Question

Choose the incorrect statement regarding root mean square speed of a molecule
1. On increasing temperature r.m.s speed increases
2. On decreasing temperature r.m.s speed increases 
3. RMS speed is dependent of mass of molecules
4. If molecular weight of molecule increases then RMS speed decreases

Answer 1

Correct Answer - Option 2 : On decreasing temperature r.m.s speed increases 

CONCEPT:

• Root Mean Square Speed is defined as the square root of the mean of squares of the speed of different molecules.
• The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
• The RMS speed of any homogeneous gas sample is given by:

\(\Rightarrow V_{rms}= \sqrt {\frac{{3RT}}{M}} \)

Where R = universal gas constant, T = temperature and M = molar mass

EXPLANATION:

• The RMS speed of any homogeneous gas sample is given by:

\(\Rightarrow V_{rms}= \sqrt {\frac{{3RT}}{M}} \)

From the above discussion it is clear that 

⇒ V_rms ∝ √T 

\(⇒ V_{rms} ∝ \frac{1}{\sqrt{M}}\)

• On increasing the temperature, the RMS speed also increases, and on increasing the molecular mass of the molecules the RMS speed decreases. Hence, option (2) is correct.