Question

The average molecular speed is greatest in which of the following gas samples?
A) 1.0mol of $ {N_2} $ at 560K (28)
B) 0.50 mol of Ne at 500K (20)
C) 0.20mol of $ C{O_2} $ at 440K (28)
D) 2.0 mol of He 140K (2)

Answer 1

Hint: According to the Kinetic Theory of gases the velocity of the gases depends on the temperature and molecular masses of the gases. The average velocity of random molecular motion is zero. The velocity is found to be directly proportional to the temperature and inversely proportional to the Molar Mass of the gas. If the temperature is increased, the velocity of the gas also increases, thereby the root mean square velocity also increases.

Complete Step By Step Answer:
The average velocity of the gas as per the Kinetic theory of gases can be given by the formula: $ {v_{average}} = \sqrt {\dfrac{{8RT}}{{\pi M}}} $
Where, R is the gas constant, T is the temperature, M is the molar mass of the gas particles in kg/mol. Therefore, the average velocity is directly proportional to the temperature T and inversely proportional to the Molar Mass of the gas.
We are given 4 different gases at 4 different temperatures. The gas with the lowest Molar Mass will have the highest average velocity. If the molar mass is the same then temperature will come into play. The order of molar mass can be given as:
 $ He < Ne < {N_2} < C{O_2} $
He has the lowest mass, hence will have the highest average molecular speed. Remember that Molecular Mass is the primary factor, Temperature is the secondary factor affecting the average velocity.
The correct option is (D).

Note:
The Maxwell distribution curve is a plot of the fraction of a molecule and the velocity/speed of the molecule at a certain temperature. The area under the curve will give us the number of molecules for that particular speed. If we heat the gas, the peak will be shifted to the right as the average speed will increase.