Question

According to Kinetic theory of gases, at absolute zero temperature:
(a) Water freezes
(b) Liquid helium freezes
(c) Molecular motion stops
(d) Liquid hydrogen freezes

Answer 1

Hint: In the molecular model of Kinetic theory of gases, we know that the molecules which are in the ideal state are in a constant random motion, also the molecules are smaller as compared to the intermolecular distance. The motion could be represented through an average velocity which is termed as root mean squared velocity. The root mean squared velocity is directly proportional to the square root of the absolute temperature and inversely proportional to the square root of the molar mass of the ideal gas; its formula when derived is given as follows,
 ${{v}_{rms}}=\sqrt{\dfrac{3\times R\times T}{M}}............Equation1$
where, ${{v}_{rms}}$is the root mean square of the velocity of the molecule.
M is the molar mass of the ideal gas in kilogram per mole
R is the molar gas constant
T is the temperature in Kelvin

Complete Step by Step Solution:
Now for the solution, we need to understand a bit about the Kinetic theory of gases or KTG as we popularly know it.
● KTG explains the macroscopic properties of gases and can be used to understand and explain the gas laws.
● KTG posits that the gas molecules are in constant motion and exhibit perfectly elastic motion
● The average kinetic energy of a collection of gas particles is directly proportional to absolute temperature only.
● Now, for the question pertaining to zero absolute temperature. We generally imagine the particle in a particular closed system and enumerate a particular average form of velocity to the system of particles. That average is typically termed as the root mean square of velocity in the Kinetic theory of gases. Using equation 1, we get that the velocity (in turn movement) is proportional only to the absolute temperature. Now, for zero absolute temperature, the velocity turns out to be zero, hence the entire system would come to a halt. So, the molecular motion would stop. Hence, the answer is Option C.

Note: Although, the answer in the above problem is as mentioned as we are considering an ideal situation. It is impossible to attain zero absolute temperature, and virtually the velocity could never reach the value of zero, it will always be non-zero.