Mole concept — calculate number of moles, molecules, and atoms in 46g of ethanol

easy CBSE JEE-MAIN NEET • NCERT Class 11 • 3 min read
Tags Atomic Structure

Question

Calculate the number of moles, molecules, and total atoms present in 46 g of ethanol (C2_2H5_5OH).

(NCERT Class 11, Chapter 1)

Solution — Step by Step

Molecular formula of ethanol: C2_2H5_5OH = C2_2H6_6O

Molar mass = 2(12)+6(1)+1(16)=24+6+16=46 g/mol2(12) + 6(1) + 1(16) = 24 + 6 + 16 = \mathbf{46 \text{ g/mol}}

 Moles=Given massMolar mass=4646=1 mol\text{Moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{46}{46} = \mathbf{1 \text{ mol}}

1 mole of any substance contains NA=6.022×1023N_A = 6.022 \times 10^{23} molecules (Avogadro’s number):

Number of molecules=1×6.022×1023=6.022×1023 molecules\text{Number of molecules} = 1 \times 6.022 \times 10^{23} = \mathbf{6.022 \times 10^{23} \text{ molecules}}

Each molecule of C2_2H6_6O contains 2+6+1=92 + 6 + 1 = 9 atoms.

Total atoms=9×6.022×1023=5.42×1024 atoms\text{Total atoms} = 9 \times 6.022 \times 10^{23} = \mathbf{5.42 \times 10^{24} \text{ atoms}}

Breaking it down: 2 C atoms + 6 H atoms + 1 O atom = 9 atoms per molecule.

Why This Works

The mole concept bridges the macroscopic world (grams, litres) and the atomic world (atoms, molecules). One mole is defined as exactly 6.022×10236.022 \times 10^{23} entities — this number (Avogadro’s constant) was chosen so that 1 mole of carbon-12 weighs exactly 12 g.

The molar mass (in g/mol) numerically equals the molecular mass (in amu). This convenient relationship lets us convert between mass and number of particles easily.

Alternative Method — Counting Specific Atoms

If the question asks for only hydrogen atoms:

  • Each ethanol molecule has 6 H atoms
  • Total H atoms = 6×6.022×1023=3.613×10246 \times 6.022 \times 10^{23} = 3.613 \times 10^{24}

For oxygen atoms: 1×6.022×1023=6.022×10231 \times 6.022 \times 10^{23} = 6.022 \times 10^{23}

The mole concept is the foundation of all stoichiometry. For NEET/JEE, master these conversions cold: mass ↔ moles (divide by molar mass), moles ↔ molecules (multiply by NAN_A), molecules ↔ atoms (multiply by atoms per molecule). A surprising number of JEE questions are just these three steps chained together.

Common Mistake

Students confuse molecules and atoms. When asked “how many atoms in 46 g of ethanol?”, many students answer 6.022×10236.022 \times 10^{23} — which is the number of molecules, not atoms. Each molecule contains 9 atoms, so you must multiply by 9. Always read the question carefully: molecules vs atoms.

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