At STP, 1 mole of any gas = 22.4 L. Moles = 5.6/22.4 = 0.25 mol. Why this is true.

Calculate Number of Moles in 5.6 L of Gas at STP — Molar Volume

Question

At STP, a gas occupies 5.6 L. Calculate the number of moles of the gas.

Solution — Step by Step

At STP (0°C, 1 atm), 1 mole of any ideal gas occupies 22.4 L. This is our bridge between volume and moles — memorise it cold.

The formula follows directly:

\text{Moles} = \frac{\text{Volume at STP}}{\text{Molar Volume}} = \frac{V}{22.4}

We divide by 22.4 because each “packet” of 22.4 L contains exactly one mole of particles.

n = \frac{5.6 \text{ L}}{22.4 \text{ L/mol}}

n = \frac{5.6}{22.4} = \frac{1}{4} = \mathbf{0.25 \text{ mol}}

Answer: 0.25 mol (or ¼ mol)

Why This Works

The molar volume (22.4 L/mol) comes from the ideal gas equation. At STP, plugging in $P = 1$ atm, $T = 273$ K, $n = 1$ mol, and $R = 0.0821$ L·atm·mol⁻¹·K⁻¹ gives $V = nRT/P = 22.4$ L. This is not a definition — it’s a derived result from kinetic theory.

The beautiful thing here: it doesn’t matter which gas. Whether it’s $\text{H}_2$ , $\text{CO}_2$ , or $\text{NH}_3$ — at STP, one mole of each takes up 22.4 L. The identity of the gas is irrelevant because we’re counting molecules, not mass.

5.6 L is exactly one-quarter of 22.4 L, which tells us intuitively we have one-quarter of a mole. Spotting this ratio first (before calculating) is how NEET toppers save time.

Shortcut for board + NEET: 22.4 L = 1 mol, so 11.2 L = 0.5 mol, 5.6 L = 0.25 mol, 2.24 L = 0.1 mol. These are the “standard” volumes that show up repeatedly in NCERT problems. Memorise the whole family.

Alternative Method — Using Number of Molecules

If the question asks for number of molecules instead of moles, we extend the calculation:

N = n \times N_A = 0.25 \times 6.022 \times 10^{23}

N = 1.505 \times 10^{23} \text{ molecules}

This two-step chain (volume → moles → molecules) appears in CBSE board questions where they ask both in a single problem. Know the chain: V ÷ 22.4 = moles, then moles × 6.022 × 10²³ = molecules.

Common Mistake

Wrong STP definition. IUPAC revised STP in 1982: the new standard is 0°C and 100 kPa (not 1 atm), giving a molar volume of 22.7 L/mol. However, NCERT Class 11 and all Indian board/entrance exams still use the old STP (0°C, 1 atm, 22.4 L/mol). Always use 22.4 L/mol for CBSE, JEE, and NEET — never 22.7.

A second trap: students sometimes confuse STP (0°C) with NTP (Normal Temperature and Pressure, 25°C). At NTP, molar volume is approximately 24.8 L/mol. Unless the question explicitly says “normal conditions” or 25°C, default to 22.4 L/mol.

Question

Solution — Step by Step

Why This Works

Alternative Method — Using Number of Molecules

Common Mistake

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