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Concentration Terms

The mass of m...

Question

The mass of molecules $A$ is twice the mass of molecule $B$ . The $r m s$ speed of $A$ is twice the $r m s$ speed of $B$ . If two samples of $A$ and $B$ contain same number of molecules, the ratio of pressure of gas samples of $A$ and $B$ in separate containers of equal volume is .....

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Solution

As we know,
$u_{r m s} = \sqrt{3 R T / M}$
$u_{r m s} = \sqrt{3 P V / M}$
at equal volume, ratio of pressure is
$P_{A} / P_{B} = u_{r m s A} M_{A} / u_{r m s B} M_{B} = 4 * 2 = 8$

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P V = \frac{1}{3} (m N_{A}) u^{2} = \frac{1}{3} M u^{2}

m N_{A} = M

N_{A} = Avogadro's number

u = root mean square velocity

Translational kinetic energy of n mole \frac{1}{2} M u^{2} = \frac{3}{2} (P V) = \frac{3}{2} (n R T)

Average translational kinetic energy per molecule = \frac{3}{2} (\frac{R T}{N_{A}}) = \frac{3}{2} (K T)

u_{r m s} = \sqrt{\frac{3 P V}{M}} = \sqrt{\frac{3 R T}{M}} = \sqrt{\frac{3 P}{d}}

u_{a v} = \sqrt{\frac{8 R T}{π M}}

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V_{A} and V_{B}

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\frac{P_{A}}{P_{B}}

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\frac{P_{A}}{P_{B}}

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