Question

The curve shows Maxwell’s distribution of velocities with increase of temperature.

Statement 1: Most probable velocity increases
Statement 2: Fraction of molecules possessing most probable velocity decreases with increasing T

• A. Statement 1 correct, Statement 2 incorrect
• B. Statement 1 and Statement 2 both are correct
• C. Statement 1 and Statement 2 are incorrect
• D. Statement 1 incorrect, Statement 2 correct
  

Answer 1

The correct option is B Statement 1 and Statement 2 both are correct

As we can see from the graph below, with the increase in temperature, the most probable velocity increases and the fraction of molecules possesing most probable velocity decreases.

Maxwell-Boltzmann Distribution of Speeds

• It is based upon the theory of probability. If a quantity Q is distributed among the N number of particles then Maxwell-Boltzmann distribution gives the probability distribution of quantity Q among the N number of particles.

• It gives the statistical average of the speeds of the whole collection of the gas molecules.

• $0\le \text{Molecular Speed}<\infty$

• The fraction of molecules possessing very high and very low speeds is very small.

• At a certain temperature, the individual speed of the molecules keeps changing but the speed distribution remains the same.

• The maximum fraction of molecules possess a speed corresponding to the peak of the curve referred to as $u_{mp}$.

Factors affecting the distribution of speed:

1. Temperature

2. Molar Mass

Effect of temperature on the distribution of speeds:

• If the temperature of a gas is increased, the height of the peak of the distribution curve decreases, and the most probable speed $\left(u_{mp}\right)$ increases.

• As the temperature increases, the molecular motion becomes rapid. Thus the curve shifts towards the right.

Maxwell’s distribution of molecular speeds:

• $\because u_{rms}>u_{avg}>u_{mp}$