Question

Find difference between the mean square speeds of hydrogen and oxygen molecules at N.T.P. Take molecular weight of hydrogen and oxygen as 2 and 32.

Answer 1

Answer to the Question#60478-Physics-Molecular Physics and Thermodynamics Task:

Find difference between the mean square speeds of hydrogen and oxygen molecules at N.T.P. Take molecular weight of hydrogen and oxygen as 2 and 32.

Solution:

NTP: Temperature $T = 273 \, K$ ;

Molar masses: $\mu_{H_2} = 0.002 \, \text{kg/mol}$ ; $\mu_{O_2} = 0.032 \, \text{kg/mol}$ ;

Root-Mean-Square speed: $V = \sqrt{\frac{3RT}{\mu}}$

For Hydrogen: $V_{H_2} = \sqrt{\frac{3RT}{\mu_{H_2}}}$ ; For Oxygen: $V_{O_2} = \sqrt{\frac{3RT}{\mu_{O_2}}}$ ;

Difference: $V_{H_2} - V_{O_2} = \sqrt{\frac{3RT}{\mu_{H_2}}} - \sqrt{\frac{3RT}{\mu_{O_2}}} = \sqrt{3RT} \left( \frac{1}{\sqrt{\mu_{H_2}}} - \frac{1}{\sqrt{\mu_{O_2}}} \right) = \sqrt{3 * 8.31 * 273} * \left( \frac{1}{\sqrt{0.002}} - \frac{1}{\sqrt{0.0032}} \right) \approx 1384 \, \text{m/s} \approx 1.4 \, \text{km/s}$

Answer:

The difference between RMS speeds of Hydrogen and Oxygen is approximately equal to $1.4 \, \text{km/s}$

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