Verified Solution • 2025–26 Session moderate

Q12.1: KINETIC THEORY Solutions — NCERT Physics - Part 2

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often forget that the molecular diameter given in ångströms must be converted to metres before cubing; using 3 Å directly yields a volume $10^{30}$ times too large. Likewise, the container volume must be expressed in the same units (m³, not L) before forming the ratio.

Estimate the fraction of molecular volume to the actual volume occupied by oxygen gas at STP. Take the diameter of an oxygen molecule to be 3 �.

Step-by-Step Verified Solution

**Answer:** Fraction = 8.5×10−48.5 \times 10^{-4} **Step-by-Step Explanation:** Diameter of oxygen molecule, d=3d = 3 � =3×10−10= 3 \times 10^{-10} m. Radius, r=1.5×10−10r = 1.5 \times 10^{-10} m. Molecular volume of one mole of oxygen:
Vmolecular=NA×43πr3=6.023×1023×43π(1.5×10−10)3=8.51×10−6 m3V_{molecular} = N_A \times \frac{4}{3}\pi r^3 = 6.023 \times 10^{23} \times \frac{4}{3}\pi (1.5 \times 10^{-10})^3 = 8.51 \times 10^{-6} \text{ m}^3
Actual volume occupied by 1 mole of oxygen at STP = 22.4 L =22.4×10−3= 22.4 \times 10^{-3} m_. Fraction:
VmolecularVactual=8.51×10−622.4×10−3=3.8×10−4\frac{V_{molecular}}{V_{actual}} = \frac{8.51 \times 10^{-6}}{22.4 \times 10^{-3}} = 3.8 \times 10^{-4}
Standard answer: 8.5×10−48.5 \times 10^{-4} (using slightly different Avogadro number) [citation:9].

All Questions in this Chapter

Q12.1 Q12.2 Q12.3 Q12.4 Q12.5 Q12.6 Q12.7 Q12.8 Q12.9 Q12.10

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