Verified Solution • 2025–26 Session moderate

QPages 34-37: Q59: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q59 Solution: The temperature and humidity of air are 27�C and 50% on a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently mistake Relative Humidity (RH) for the absolute pressure of the vapour; you must calculate the actual partial pressure by multiplying the saturation vapour pressure by the RH percentage ($P_{actual} = RH \times P_{sat}$) before applying the ideal gas law.

The temperature and humidity of air are 27�C and 50% on a particular day. Calculate the amount of vapour that should be added to 1 cubic metre of air to saturate it. The saturation vapour pressure at 27�C = 3600 Pa. Use R=8.3 J K−1 mol−1R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** Mass of vapour to add = 13.0 g **Step-by-Step Explanation:** At 27�C, saturation vapour pressure = 3600 Pa. RH = 50%, so actual vapour pressure = 1800 Pa. Moles of vapour present in 1 m_:
n1=P1VRT=1800×18.3×300=0.723 moln_1 = \frac{P_1 V}{RT} = \frac{1800 \times 1}{8.3 \times 300} = 0.723 \text{ mol}
Moles needed for saturation:
n2=3600×18.3×300=1.446 moln_2 = \frac{3600 \times 1}{8.3 \times 300} = 1.446 \text{ mol}
Moles to add = 1.446−0.723=0.7231.446 - 0.723 = 0.723 mol. Mass = 0.723×18=13.00.723 \times 18 = 13.0 g.

All Questions in this Chapter

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