Why does the gas with the smallest molar mass have the highest pressure?

[codcodo]

Homework Statement

If equal masses of Xenon, Argon and Neon are placed in separate flasks of equal volume and same temperature, which one of the following statements is correct:
a) The pressure of Neon flask is greatest.
b) The pressure of Argon flask is greatest.
c) The pressure of Xenon flask is greatest.
d) The pressure in all 3 flasks is the same.

Homework Equations

None

The Attempt at a Solution

The answer stated was Neon because it contains the smallest molar mass out of the three. The smallest molar mass will contain the greatest number of moles. Since pressure is directly proportional to the number of moles in a gas, the pressure of Neon flask is the greatest.

I know that the pressure is directly proportional to the number of moles. But why does the smallest molar mass contain the greatest number of moles?

 

[phyzguy]

Because it says equal masses of each gas are in the flask. If you have two piles with the same mass, and one pile consists of bowling balls and one consists of ping-pong balls, which pile has more balls?

 

[codcodo]

Ping-pong balls! Thank you for the wonderful analogy. It makes perfect sense now.

 

[Orodruin]

Homework Equations

None

Just to point out that there is a relevant equation. The ideal gas law $PV = RnT$. You can rewrite this as
$$
P = \frac{RnT}{V}.
$$
Since $n = M/m$, where $m$ is the molar mass and $M$ is the total mass, you would find
$$
P = \frac{RMT}{V} \frac{1}{m}.
$$
Since $R$, $M$, $T$, and $V$ were assumed to be the same, the gas with the smallest molar mass $m$ will have the highest pressure.

 

[Borek]

Since $n = M/m$, where $m$ is the molar mass and $M$ is the total mass

Funny, I would switch M and m (using the capital letter to mark molar mass and the small one for the gas mass). I feel like it is an accepted convention (but I can be wrong).

 

[Orodruin]

Funny, I would switch M and m (using the capital letter to mark molar mass and the small one for the gas mass). I feel like it is an accepted convention (but I can be wrong).

That may be, it is not my direct field so I may have introduced conventions contrary to what is usually used. Of course, the notation has no impact on the physics.

 

[Borek]

@Orodruin Sure thing, what you wrote is perfectly correct. Actually I thought about posting exactly the same, just assumed OP already got it.

 

[codcodo]

Funny, I would switch M and m (using the capital letter to mark molar mass and the small one for the gas mass). I feel like it is an accepted convention (but I can be wrong).

I use M for molar mass and m for gas mass.

 

[codcodo]

Just to point out that there is a relevant equation. The ideal gas law $PV = RnT$. You can rewrite this as
$$
P = \frac{RnT}{V}.
$$
Since $n = M/m$, where $m$ is the molar mass and $M$ is the total mass, you would find
$$
P = \frac{RMT}{V} \frac{1}{m}.
$$
Since $R$, $M$, $T$, and $V$ were assumed to be the same, the gas with the smallest molar mass $m$ will have the highest pressure.

Thank you.