Molarity is defined as the number of moles of solute dissolved in one litre of solution. It helps chemists measure and compare the concentration of different solutions easily. The value of molarity depends on the volume of the solution, which means it can change with temperature because the volume of liquids may expand or contract.
Example: If 1 mole of solute, such as Sodium chloride is dissolved in 1 litre of water, the molarity of the solution is: 1 M. This means the solution contains one mole of solute in one litre of solution.
Molarity Formula
The formula to calculate molarity is:
M = \frac{n}{V}
Where,
- M = Molarity of the solution
- n = Number of moles of solute
- V = Volume of solution in litres (L)
Unit of Molarity
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 = mol/m³
- mol/L is commonly used
Molarity Equation
When a solution is diluted by adding more solvent, the number of moles of solute remains constant. In such cases, the dilution equation is used. This equation helps in calculating the new concentration of a solution after dilution.
M1 V1 = M2 V2
Where,
- M1 = initial molarity
- V1 = initial volume
- M2 = final molarity
- V2 = final volume
Method for calculating Molarity
To determine the concentration of a solution, chemists calculate its molarity. The calculation involves finding the number of moles of solute and the volume of the solution in litres.
The steps for calculating molarity are:
Step 1: Find the mass of the solute
First, determine the mass of the solute present in the solution. The mass is usually given in grams (g).
Step 2: Calculate the number of moles
Convert the mass of the solute into moles using the formula:
n = \frac{\text{mass of solute}}{\text{molar mass}}
Step 3: Convert the volume into litres
Measure the volume of the solution and convert it into litres (L) if it is given in millilitres.
1000 mL = 1 L
Step 4: Apply the molarity formula
Finally, substitute the values into the molarity formula:
M = \frac{n}{V}
Relation between Molarity and Normality
Both molarity and normality are units used to express the concentration of a solution. They are related to each other because both depend on the amount of solute present in a solution. However, molarity is based on moles of solute, while normality is based on gram equivalents of solute.
The relation between molarity and normality is given by the formula:
N = M × n N
Where,
- N = Normality of the solution
- M = Molarity of the solution
- n= Number of equivalents (valency factor) of the solute
Example:
For Sulfuric acid, the valency factor is 2 because it can release two hydrogen ions (H⁺).
If the molarity of the solution is 1 M, then:
N = M × n
N = 1 × 2 = 2N
So, a 1 M solution of sulfuric acid is equal to 2 N.
Molarity | Normality |
|---|---|
| Molarity is the number of moles per liter of solution. | Normality is the number of grams equivalent per liter of solution. |
| Molarity is also known as molar concentration. | Normality is also termed equivalent concentration. |
| The unit of molarity is M or Moles L-1. | The units of normality are N or eq L-1. |
Solved Examples
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) = 1.825 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) = 1.28 M
The volume of the new solution (V2) =?
We know that,
M1V1 = M2V2
⇒ V2 = M1V1/M2
⇒ V2 = (2.56 × 25) / 1.28
= 64 / 1.28 = 50 mL
Hence, the volume of the new solution is 50 mL.