IMAT 2018 Q59 [Molecule Motion]

The Earth’s atmosphere contains oxygen and nitrogen. The mass of an oxygen molecule is greater than the mass of a nitrogen molecule. The temperature of air in a room on a particular day is 300 K.

Below are four statements about the motion of the two types of molecule in this room.

  1. They have an equal mean square velocity \overline{(v^2)}.

  2. A nitrogen molecule has a greater mean square velocity \overline{(v^2)} than an oxygen molecule.

  3. A nitrogen molecule has a greater mean kinetic energy than an oxygen molecule.

  4. An oxygen molecule has a greater mean kinetic energy than a nitrogen molecule.

Which of the statements is/are correct?

A. statement 1 only
B. statement 1 and 3 only
C. none of them
D. statement 2 only
E. statement 2 and 4 only

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Statement 1 mentions a “mean square velocity” which is the average value of the square of the velocities of a group of particles, like molecules. We know that mass affects velocity, therefore it is incorrect to claim they could have an equal mean square velocity. We can therefore eliminate A and B.

Statement 2 is correct, proven by the equation for Root Mean Square Velocity, we know that mass is inversely proportional. So, the lighter molecule will have a greater mean square velocity.

We can hence eliminate C.

Statement 3 and 4 are also incorrect, as we find that the mean transitional kinetic energy of these gases should be equal, since they are placed in the same conditions and they are both diatomic.

Making our answer D.