How to calculate the Molarity of a Solution? (original) (raw)

Last Updated : 23 Jul, 2025

**Molarity (M) measures the concentration of a solute in a solution, defined as the number of moles of solute per litre of solution. It provides a way to express the ratio of solute to solvent and is crucial in chemical calculations for reactions and solutions. In this article, we will learn what molarity is, how to calculate molarity and some sample problems on the molarity concept.

Table of Content

• What is Molarity?
• How to Calculate Molarity Of A Solution
• Sample Problems on Molarity

What is Molarity?

Molarity is used to measure the concentration of a solution. It is used to calculate the volume of solvent or the amount of solute dissolved in per litre of solution. It is denoted by the upper case letter "M." The smallest particle of matter that can take part in a chemical reaction is called the atom.

Mole is a fundamental SI unit for the Amount of Substance. It is used to measure the amount of substance. A mole of any substance (atom, molecule, etc.) is 6.022 × 1023 molecules. Molecular mass is defined as the sum of atomic masses of all atoms in a molecule of a substance. It is expressed in the atomic mass unit (u). For example,

**2H + **+ O 2 **⇢ H 2 O = 1×2 +16 = 18u

Dilution is the process by which a solution is made by the addition of more solvent to make it less concentrated. The concentration of a solution is the amount of solute in a solution. There is a difference between molarity and molar mass, molarity is the number of moles of solute per liter of solution, whereas molar mass is the number of grams per mole of some substance.

How to Calculate Molarity Of A Solution

Molarity is defined as the number of moles of solute that is dissolved in one liter of solution. It is also known as molar concentration and is denoted by the letter “M.”

**Molarity Formula

M = n/v

Where,

• M denotes the molar concentration
• n denotes the number of moles
• v denotes the total volume of solution in liters

**Steps to follow to calculate the molarity of a solution by using the above formula,

• To find the molarity of a solution, we divide the number of moles of solute by the total volume of liters of solution.
• When the amount of solute is given in grams, then we must first find or calculate the number of moles of solute.
• To find the number of moles of solute, we can calculate by dividing by the solute molecular mass. So, when it is divided by total volume, the answer is molarity.
• The volume of specific mass in given grams of solution can also be calculated by the process by finding the number of moles of solute as above. Then divided with molarity given to find the total volume of the solution.

**Also Check:

• **Difference Between Molarity and Molality
• **Types of Chemical Reactions
• **Chemical Equations

Sample Problems on Molarity

**Problem 1: What is the molarity of a solution by dissolving 42.5g of H 2 SO 4 in 1 liter of the solution?

**Solution:

Given mass = 42.5g, volume of solution = 1L

By using the formula,

M = n/v

But, we must find number of moles,

n = mass given/molecular mass

n = 42.5g/98.076 g mol-1

n = 0.43 moles

Now divide the no. of moles with a total volume of solution.

M = 0.43 moles/1L

M = 0.43

The molarity of H2SO4 is 0.43M.

**Problem 2: If seawater contains 40g of sodium chloride per 500ml, then what is the molarity of a solution?

**Solution:

Given mass = 40g, volume of solution = 500mL

By using the formula,

M = n/v

but, we must find number of moles

n = mass given/molecular mass

n = 40g/58.443 g mol-1

n = 0.68 moles

Now divide the no. of moles with the total volume of solution,

Convert ml to L

M = 0.68g/0.500L

M = 1.36

The molarity of NaCl is 1.36M.

**Problem 3: How many moles of Na 2 CO 3 are present in 15L of a 2M solution?

**Solution:

Given M = 2, v = 15L and n = ?

By using the formula

M = n/v

2M = n/15L

n = 2M × 15L

n = 30 moles

There are 30 moles of Na2CO3 present in 15L of a 2M solution.

**Problem 4: In a 20.0ml HCL of 2.0 M solution, how many moles are present?

**Solution:

Given: M = 2.0, v = 20.0ml and n = ?

Convert milliliter to liter

By using the formula

M = n/v

2.0M = n/0.0200L

n = 2.0M × 0.0200L

n = 0.040 moles.

There are 0.040 moles in 20.0ml HCl of 2.0 M solution.

**Problem 5: How many grams of H 2 SO 4 in weight are required to make 950ml of 0.500 M solution?

**Solution:

Given: M = 0.500, v = 950ml

M = n/v

To find mass (grams),

Mv = n

Where n = mass/molecular mass

Mv = mass/molecular mass

0.500M × 0.950L = x/98.0768 g mol-1

x = 0.500M × 0.950L × 98.0768 g mol-1

x = 46.6g

46.6 grams of H2SO4 in weight required to make 950ml of 0.500 M solution.

**Problem 6: How many grams of Ca(OH) 2 are needed to make 250 ml of 0.350M solution?

**Solution:

Given M = 0.350, v = 250ml

M = n/v

To find mass (grams),

Mv = n

n = mass/molecular mass

n = x/74.0918 g mol-1

Mv = x/74.0918 g mol-1

x = 0.350M × 0.250L × 74.0918 g mol-1

x = 6.48g

6.48g of Ca(OH)2 are needed to make 250 ml of 0.350M solution.

**Problem 7: What is the total volume in ml of 10.0M HCl is needed to contain 5.00 moles of HCl solution?

**Solution:

Given M = 10.0, n = 5.00 moles and v = ?

By using the formula,

M = n/v

v = n/M

v = 5.00 moles/10.00M

v = 0.500L

Convert liters to milliliters,

v = 500ml

Therefore, 500ml of volume is needed to make 10.0M HCl contain 5.00 moles of HCl solution.

**Problem 8: What is the molarity of 25g of NaCl solution, which is dissolved in water to produce 2L of the solution?

**Solution:

Given mass = 25g, v = 2L and M = ?

First, we must convert grams into moles by dividing with molecular weight NaCl 58.4 g/mole.

M = n/v

n = mass given/molecular mass

n = 25g/58.4 g mol-1

n = 0.42 moles.

Now divide the no. of moles with the total volume of solution

M = 0.42 moles/2L

M = 0.2

The molarity of NaCl is 0.2M.