Molarity - Definition, Formula and Solved Examples

Molarity is defined as total number of moles of solute per litre of solution. It is represented by M. In chemistry, the molarity is one of the concentration units. The concentration of solutions can be expressed more effectively using measurements based on moles. The SI unit of Molarity is Mole.

A mole is an SI unit that measures the amount of a substance, where the amount of a substance is a measurement of the number of its elementary entities present in an object or sample. According to the definition, a mole contains exactly 6.022 × 10²³ elementary entities, where 6.022 × 10²³ is called Avogadro's number (N_A). Molarity is used to measure the concentration of a solution, where a concentrated solution is a solution with more solute and less solvent.

What is Molarity

The molarity is defined as the total number of moles of solute present in a given solution per liter. It is also known as "molar concentration" and is read as "molar." It is represented by the letter "M," and its unit is mol/L. The molarity of a solution is said to be one molar if one mole of the solute dissolves in one liter of the solution. The molarity of a solution depends on the volume of the solution but not the volume of the solvent.

As the volume of the solutions changes with the change in physical conditions of the system, the molarity of the given solution depends on the physical properties of the system, such as pressure and temperature, unlike mass. There is one drawback of molarity, namely that the volume of most of the solutions slightly depends on temperature due to thermal expansion. Because of this, molarity is not often used in thermodynamics.

Molarity Formula

The formula to determine the Molarity of a solution is given as follows:

Molarity (M) = n / V

where,
"n" is the number of moles of the solute.
"V" is the volume of solution in liters.

Formula to calculate the Number of Moles of Solute

(n) = Mass of the solute / Molar mass of the solute

Unit of Molarity

Molarity of a solution is said to be one molar if one mole of the solute dissolves in one liter of the solution. The molarity of a solution depends on the volume of the solution but not the volume of the solvent.

• Molarity is represented by the letter “M” 
• SI unit of molarity is mole / litre

Molarity Equation

In the lab, chemists frequently prepare solutions of known molarities. So, to prepare a concentrated solution, it has to be diluted with the solvent. Now, as a result, the volume of the solution changes. The equation given below is used to determine the volume of an unknown solution from a known molarity solution:

M₁V₁ = M₂V₂

where,
"M₁" is the initial molarity of the given solution,
"M₂" is the molarity of the new solution,
"V₁" is the initial volume of the given solution, and
"V₂" is the volume of the new solution.

How to Calculate Molarity?

In order to calculate molarity of a solution, follow the steps given below:

Step 1: Calculate the moles of the solute present in the solution.

Step 2: Mark the volume of solution in liters.

Step 3: Use the formula for finding molarity of the solution'

Molarity = Number of Moles of Solute / Volume of Solution in liters

Step 4: Substitute all the values in the above formula to get the Molarity of the solution.

Relation between Molarity and Normality 

Two significant and usually utilized terms in chemistry are normality and molarity. They are employed to denote a substance’s quantitative measurement. It is a chemical unit of concentration, similar to normality. The number of moles of solute per liter of solution is known as molarity. It also goes by the name “molar concentration.” Molarity, such as dissociation or equilibrium constants, is frequently utilized in the determination of pH.

Normality (N) = Molarity × (Molar mass) / (Equivalent mass)

Differences Between Molarity and Normality

Must Read

• Concentration of Solution
• Molar Concentration Formula
• Mole fraction
• Difference Between Molarity and Molality

Solved Examples on Molarity

Example 1: A solution was prepared using 20 g of sodium hydroxide. Calculate the molarity of the given solution of sodium hydroxide if the volume of the solution is 125 ml.

Solution:

Mass of sodium hydroxide (NaOH) in the given solution = 20 g

The volume of the solution = 125 ml = 125/1000 = 0.125 L

The molar mass of sodium hydroxide = 40g/mol

Number of moles of sodium hydroxide (n) = Mass of NaOH/Molar mass of NaOH

= 20/40 = 0.5 moles

We know that,

Molarity (M) = Moles of NaOH/Volume of the solution

M = 0.5/0.125 = 4

Hence, the molarity of the solution is 4M.

Example 2: A solution is prepared by mixing 10 grams of ethanol. Calculate the molarity of the given solution if the volume of the solution is 25.6 ml.

Solution:

The volume of the solution (V) = 25.6 ml = 25.6/1000 = 0.0256 L

Mass of ethanol in the given solution= 10 g

The molecular weight of ethanol = 46.07 g/mol

Number of moles of ethanol (n) = 10 g/46.07 g/mol

= 0.217 moles

We know that,

Molarity (M) = n/V

M = 0.217/0.0256 = 8.477 M

Hence, the molarity of the solution is 8.477M.

Example 3: A solution is prepared by bubbling 1.825 grams of hydrochloric acid in water. Calculate the molarity of the given solution if the volume of the solution is 12.8 ml.

Solution:

The volume of the solution (V) = 12.8 ml = 12.8/1000 = 0.0128 L

The mass of HCl in the given solution = 1.825 g

The molecular weight of HCl = 36.5 g/mol

Number of moles of hydrochloric acid (n) = 7.3 g/36.5 g/mol

= 0.05 moles

We know that,

Molarity (M) = n/V

M = 0.05/0.0128 = 3.91 M

Hence, the molarity of the solution is 3.91M.

Example 4: A solution is prepared by mixing 10 grams of calcium chloride. Calculate the molarity of the calcium chloride solution if the volume of the solution is 200 ml.

Solution:

The mass of CaCl₂ in the given solution = 10 g

The molecular weight of CaCl₂ = 110.98 g/mol

Number of moles of CaCl₂ = 10 g/ (110.98 g/mol)

= 0.0901 moles

The volume of the solution (V) = 200 ml = 200/1000 = 0.2 L

We know that,

Molarity (M) = n/V

M = 0.0901/0.2 = 0.4505 M

Hence, the molarity of the solution is 0.451 M.

Example 5: We have 25 mL of a 2.56 M carbon tetrachloride solution, but we need a 1.28 M solution. So, how many mL of the 1.28M solutions can we prepare?

Solution:

Initial Molarity of the solution (M1) = 2.56 M

The initial volume of the given solution (V1) = 25 mL

Molarity of the new solution (M2) = 2.56 M

The volume of the new solution (V2) =?

We know that,

M₁V₁ = M₂V₂

⇒ V₂ = M₁V₁/M₂

⇒ V₂ = (2.56 × 25/1000)/1.28

= 50/1000 = 50 mL

Hence, the volume of the new solution is 50 mL.

Define molarity?

The molarity is defined as the total number of moles of solute present in a given solution per liter. It is read as "molar" and is represented by the letter "M," and its unit is mol/L.

What is the formula of molarity for solution?

The formula to determine the Molarity of a solution is given as follows:

Molarity (M) = n / V

where,
"n" is the number of moles of the solute.
"V" is the volume of solution in liters.

What is the effect of temperature on molarity?

The molarity of a solution depends on the volume of the solution but not the volume of the solvent. As the volume of the solutions changes with the temperature change, the molarity of the given solution also gets affected by temperature. So, as the temperature increases, the volume of the solution increases, and as a result, the molarity of the solution decreases, and vice versa.

What is Gram equivalent?

The gram equivalent is defined by the amount or the mass of the substances that is utilized to displaces a fixed amount of another substance.