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

• codcodo
In summary: This is a great way to explain it. It makes it easier to visualize and understand why the pressure of Neon flask is the greatest. In summary, according to the ideal gas law, the pressure of a gas is directly proportional to the number of moles present. Since the number of moles is inversely proportional to the molar mass, the gas with the smallest molar mass will have the highest pressure. Therefore, in the given scenario, the pressure of the Neon flask will be the greatest.
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.

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?

Last edited:
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.

codcodo said:

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.

codcodo
Orodruin said:
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).

codcodo
Borek said:
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.

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

Borek said:
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.

Orodruin said:
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.

1. What is a conceptual gas law problem?

A conceptual gas law problem is a type of question or scenario that tests an individual's understanding of the relationships between variables in the ideal gas law, including pressure, volume, temperature, and amount of gas.

2. How do you solve a conceptual gas law problem?

To solve a conceptual gas law problem, you must identify the given variables and use the appropriate gas law equation (e.g. Boyle's law, Charles's law, etc.) to determine the relationship between the variables. Then, you can manipulate the equation to solve for the desired variable.

3. What are the key principles of the ideal gas law?

The key principles of the ideal gas law include: 1) the volume of a gas is directly proportional to its temperature, if pressure and amount of gas are held constant; 2) the pressure of a gas is inversely proportional to its volume, if temperature and amount of gas are held constant; and 3) the amount of gas is directly proportional to its temperature and pressure, if volume is held constant.

4. How does changing one variable affect the other variables in the ideal gas law?

Changing one variable in the ideal gas law will affect the other variables in a predictable way. For example, increasing the temperature of a gas while holding pressure and amount constant will result in an increase in volume. Likewise, decreasing the pressure while holding volume and temperature constant will result in an increase in volume.

5. What are some real-world applications of the ideal gas law?

The ideal gas law has many real-world applications, including in weather forecasting, scuba diving, and industrial processes such as refrigeration and gas storage. It is also essential in understanding the behavior of gases in everyday situations, such as filling up a tire with air or using a propane grill.

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