Question

Assertion
Most probable velocity is the velocity possessed by a maximum fraction of molecules at the same temperature.
Reason
On collision, more and more molecules acquire higher speed at the same temperature.
A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.

Answer 1

Hint: Most probable speed is based on the Maxwell-Boltzmann equation which in turn shapes the kinetic theory of gases. From the formula of the most probable velocity of a gas, we can deduce the factors on which it depends.

Complete step by step solution:
Most probable velocity of molecules is calculated in accordance with the kinetic theory of gases. The kinetic theory is used to explain the macroscopic properties of gases and it is based on certain assumption:
-The volume occupied by a gas is infinitely large in comparison to the volume occupied by the individual particles of the gas.
-There are no forces of attraction existing between the particles of a gas and their surroundings.
-All the particles of the gas are always in a constant state and random motion. They travel in straight lines and may change their direction on collision.
-All the collision exhibited by the particles of a gas are elastic i.e. the total kinetic energy is conserved when two particles of a gas collide.
-The average kinetic energy of a gas is directly proportional to the absolute temperature i.e. the temperature in kelvin.
The basis of the kinetic theory of gases is the Maxwell-Boltzmann equation. This equation explains the distribution of speeds possessed by the particles of a gas at a particular temperature. We can calculate the root mean square speed, the average speed and the most probable speed from this distribution. According to the Maxwell-Boltzmann distribution, the velocity of a gas depends upon its absolute temperature.
The most probable speed or velocity of a gas is the velocity possessed by its maximum fraction of the total number of particles (atoms/molecules) of the gas at a constant temperature. Its formula is given below:
$ \begin{matrix} { \nu }_{ mp } \\ most\quad probable\quad velocity \end{matrix}=\sqrt { \cfrac { 2RT }{ M } } $
Where R is the gas constant, T is the temperature of the gas in Kelvin and M is the molar mass of the gas.
From the above formula, it is clear that the most probable speed of a gas depends upon its absolute temperature and its molar mass. For a particular gas, the most probable velocity increases with the increase in temperature but the fraction of the total molecules possessing that speed will decrease with the increase in temperature. This is so because at lower temperature the kinetic energy possessed by the molecules is low due to which the speeds of the individual molecules are low and the Maxwell-Boltzmann distribution has a lower range. But at higher temperature, the energy of the molecules increases and the range of the velocity possessed by different molecules of the gas becomes wider.
Therefore the correct answer is C. Assertion is correct but Reason is incorrect since on collision, the velocities of the individual particles changes such that the total kinetic energy remains conserved.

Note: More and more molecules can acquire higher speed only when the temperature is raised. As the temperature is raised, the kinetic energy of the particles will increase and hence their velocities will increase.