Molarity

1.0What is Molarity? 

Molarity, denoted by the symbol M, is a key chemistry concept defining a solution's concentration. It measures the number of moles of a solute present per litre of solution. Simply put, molarity tells you the amount of a substance dissolved in a specified volume of liquid, making it an essential tool for understanding chemical reactions and solution preparation.

The formula to calculate molarity is:

$M=\frac{MolesofSolute}{VolumeofSolution}$

Where:

• M = Molarity (mol/L)
• Moles of Solute = The amount of substance being dissolved in moles
• Volume of Solution = The total volume of the solution in litres

2.0Relationship Between Moles and Mass

A mole is a unit that measures the amount of a substance. It is defined as the quantity of material that contains the same number of fundamental particles (such as atoms, molecules, or ions) as there are atoms in exactly 12 grams of pure carbon-12. This number, known as Avogadro's, is approximately 6.022×10²³. 

Thus, one mole of any substance contains 6.022×10²³  particles, and the mass of these particles is called the molar mass.

The formula can describe the relationship between moles and mass:

$M=\frac{MolesofSolute}{VolumeofSolution}$

Where:

• Number of Moles: Indicates how many moles of a substance are present.
• Mass of Substance (g): The actual mass of the sample being measured.
• Molar Mass (g/mol): The mass of one mole of that particular substance.

3.0Dilution And Molarity

In simple terms, dilution refers to decreasing the concentration of a solution by adding more solvent while keeping the amount of solute constant. As a result, the concentration of the solution decreases because the solute is now spread over a larger volume of solvent.

The question is: What will the molarity of the new solution be after dilution?

4.0Deriving the Formula for Molarity After Dilution

To determine the molarity of the new solution after dilution, we can apply the dilution equation, which relies on the principle that the amount of solute in moles stays the same before and after dilution. This can be expressed as:

                                                           M₁×V₁ = M₂×V₂

Where:

• M₁​ = Initial molarity of the solution
• V₁ = Initial volume of the solution
• M₂​ = Final molarity of the solution (after dilution)
• V₂ = Final volume of the solution (after dilution)

Steps to Calculate the Molarity After Dilution:

• Determine the initial molarity M₁​ using the amount of solute and initial volume.
• Use the dilution equation to solve for M₂​, the molarity after dilution.

Solved Example: Suppose you dissolve 25 g of sugar (sucrose) in 200 mL of water and add 300 mL to dilute the sugar solution. What is the molarity of the new solution after dilution?

Step-by-Step Solution:

Step 1: Calculate the moles of sugar

Identify the molar mass of sugar (sucrose): The chemical formula for sucrose is C₁₂H₂₂O₁₁

• Molar mass of sucrose:
• • Carbon (C): 12 × 12.01 = 144.12 g/mol
  • Hydrogen (H): 22 × 1.01 = 22.22 g/mol
  • Oxygen (O): 11 × 16.00 = 176.00 g/mol
  • Total molar mass of sucrose = 144.12 + 22.22 + 176.00 = 342.34 g/mol
• Calculate the moles of sugar dissolved:

Moles of Sugar = $\frac{MassofSugar}{MolarMassofSugar}=\frac{25g}{342.34g/mol}=0.073moles$

Step 2: Determine the initial volume and final volume of the solution

• Initial volume of water = 200 mL = 0.200 L
• After dilution (additional 300 mL of water added):
• Final volume = 200 mL + 300 mL = 500 mL = 0.500 L

Step 3: Calculate the initial molarity of the solution

1. Initial molarity is based on the initial volume of the solution (0.200 L):

Initial Molarity = $\frac{MassofSugar}{InitialVolume}=\frac{0.073moles}{0.200L}=0.365M$

Step 4: Use the dilution formula to find the final molarity

The dilution formula is: $M_2=\frac{M_1\times V_1}{V_2}=\frac{0.365M\times 0.200L}{0.500L}=0.146M$

Where:

M₁​ = Initial molarity of the solution

V₁ = Initial volume of the solution

M₂​ = Final molarity of the solution (after dilution)

V₂ = Final volume of the solution (after dilution)

2. Solve for M₂  (final molarity):

$M_2=\frac{M_1\times V_1}{V_2}=\frac{0.365M\times 0.200L}{0.500L}=0.146M$

The molarity of the new solution after dilution is 0.146 M.

5.0Mixing Solutions with Different Molarities

To calculate the molarity of a mixture, two solutions containing the same solute are combined, each having different molarities and volumes. One solution has molarity M₁ and volume V₁​, while the other has molarity  M₂​ and volume V₂​. The final molarity of the mixture is determined by the total amount of solute from both solutions and the combined volume after mixing.

Solved Example

You are mixing two hydrochloric acid solutions:

• Solution 1: 100 mL of 0.5 M HCl
• Solution 2: 200 mL of 0.2 M HCl

What is the final molarity (Mₓ) of the solution after mixing?

Solution

Given:

• Molarity of Solution 1: M₁ = 0.5 M
• Volume of Solution 1: V₁ = 100 mL = 0.1 L
• Molarity of Solution 2: M₂ = 0.2 M
• Volume of Solution 2: V₂ = 200 mL = 0.2 L

Step-by-Step Solution:

Calculate the moles of solute in each solution:

• Moles in Solution 1:
  M₁ × V₁ = 0.5 × 0.1 = 0.05 moles
• Moles in Solution 2:
  M₂ × V₂ = 0.2 × 0.2 = 0.04 moles

Find the total number of moles after mixing:
nₓ = M₁V₁ + M₂V₂
nₓ = 0.05 + 0.04 = 0.09 moles

Calculate the final volume after mixing:
Vₓ = V₁ + V₂
Vₓ = 0.1 L + 0.2 L = 0.3 L

Find the final molarity (Mₓ) using the formula:

$M_x=\frac{M_1{V}_1+M_2{V}_2}{(V_1+V_2)}$
Mₓ = (0.5 × 0.1 + 0.2 × 0.2) / (0.1 + 0.2)
Mₓ = (0.05 + 0.04) / 0.3
Mₓ = 0.09 / 0.3
Mₓ = 0.3 M

The final molarity of the solution after mixing is 0.3 M.