How many molecules in 36g of water

Question

Calculate the number of molecules present in 36 g of water ( $H_2O$ ).

Solution — Step by Step

Molar mass of $H_2O$ :

Hydrogen (H): atomic mass = 1 u, and there are 2 atoms → $2 \times 1 = 2$
Oxygen (O): atomic mass = 16 u, 1 atom → $1 \times 16 = 16$

M_{H_2O} = 2 + 16 = 18 \text{ g/mol}

\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{36}{18} = 2 \text{ mol}

36 g of water is exactly 2 moles.

1 mole of any substance contains $6.022 \times 10^{23}$ particles (Avogadro’s number, $N_A$ ).

\text{Number of molecules} = \text{moles} \times N_A

= 2 \times 6.022 \times 10^{23}

= 1.2044 \times 10^{24} \text{ molecules}

Why This Works

The mole is the bridge between the microscopic world of atoms and the macroscopic world of grams. We can’t count $10^{24}$ molecules directly, but we can weigh 36 g on a balance. The mole concept lets us convert between these two worlds using one formula and Avogadro’s constant.

Think of a mole like a “dozen” — a dozen means 12 of anything. A mole means $6.022 \times 10^{23}$ of anything. Just as 2 dozen eggs = 24 eggs, 2 moles of water = $2 \times 6.022 \times 10^{23}$ molecules.

In CBSE Class 9 numericals, 36 g of water is a very common choice precisely because it gives exactly 2 moles. Other common “nice” values: 18 g = 1 mol, 9 g = 0.5 mol. Recognising these saves time in exams.

Extension — How Many Atoms?

Each water molecule has 3 atoms (2 H + 1 O). So the total number of atoms in 36 g:

= 1.2044 \times 10^{24} \times 3 = 3.6132 \times 10^{24} \text{ atoms}

CBSE sometimes asks for number of hydrogen atoms or oxygen atoms specifically:

H atoms: $1.2044 \times 10^{24} \times 2 = 2.4088 \times 10^{24}$
O atoms: $1.2044 \times 10^{24} \times 1 = 1.2044 \times 10^{24}$

Common Mistake

The most common error is using $N_A = 6.022 \times 10^{23}$ but forgetting to multiply by the number of moles — writing the answer as $6.022 \times 10^{23}$ (as if it were 1 mole). Always calculate moles first, then multiply by $N_A$ . In this case, 2 moles × $N_A$ = $1.2044 \times 10^{24}$ , not $6.022 \times 10^{23}$ .

Question

Solution — Step by Step

Why This Works

Extension — How Many Atoms?

Common Mistake

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