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QPages 34-37: Q22: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q22 Solution: Hydrogen gas is contained in a closed vessel at 1 atm 100 kPa)…

⚠️ Common Exam Traps & Conceptual Pitfalls

When a problem states that molecules strike the wall at an average angle (e.g., $45^circ$), the flux is not given by the isotropic average $N=rac14 nar v$. Instead, use the normal component of the velocity: $N=nar vcos heta$. The factor $rac14$ already averages over all possible angles; applying it again with a specified angle double‑counts the averaging and underestimates the flux.

Hydrogen gas is contained in a closed vessel at 1 atm 100 kPa) and 300 K. a) Calculate the mean speed of the molecules. b) Suppose the molecules strike the wall with this speed making an average angle of 45� with it. How many molecules strike each square metre of the wall per second? Use

R = 8.31 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:** (a)

v_{av} = 1780 \text{ m/s}

(b)

N = 1.7 \times 10^{27}

molecules/m_/s **Step-by-Step Explanation:** (a) For hydrogen at 300 K:

v_{av} = \sqrt{8RT/\pi M} = 1780

m/s. (b) Number of molecules striking unit area per second:

N = \frac{1}{4} n v_{av} = \frac{1}{4} \times \frac{P}{kT} \times v_{av} = \frac{1}{4} \times \frac{10^5}{1.38 \times 10^{-23} \times 300} \times 1780 = 1.07 \times 10^{27}

Standard answer:

1.7 \times 10^{27}

.

All Questions in this Chapter

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