3.6.1 Molarity (M) (mol/dm³)

Introduction

If you read the label on a bottle of concentrated H₂SO₄, you will notice it says 98% by mass and also 18M.

What does 18M stand for? This means there are 18 moles of H₂SO₄ in each dm³ of solution.

Similarly, concentrated HCl is 37% and 12.1 M HCl. This means there are 12.1 moles of HCl in each dm³ of solution.

We can express the concentration in terms of moles of solute in the given volume of solution. This is called molarity.

Definition

Molarity (M): Molarity is the concentration unit in which the amount of solute is expressed in moles and the quantity of solution in dm³.

Molarity is defined as the number of moles of solute dissolved per dm³ of solution.

In simple words: Molarity tells you how many moles of solute are present in one cubic decimeter (1 dm³ = 1 litre) of solution.

Main Idea

• Molarity is expressed in mol/dm³ (also written as M).
• It tells us the concentration of a solution in terms of moles per unit volume.
• The formula is:

M = moles of solutedm³\ of solution

- Molarity is one of the most commonly used concentration units in chemistry.

Core Concept

M = moles of solutedm³\ of solution

Simple explanation: If you dissolve 1 mole of solute in enough water to make 1 dm³ of solution, the molarity is 1 M.

If you dissolve 2 moles of solute in enough water to make 1 dm³ of solution, the molarity is 2 M.

Key point: Molarity depends on the volume of the solution, not the volume of the solvent.

Detailed Explanation

Understanding Molarity

What it tells us:

• The concentration of a solution in terms of moles per dm³.
• How many moles of solute are present in a given volume of solution.

Key points:

• The volume in the formula is the volume of the solution, not the solvent.
• Molarity is temperature-dependent because volume changes with temperature.
• Molarity is usually expressed as M (e.g., 0.1 M, 1 M, 12.1 M).

Converting Between Units

Volume conversion:

1\ dm³ = 1000\ cm³

To convert cm³ to dm³:

Volume in dm³ = Volume in cm³1000

Moles conversion:

Moles = MassMolar mass

n = mM

Combined formula:

Molarity = Mass of solute / Molar mass of soluteVolume of solution in dm³

Steps for Calculating Molarity

Step 1: Determine the mass of solute (if given in grams).

Step 2: Convert mass to moles using:

n = mM

Step 3: Convert the volume of solution to dm³ (if given in cm³).

V(dm³) = V(cm³)1000

Step 4: Use the molarity formula:

M = nV

Intermediate Level

Steps for calculating molarity:

1. Find the moles of solute: n = mM 2. Convert volume to dm³: V(dm³) = V(cm³)1000 3. Use the formula: M = nV

Example: 40 g urea (molar mass = 60 g/mol) in 500 cm³:

• Moles = 4060 = 0.667
• Volume = 5001000 = 0.5\ dm³
• Molarity = 0.6670.5 = 1.334\ M

Formula / Mathematical Form

M = moles of solutedm³\ of solution

M = nV

Where:

• M = molarity (mol/dm³ or M)
• n = number of moles of solute (mol)
• V = volume of solution (dm³)

Alternative form:

n = M × V

V = nM

Volume conversion:

1\ dm³ = 1000\ cm³

Solved Example

Example 3.8

Urea is a white solid used as fertilizer and starting material for synthetic plastic. A solution contains 40 g urea dissolved in 500 cm³ of solution. Calculate the molarity of this solution.

Problem Solving Strategy:

To calculate the molarity, you need:

• the number of moles of solute (which are not given)
• the volume of solution in dm³

Convert the volume of solution 500\ cm³ to dm³.

Determine moles of solute from its mass using its molar mass.

Solution:

Given: Mass of urea = 40\ g Volume of solution = 500\ cm³

Step 1: Calculate molar mass of urea.

Urea = NH₂CONH₂

M = 14 + (1 × 2) + 12 + 16 + 14 + (1 × 2)

= 14 + 2 + 12 + 16 + 14 + 2 = 60\ g/mol

Step 2: Calculate moles of urea.

n = 4060 = 0.667\ mol

Step 3: Convert volume to dm³.

V = 5001000 = 0.5\ dm³

Step 4: Calculate molarity.

M = nV

M = 0.6670.5

M = 1.334\ M

Final Answer: The molarity of the urea solution is 1.334 M.

Example 3.9

Calculating molarity from moles of solute and volume of solution.

