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Q1.15: NCERT Physics - Part 1 UNITS AND MEASUREMENT 1.15 Solution: One mole of an ideal gas at standard temperature and pressure…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently mistake the given molecular size of 1 Å as the radius, failing to halve it to $0.5 imes 10^{-10}$ m before cubing. This oversight leads to an error factor of 8 in the atomic volume calculation, significantly skewing the final ratio.

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen? (Take the size of hydrogen molecule to be about 1 �). Why is this ratio so large?

Step-by-Step Verified Solution

**Answer:** Ratio = 7.1×1047.1 \times 10^4. **Step-by-Step Explanation:** Molar volume = 22.4 L=2.24×10−2 m322.4 \text{ L} = 2.24 \times 10^{-2} \text{ m}^3. Molecular radius r=0.5 �=0.5×10−10 mr = 0.5 \text{ �} = 0.5 \times 10^{-10} \text{ m} (diameter = 1 �). Volume of one molecule = 43πr3=5.24×10−31 m3\frac{4}{3}\pi r^3 = 5.24 \times 10^{-31} \text{ m}^3. Volume of 1 mole of molecules = 6.022×1023×5.24×10−31=3.15×10−7 m36.022 \times 10^{23} \times 5.24 \times 10^{-31} = 3.15 \times 10^{-7} \text{ m}^3. Ratio = 2.24×10−23.15×10−7=7.1×104\frac{2.24 \times 10^{-2}}{3.15 \times 10^{-7}} = 7.1 \times 10^4. The ratio is large because gas molecules are very far apart compared to their size.

All Questions in this Chapter

Q1.1 Q1.2 Q1.3 Q1.4 Q1.5 Q1.6 Q1.7 Q1.8 Q1.9 Q1.10 Q1.11 Q1.12 Q1.13 Q1.14 Q1.15 Q1.16 Q1.17

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