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1.19.

Expert-verifiedFound in: Page 13

Book edition
1st

Author(s)
Daniel V. Schroeder

Pages
356 pages

ISBN
9780201380279

Suppose you have a gas containing hydrogen molecules and oxygen molecules, in thermal equilibrium. Which molecule are moving faster, on average? By what factor?

In thermal equilibrium, hydrogen molecules moves faster by a factor of 4

Thermal equilibrium refers that both the molecules have same temperature, Hence we can write

$\frac{3}{2}KT=\frac{1}{2}m{v}^{2}\phantom{\rule{0ex}{0ex}}v=\sqrt{\frac{3KT}{m}}$

From the above equation we can say that $v\alpha \frac{1}{\sqrt{m}}$

Thus the molecule with least mass will have maximum rms speed.

Now O_{2} had molecular mass of 32 & H_{2} has molecular mass of 2

$\frac{{{m}_{H}}_{2}}{{{m}_{O}}_{2}}=16$

Thus we can say that hydrogen with least mass has the maximum rms speed and

$\frac{{v}_{{H}_{2}}}{{v}_{{O}_{2}}}=\sqrt{\frac{{m}_{{O}_{2}}}{{m}_{{H}_{2}}}=}\sqrt{\frac{1}{16}}\phantom{\rule{0ex}{0ex}}{v}_{{O}_{2}}=4{v}_{{H}_{2}}$

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