The mass of molecule A is twice the mass of molecule B. The rms speed of A is twice the rms speed of B. If two samples of A and B contain same no. of molecules, what will be the ratio of P of two samples in separate containers of equal volume? (P=Pressure)

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answer is 8.

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Detailed Solution

Given, $m_{A} = 2 m_{B}$
$∴ M o l . w t . o f A = 2 \times m o l . w t . o f B ........ (1)$
Given $u_{r m s} o f A = 2 \times u_{r m s} o f B ........ (2)$
Also no. of molecules of $A = N o .$ of molecules of B $........ (3)$
For gas A $P_{A} V_{A} = \frac{1}{3} M_{A} u_{r m s A}^{2}$
For gas B $P_{B} V_{B} = \frac{1}{3} M_{B} u_{r m s B}^{2}$
$∴ \frac{P_{A} V_{A}}{P_{B} V_{B}} = \frac{M_{A}}{M_{B}} \times \frac{u_{A}^{2}}{u_{B}^{2}} v_{A} = v_{B} ........... (4)$
Given
$∴$ By Eqs. (1), (2), (4) and (5) $\frac{P_{A}}{P_{B}} = 2 \times {(2)}^{2} = 8$
$P_{A} = 8 P_{B}$