Potassium permanganate (KMnO₄) is a dark blue-black compound. When it is dissolved in water, it forms a bright purple solution. It is used as a disinfectant in water tanks. It is also known as pinky.

A solution contains 0.05 moles of KMnO₄ in 600 cm³ of solution. Calculate the molarity of this solution.

Problem Solving Strategy:

To calculate molarity, you need:

• moles of solute (given)
• the volume of solution in dm³

But volume is given in cm³. So convert cm³ to dm³ by dividing with 1000.

Use the formula to calculate molarity.

Solution:

Given: Moles of KMnO₄ = 0.05\ mol Volume of solution = 600\ cm³

Step 1: Convert volume to dm³.

V = 6001000 = 0.6\ dm³

Step 2: Calculate molarity.

M = moles of solutedm³\ of solution

M = 0.050.6

M = 0.083\ M

Final Answer: The molarity of the KMnO₄ solution is 0.083 M.

Concept Assessment Exercise 3.9

Potassium chlorate (KClO₃) is a white solid. It is used in making matches and dyes. Calculate the molarity of the solution that contains:

(a) 1.5 moles of this compound dissolved in 250 cm³ of solution

Solution:

Given: Moles = 1.5\ mol Volume = 250\ cm³ = 0.25\ dm³

Formula:

M = nV

Substitution:

M = 1.50.25

Calculation:

M = 6\ M

Answer: 6 M

(b) 75 g of this compound dissolved to produce 1.25 dm³ of solution

Solution:

Given: Mass = 75\ g Volume = 1.25\ dm³

Molar mass of KClO₃:

= 39 + 35.5 + (3 × 16) = 39 + 35.5 + 48 = 122.5\ g/mol

Moles:

n = 75122.5 = 0.612\ mol

Molarity:

M = 0.6121.25 = 0.49\ M

Answer: 0.49 M

(c) What is the molarity of a 50 cm³ sample of potassium chlorate solution that yields 0.25 g residue after evaporation of the water?

Solution:

Given: Volume = 50\ cm³ = 0.05\ dm³ Mass of residue = 0.25\ g

Molar mass of KClO₃ = 122.5 g/mol

Moles:

n = 0.25122.5 = 0.00204\ mol

Molarity:

M = 0.002040.05 = 0.0408\ M

Answer: 0.0408 M

Summary Table

Important Points

• - Molarity (M) = number of moles of solute dissolved per dm³ of solution.
• - Formula:
• M = moles of solutedm³\ of solution
• - Unit: mol/dm³ or M.
• - Moles = mass / molar mass.
• - Volume conversion: 1\ dm³ = 1000\ cm³.
• - Molarity depends on the volume of the solution, not the solvent.
• - Molarity is temperature-dependent.
• - Molarity is used in titrations, pharmaceuticals, and industry.

Remember

• - Molarity = moles of solute per dm³ of solution.
• - M = n/V.
• - Unit: mol/dm³ or M.
• - 1\ dm³ = 1000\ cm³.
• - n = m/M.
• - Molarity is temperature-dependent.
• - Used in titrations and industry.
• - Examples:
• - 40 g urea in 500 cm³ → 1.334 M
• - 0.05 mol KMnO₄ in 600 cm³ → 0.083 M

Common Mistakes

Quick Revision

• Concentration:
• The quantity of a solute present in a given amount of solvent or solution is called the concentration of a solution.

• Dilute solution — concentration is relatively low.
• Concentrated solution — concentration is relatively high.

• Molarity (M):
• Molarity is the concentration unit in which the amount of solute is expressed in moles and the quantity of solution in dm³.

Molarity is defined as the number of moles of solute dissolved per dm³ of solution.

Formula:

• M = moles of solutedm³\ of solution

Examples:

• 40 g urea in 500 cm³ → 1.334 M
• 0.05 mol KMnO₄ in 600 cm³ → 0.083 M

Key conversions:

• 1\ dm³ = 1000\ cm³
• n = mM

60-Second Revision

• Molarity (M) = moles of solute per dm³ of solution.
• M = n/V.
• Unit: mol/dm³ or M.
• 1\ dm³ = 1000\ cm³.
• n = m/M.
• Molarity is temperature-dependent.
• Used in titrations and industry.
• Example: 40 g urea in 500 cm³ → 1.334 M.
• Example: 0.05 mol KMnO₄ in 600 cm³ → 0.083 M.
• ⚠️ Warning: molarity uses the volume of the solution, not the solvent.