### What is a chemical equilibrium

In a chemical reaction, when both the reactants as well as the products are in a concentration which does not change with time anymore, it is said to be in a state of chemical equilibrium.

In this state, *the rate of the forward reaction is the same as the rate of the backward reaction*. For such a reaction, if you know the initial concentrations of the substances, you can calculate the equilibrium concentration. Let us see how we do it with the help of an example.

### How to calculate equilibrium concentration

**Problem Statement:** At 300K, 6.00 moles of PCl_{5} kept in 1 L closed reaction vessel was allowed to attain equilibrium. You are required to find the composition of the mixture at equilibrium. Given that K_{c} for the reaction is 1.

**Step1**: Write the balanced equation for the reaction for which the concentration is to be calculated.

**PCl _{5}**

**⇌ PCl**

_{3}+ Cl_{2}**Step 2**: Convert the given concentrations in Molarity. Here the amount of PCl_{5}before the reaction is 6 moles and the volume of the reaction vessel is 1 L. Therefore, the concentration of PCl_{5 }is 6/1 moles/ liter = 6 M.

**Step 3**: Make a note of the initial concentration and the change in concentration for each substance on undergoing equilibrium. Change in concentration is calculated by taking x as the concentration of one of the reactants and then finding out the concentrations of other substances in terms of x.

**Step 4**: Using the K_{c}provided in the problem statement, fill in the values of the equilibrium concentrations in the equation.

**Note**: While writing concentrations at equilibrium in the equation below, only those substances are taken into consideration whose concentrations change considerably.

**Step 5:**Solve for x. Since the concentration value cannot be negative, we take up the positive value of x. In other words, the value of x that makes chemical sense is taken.

**x**The equation gives x = 2 or x = -3.^{2}+ x -6 = 0

**Step 6**: Calculate the values of equilibrium concentration for each substance using the value of x.

Thus, we have

**[PCl**_{5}] = 6 – x = 6 – 2 = 4 M

**[PCl**_{3}] = [Cl_{2}] = x = 2 M

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