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#Avogadro's number

3 public questions tagged with this topic.

Internal Energy of Ideal Gases

A gas occupies 33.6 litres at STP. How many molecules are present? (N_A = 6.02 × 10²³ mol⁻¹, molar volume at STP = 22.4

**Ideal gas internal energy** proportional to temperature, U = (f/2) R T per mole, monatomic 3/2 R T, diatomic 5/2 R T, change ΔU = f/2 n R ΔT, for temperature increase internal energy rises, explaining why heating gas at constant volume raises U entirely as heat. Number of moles (μ) = VolumeMolar volume = (33.6)/(22.4) = 1.5 mol.Number of molecules = μ × N_A = 1.5 × 6.02 × 10²³ = 9.03 × 10²³. Substituting values gives 9.03 × 10²³, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Internal Energy of Ideal Gases

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Mean Free Path and Molecular Diameter

A gas occupies 67.2 litres at STP. How many molecules are present? (N_A = 6.02 × 10²³ mol⁻¹, molar volume at STP = 22.4

**Mean free path** λ = 1/(√2 n π d²) is average distance molecule travels between collisions, n number density (m⁻³), d molecular diameter (m), π≈3.14. Inversely proportional to n and d², larger n or d reduces λ. Rearranged d² = 1/(√2 n π λ), so d = √(1/(√2 n π λ)), enabling diameter estimation from measured λ and n. Number of moles (μ) = VolumeMolar volume = (67.2)/(22.4) = 3.0 mol.Number of molecules = μ × N_A = 3.0 × 6.02 × 10²³ = 1.806 × 10²⁴. Substituting values gives 1.806 × 10²⁴, which matches expected kinetic theory result, confirming mean free path λ =

Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Mean Free Path and Molecular Diameter

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Water and Mole Concept

Which of the following represents Avogadro’s number?

6.022 × 10²³ accurately defines or describes the concept asked in this question. Within Water and Mole Concept, precise definitions and terminology are essential for clear scientific communication. The other options (6.022 × 10²², 6.022 × 10²⁴, and 6.022 × 10²⁵) either describe related but distinct concepts, use incorrect terminology, or confuse similar-sounding terms that have different scientific meanings. A thorough understanding of exact definitions helps distinguish between closely related biological concepts and is crucial for competitive examinations.

Ref: Lehninger Principles of Biochemistry, Nelson & Cox, 8th Ed., Ch. 2

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