Question

How would you determine what gas has molecules with the greatest average molecular speed at a certain temperature?

Answer 1

Hint: We know that, most probable speed or velocity is the speed which is possessed by the maximum number of gas molecules at a given temperature. There are three different types of molecular speed such as most probable speed, average speed and root mean square speed.

Complete step by step answer:
Let’s discuss the kinetic theory of gases. This theory represents a microscopic for different gases as it throws light on the behavior of the particles which constitute the gases. This theory was developed by Joule, Bernoulli, Clausius and many other scientists.
Now, we discuss some postulates of the kinetic theory of gases.
1) Every gas consists of very small particles called molecules.
2) Volume occupied by the gas molecules is negligible as compared to the total volume of the gas.
3) The gas molecules collide with each other and with the walls of the container and these collisions are elastic in nature.
4) The average kinetic energy of the gas molecule is directly proportional to the Kelvin temperature.
From the 4th postulate,
Kinetic energy$\alpha $Temperature
$\dfrac{1}{2}m{v^2}\alpha \,T$
$ \Rightarrow \dfrac{1}{2}m{v^2} = kT$
Where, m is mass, v is velocity, k is proportionality constant and T is temperature.
If we rearrange the above equation to calculate v, we get,
$ \Rightarrow v = \sqrt {\dfrac{{2kT}}{m}} $
The above equation shows that velocity is dependent only on the temperature. So, all the gases have the same molecular speed at a given temperature.

Note: It is to be remembered that the molecules of gas are so distributed that they do not have mutual forces of interaction that are attraction or repulsion. This is supported by the fact that when the pressure on the gas is decreased, it expands accordingly provided the temperature is constant.