Question

A gas mixture consists of molecules of type 1, 2 and 3 with molar masses $m_{1} > m_{2} > m_{3}$. $v_{rms}$and$\bar{K}$ are the rms speed and average kinetic energy of the gases. Which of the following is true

• A. $(v_{rms})_{1} < (v_{rms})_{2} < (v_{rms})_{3}$and$(\bar{K})_{1} = (\bar{K})_{2} = (\bar{K})_{3}$
• B. $(v_{rms})_{1} = (v_{rms})_{2} = (v_{rms})_{3}$and$(\bar{K})_{1} = (\bar{K})_{2} > (\bar{K})_{3}$
• C. $(v_{rms})_{1} > (v_{rms})_{2} > (v_{rms})_{3}$and$(\bar{K})_{1} < (\bar{K})_{2} > (\bar{K})_{3}$
• D. $(v_{rms})_{1} > (v_{rms})_{2} > (v_{rms})_{3}$and$(\bar{K})_{1} < (\bar{K})_{2} < (\bar{K})_{3}$

Answer 1

Answer: (A)

$(v_{rms})_{1} < (v_{rms})_{2} < (v_{rms})_{3}$and$(\bar{K})_{1} = (\bar{K})_{2} = (\bar{K})_{3}$

Answer 2

The rms speed depends upon the molecular mass $v_{rms} \propto \frac{1}{\sqrt{M}}$ but kinetic energy does not depends on it $E \propto M^{0}$

In the problem $m_{1} > m_{2} > m_{3}$ ∴ $(v_{rms})_{1} < (v_{rms})_{2} < (v_{rms})_{3}$but $({\bar{K}}_{1}) = ({\bar{K}}_{2}) = ({\bar{K}}_{3})$