How to calculate the Molarity of a Solution?

Molarity of a solution can be calculated by finding the ratio of number of moles of solute dissolved in the solution with the volume of the solution in liters. Molarity is the measure of concentration of a solute present in a solution. In this article we are going to learn what is molarity, how to calculate molarity and some sample problems on molarity concept.

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 liter of solution. It is denoted by the upper case letter “M.” The smallest particle of matter which can take part in a chemical reaction is called the atom. Mole is a fundamental SI unit for 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⁺ + O₂ ⇢ H₂O = 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

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

Check: Molar Concentration Formula

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

1. To find the molarity of a solution, we divide the number of moles of solute by the total volume of liters of solution. 
2. When the amount of solute is given in grams, then we must first find or calculate the number of moles of solute.
3. 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.
4. 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.

Check: Difference Between Molarity and Molality

Sample Problems on Molarity

Problem 1: What is the molarity of a solution by dissolving 42.5g of H₂SO₄ 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 Na₂CO₃ 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 H₂SO₄ 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.

Frequently Asked Questions 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 liter of solution.

What is the formula for Molarity?

M = n/v

Where,

M = molar concentration

n = number of moles

v = total volume of solution in liters

What is the SI unit of Molarity?

Molarity is the number of moles per liter, having the unit symbol mol/L or mol/dm³ in SI units

What is the difference between Normality and Molarity?

Normality describes the amount of gram equivalent of compound present in the solution while Molarity describes the number of moles present in the solution.

What is the difference between Molality and Molarity?

Molality is the number of solvent moles per kilogram while Molarity describes the number of moles present in the solution.