.

The fifth and final step is to solve the quadratic equation so formed and find the value of ‘x’.

Solved Example

Question: A mixture of 0.40 mol N2 and 0.96 mol H2 are placed in a 2.00 L container at a constant temperature. The mixture is allowed to reach equilibrium. At the stage of equilibrium, the concentration of NH3 is 0.14 M.  

Using the equilibrium constant, find the equilibrium constant Kc for the given equation:

 N2 + 3 H2 → 2 NH3

Solution: 

Step 1: Write the balanced equation of the reaction.

N2 + 3 H2 → 2 NH3

Step 2: Write the concentration of the reactants and products in molar units.

The known molar concentrations are:  

[N2]i    = 0.40 mol/2.00 L   = 0.20 M

[H2]i    = 0.96 mol/2.00 L   = 0.48 M

[NH3] eq                               = 0.14M

Step 3:  Create the ICE Table.

Using the known concentrations of the reactants and the products, we determine the equilibrium concentrations of N2 and H2:

Step 4: Solve for x.

We know that the equilibrium concentration of NH3 is 0.14 M,

Therefore, 

2x = 0.14 M 

Thus, 

x = 0.07 M

Since we already know the value of x, we can now calculate the equilibrium concentrations of N2and H2. These are as follows:

[N2] eq = 0.20-0.07             = 0.13M

[H2] eq  = 0.48 – 3(0.07)       = 0.27M

Step 5: Finding the equilibrium constant.

We know the equilibrium constant formula is:

K = kfkb

=[C]c  [D]d [A]a [B]b

Therefore, the equilibrium equation for the given reaction will be:

Kc = [NH3]2 / [N2][H2]3 = [NH3]2[N2]2 [H2]3

Thus,

 Kc =  [0.14]2[0.13]2 [0.27]3 = 7.66

Conclusion

The equilibrium constant tells us about the connection between the products and reactants when a chemical process reaches equilibrium. The equilibrium constant is indicated by Kc in a chemical reaction at equilibrium. 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.