Mole Concept: Atomic and Molar Mass, Formula, Examples, Worksheet, for JEE/NEET/Class 11 CBSE

ANAND CLASSES Study Material and Notes to learn the Mole Concept with a clear understanding of atomic mass, molar mass, formulas, and solved examples tailored for JEE, NEET, and Class 11 CBSE. Strengthen your basics for competitive exams with this comprehensive guide.

🌟 Mole Concept

Atoms and molecules are extremely small — so small that we can’t measure them individually in practical scenarios. So, chemists count particles using a group of particles, and this group is called a mole.

✅ Definition of 1 Mole: The amount of substance that contains as many entities (atoms, molecules, ions, electrons, or other particles) as there are in 12 g of pure carbon-12 isotope.

This number is: 6.022×10²³ particles

This constant is called Avogadro’s Number (Nₐ).

🔹 Why Do We Need the Mole Concept?

Imagine calculating how many oxygen atoms are present in 16 g of oxygen. Since one oxygen atom weighs about 2.66 × 10⁻²³ grams, you’d need to divide: $$\frac{16}{2.66 \times 10^{-23}} \approx 6 \times 10^{23} \text{ atoms}$$

That’s why scientists prefer to group such atoms into a mole, just like we group eggs into dozens.

🔹 Fundamental Relationships in Mole Concept

(A) Mole & Number of Particles

$$n = \frac{N}{N_A}$$

Where:

Where:

• n = number of moles
• N = actual number of particles
• N_A = Avogadro’s number = 6.022×10²³

(B) Mole & Mass of Substance

$$n = \frac{\text{Given mass (w)}}{\text{Molar mass (M)}}$$

Where:

• w = actual mass of sample (in grams)
• M = molar mass (in g/mol)

Note: Molar mass = atomic/molecular mass in grams
E.g.,

• 1 mole of H = 1 g
• 1 mole of H₂O = 18 g

(C) Mole & Volume (for Gases at STP)

$$n = \frac{V}{22.4 \, \text{L}}$$

Where:

• V = Volume of gas at STP (Standard Temperature and Pressure)
• 1 mole of any ideal gas occupies 22.4 L at STP

(D) Mole & Number of Atoms in a Molecule

Multiply the number of molecules by the number of atoms per molecule.

For example:
1 mole of CH₄ has:

• 6.022×10²³ molecules
• Each has 5 atoms → 5×6.022×10²³ atoms

🔹 Molar Mass – Deep Dive

• The molar mass of an element or compound is its mass in grams of 1 mole of that substance.
• Molar mass = Relative atomic/molecular mass, but with units g/mol

🔹 Illustrative Examples

🌟 Example 1:

Q: Calculate the number of molecules in 36 g of water.

Solution:
Molar mass of water (H₂O) = 18 g/mol

$$n = \frac{w}{M} = \frac{36}{18} = 2 \text{ moles}$$

Number of molecules = $$n \times N_A = 2 \times 6.022 \times 10^{23} = 1.2044 \times 10^{24}$$

🌟 Example 2:

Q: What is the mass of 0.5 mole of carbon dioxide (CO₂)?

Molar mass of CO₂ = 12 + (16×2) = 44 g/mol

$$w = n \times M = 0.5 \times 44 = 22 \, \text{g}$$

🔹 Special Case: Atoms vs Molecules

• 1 mole of O atoms = 16 g
• 1 mole of O₂ molecules = 32 g

✨ Be careful! “O” and “O₂” are not the same in mole concept problems.

🔹 Mole and Chemical Equations

Balanced chemical equations tell us the mole ratio of reactants and products.

Example: $$2H_2 + O_2 \rightarrow 2H_2O$$

This means:

• 2 moles of H₂ react with 1 mole of O₂ to produce 2 moles of water.

From this, we can calculate:

• Volumes (at STP),
• Masses,
• Number of molecules involved.

🔹 Real-Life Analogy

• Buying 1 dozen bananas = 12 bananas
• Buying 1 mole of bananas = 6.022×10²³ bananas

But unlike dozens, a mole is used to count microscopic particles — too tiny to count individually.

🔹 NEET/JEE Style Questions

❓ Q1:

How many moles are there in 11.2 L of CO₂ gas at STP?

Solution: $$n = \frac{V}{22.4} = \frac{11.2}{22.4} = 0.5 \text{ moles}$$

❓ Q2:

What is the number of atoms in 1 mole of methane (CH₄)?

Each CH₄ has 5 atoms (1 C + 4 H)
So total = $5 \times 6.022 \times 10^{23} = 3.011 \times 10^{24} atoms\:$

🔹 Do You Know? (Interesting Facts)

• The mass of 1 mole of electrons is only 0.000548 g
• 1 mole of glucose (C₆H₁₂O₆) contains 6.022 × 10²³ molecules, but 24.088 × 10²³ atoms (6 + 12 + 6 = 24 atoms/molecule)

🔹 Quick Revision Table

📄 Worksheet & Practice Questions

Q1: Find the number of atoms in 4.6 g of sodium (Na).
Molar mass of Na = 23 g/mol

Q2: What is the volume occupied by 3.5 moles of a gas at STP?

Q3: Calculate the mass of 3.011 × 10²³ molecules of SO₂.

Q4: How many moles are present in 6 g of carbon?