## Molarity formula

Molarity, also called the molar concentration of a solution, refers to the ratio of moles of a solute and its volume. It refers to the number of moles in one litre of a given solution. It is dependent on different factors like pressure, temperature, etc.

It is different from molality because molality is the division of moles of solute. By the weight of solvent whereas molarity is the division of volume and number of moles.

## The formula for calculating molarity:

M= n/v

M is the molarity of the solution, n is the total number of moles in that solution and v is the volume. The volume is to be taken in litres. N (number of moles) can be counted by dividing the given mass of a solute and its molecular weight (molar mass). The molar mass is given in the periodic table.

### Solved examples

**Example 1:** If a solution contains 1.56 grams of diluted HCl acid in water and the volume is 26.8 ml, calculate the molarity of the solution.

**Ans:** We know that M=n/v.

We don’t have the exact number of moles in the diluted acid. Therefore we will calculate moles by finding out the molecular weight of HCl which is 36.5 gm. Further, we know that a total of 1.56 grams of HCl is dissolved.

So the number of moles can be calculated by dividing the given mass by the molecular weight of the particular compound.

Thus n= given mass of HCl/ molecular weight of HCl calculated by adding the respective molecular weights of Hydrogen and Chlorine.

n= 1.56/36.5 = 4.27×10^{-2} moles

Further, volume is in ml. So we need to convert it to litre. For that, we divide it by 1000.

Thus the volume of the solution comes out to be 2.68x 10^{-2} litres.

Putting in the original formula, m= n/v =4.27×10^{-2} moles / 2.68x 10^{-2} litres

The answer is 1.59 M.

**Example 2:** If a solution contains 15 grams of sodium sulphate and the volume comes out to be 125 millilitres. What is the molarity of the given solution?

**Ans:** First we need to calculate n. So the given weight is 15 gm and the molecular weight is calculated by adding the weight of Na2SO4. So the molecular weight is 23×2 + 32+ 16×4 = 142 gm.

n= 15/142 (given mass/ molecular weight)= 0.106 gm

The volume is 0.125 litre.

M= n/v = 0.106/0.125= 0.85 M