Verified Solution • 2025–26 Session moderate

QPages 34-37: Q12: HC Verma: Concepts of Physics - Volume 2 Kinetic Theory of Gases Pages 34-37: Q12 Solution: Find the rms speed of hydrogen molecules in a sample of…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently insert the molar mass of H₂ as 2 g mol⁻¹ directly into $v_{rms}=\sqrt{3RT/M}$ while $R$ is in J mol⁻¹ K⁻¹, producing a unit mismatch and a wildly incorrect speed; always convert the molar mass to kilograms per mole ($2\times10^{-3}\,$kg mol⁻¹) before evaluating the expression.

Find the rms speed of hydrogen molecules in a sample of hydrogen gas at 300 K. Find the temperature at which the rms speed is double the speed calculated in the previous part. Use

R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}

Step-by-Step Verified Solution

**Answer:**

v_{rms} = 1930 \text{ m/s}

,

T = 1200 \text{ K}

**Step-by-Step Explanation:** For hydrogen,

M = 2 \times 10^{-3}

kg/mol,

T = 300

K.

v_{rms} = \sqrt{\frac{3RT}{M}} = \sqrt{\frac{3 \times 8.3 \times 300}{2 \times 10^{-3}}} = 1930 \text{ m/s}

For double speed:

v' = 2v_{rms}

,

T' = 4T = 1200

K.

All Questions in this Chapter

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