Ncert Exercises & Solutions

A gas mixture consists of molecules of A, B and C with masses $m_{A} > m_{B} > m_{C}$ . Rank the three types of molecules in decreasing order of (a) average KE (b) RMS speeds.

Hint: The KE depends on the temperature and the RMS speed depends on the molar mass.

(a) Step 1: Find the ratio of the KE.

The average KE will be the same, as conditions of temperature and pressure are the same.

Step 2: Find the ratio of the RMS speed.

(b) Now as,

v_{r m s} = \sqrt{\frac{3 p V}{M}} = \sqrt{\frac{3 R T}{M}}

= \sqrt{\frac{3 R T}{m N}} = \sqrt{\frac{3 k T}{m}}

where M =molar mass of the gas
m=mass of each molecule of the gas,
R = gas constant

Clearly,

v_{r m s} \propto \sqrt{\frac{1}{m}}

As k = Boltzmann constant, T = absolute temperature (same for all)
But,

m_{A} > m_{B} > m_{C}

{(v_{r m s})}_{A} < (v

_rms)B<(vrms)C

∴ {(v_{r m s})}_{C} > {(v_{r m s})}_{B} > {(v_{r m s})}_{A}

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