Question

Its not iii only and its not ii only so what is it?

Consider two gas samples at the same temperature.
Gas sample X has a higher molar mass
than gas sample Y. Which of the following
statements is/are true?
I. Gas sample X will have a higher average
particle velocity.
II. Gas sample Y will have a broader range of
particle velocities.
III. The particles in both gas samples have
the same average kinetic energies

Answer 1

It's both II and III.

Explanation:

Let's examine each of these statements.

I. Gas sample X will have a higher average particle velocity

According to the Kinetic Molecular Theory, the average molecular velocity is directly proportional to the Kelvin temperature.

`"KE" = "½mv"^2 ∝ T`

If `T` is constant, then

`v ∝ 1/sqrtm`

The molecules with higher mass will have a slower velocity.

Statement I is false.

II. Gas sample Y will have a broader range of particle velocities

The diagram below shows the molecular speed distribution for the noble gases at a given temperature.

The molecular speed distribution for smaller atoms like hydrogen (Gas B) is much broader (0 m/s to 2500 m/s) than it is for larger atoms like xenon (Gas A), which has a range of 0 m/s to 500 m/s.

Statement II is true.

III. The particles in both gas samples have the same average kinetic energies

If `"KE" prop T` and if `T` is constant, then `"KE"` is constant.

The average kinetic energy of all gases is the same at a given temperature.

Statement III is true.