Question

The rms speed of gas molecules in a container is 'v'. If the pressure in the container is quadrupled while keeping the temperature constant, the increase in rms speed will be
1. 40 %
2. 12%
3. 25 %
4. 0 %

Answer 1

Correct Answer - Option 4 : 0 %

The correct answer is option 4) i.e. 0 %

CONCEPT:

• Root-mean-square (rms) speed: The root-mean-square speed is a measure of the speed of gas molecules taking into account their molecular weight and temperature.
  • It is defined as the square root of the average velocity-squared of the gas molecules.

It is given by the equation:

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

Where R is the universal gas constant = 8.314 J mol-1 K-1, T is the temperature of the gas and M is the molecular mass of gas.

• The molecules of a gas are in random motion and exert pressure on the wall of the container they are kept in.

The pressure exerted by n moles of an ideal gas is given by:

Pressure, \(P = \frac{nMv_{rms}^2}{3V}\)

Where M is the molecular mass of gas, V is the volume, and v_rms is the rms speed.

EXPLANATION:

We know that pressure, P ∝ v_rms² and v_rms ∝ √T

• Since the pressure is increased by keeping the temperature constant, v_rms remain unchanged.
• Therefore, the change in rms speed will be 0%.