Question

A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is $27{}^{\circ }C$. The ratio of average kinetic energies of two gases per molecule is
A. 1 : 1
B. 2 : 1
C. 3 : 1
D. 6 : 1

Answer 1

Hint: To solve the given problem, use the formula for the kinetic energy of a molecule of a gas at a given temperature. Find the kinetic energy per molecule of both gases. Then divide the two energies to find the ratio.

Formula used:
$K=\dfrac{3}{2}kT$

Complete answer:
It is given that the two gases of argon and chlorine are contained inside a flask. The relation between the masses of the gases are given. It is said that the ratio of the mass of argon gas to the mass of the chlorine gas is 2 : 1.
It is also given that the temperature of the mixture is 27${}^{\circ }$C.
With this information we are supposed to find the ratio of the average kinetic energies per molecule of the both the gases.
The average kinetic energy of a molecule of a gas is given as $K=\dfrac{3}{2}kT$ …. (i).
Here, k is the Boltzman constant and T is the temperature of the gas.
From equation (i) we get that the kinetic energy of a molecule of a gas only depends on the temperature of the gas. It is independent of the mass of the gas.
We know that both the gases in the mixture are at the same temperature. Hence, the average kinetic energies per molecule of each gases are equal.
Therefore, the ratio of the kinetic energy per molecule of both the gases will be 1 : 1.

Hence, the correct option is A.

Note:
Note that the formula for the average kinetic energy per molecule that we used is for an ideal gas. We have to assume the gases to be ideal gases.
Also note that to apply this formula, the gases in the mixture must not interact with each other. Otherwise, due to the interaction the kinetic energies may change.
Argon gas is non-reactive gas. Hence, the two gases will not interact with each other.