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Standard XII

Chemistry

Root Mean Square Velocity

The mass of m...

Question

The mass of molecule $A$ is twice that of molecule $B$ . The root mean square velocity of molecule $A$ is twice that of molecule $B$ . If two containers of equal volume have same number of molecules, the ratio of pressure $\frac{P_{A}}{P_{B}}$ will be:

8 : 1

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1 : 8

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4 : 1

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1 : 4

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Solution

The correct option is A 8 : 1
Given that, $M_{A} = 2 M_{B}$ , and $(v_{rms})_{A} = 2 (v_{rms})_{B}$

$v_{rms} = \sqrt{\frac{3 P V}{n M}}$
For same number of moles n and volume V,
$v_{rms} \propto \sqrt{\frac{P}{M}}$

$\frac{(v_{rms})_{A}}{(v_{rms})_{B}} = \sqrt{\frac{P_{A}}{P_{B}} \times \frac{M_{B}}{M_{A}}}$

Squaring both sides, we get,

$4 = \frac{P_{A}}{P_{B}} \times \frac{1}{2}$
$\frac{P_{A}}{P_{B}} = 8 : 1$

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Root Mean Square Velocity

Standard XII Chemistry

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The mass of molecule A is twice that of molecule B. The root mean square velocity of molecule A is twice that of molecule B. If two containers of equal volume have same number of molecules, the ratio of pressure PAPB will be:

The correct option is A 8 : 1Given that, MA=2MB, and (vrms)A=2(vrms)B vrms=√3PVnM For same number of moles n and volume V, vrms∝√PM (vrms)A(vrms)B=√PAPB×MBMA Squaring both sides, we get, 4=PAPB×12 PAPB=8:1

The mass of molecule $A$ is twice that of molecule $B$ . The root mean square velocity of molecule $A$ is twice that of molecule $B$ . If two containers of equal volume have same number of molecules, the ratio of pressure $\frac{P_{A}}{P_{B}}$ will be: