# Measuring the number of moles of a gas

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S91005774

## Main Question or Discussion Point

In the ideal gas law, the symbol n represents the number of moles of gas. My question is how, given a volume of a certain gas, one determines how many moles one has. My understanding is that a mole in this case denotes a quantity of particles. How does one determine how many moles one has without actually counting the number of particles in the volume of gas? Thanks for any comments.

## Answers and Replies

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Nugatory
Mentor
It depends on what we already know about our sample of gas. Often we know the pressure, volume, and temperature so we use the ideal gas law to calculate the number of moles. Other times we know the weight of the sample of gas (for example, it came from a cylinder of pressurized gas, and the before and after weights of the cylinder tell us the weight of the gas we took out) and then we can calculate the number of moles we have from that and the molecular weight of the gas.

In many common situations we don't even need the number of moles. For example, we can calculate the effect of a change in pressure, temperature, or volume on a fixed amount of gas without knowing how many moles we have because $n$ is a constant.

S91005774
Thank you Nugatory.

I'm looking for an understanding of how one determines the number of moles of a gas without recourse to the ideal gas law.

Your second point is the most helpful to me in this sense.

I now realise that my question has two parts. First, how one determines the number of moles of gas. Second, how one determines the number of particles in a mole. I'm looking into the first question now and therefore ignore the second question for the moment.

I understand that a mole is a unit for quantifying "amount of substance". I further understand that 12g of carbon-12 constitutes one mole of "substance" by definition.

My question at this point is how one would go about calculating the number of moles from the weight of a gas and its molecular weight.

Wikipedia confuses me on this occasion because the concepts involved seem to be denoted by multiple names, some of which are apparently historical.

Any help is much appreciated.

jtbell
Mentor
I further understand that 12g of carbon-12 constitutes one mole of "substance" by definition.

My question at this point is how one would go about calculating the number of moles from the weight of a gas and its molecular weight.
OK, try working out an example for us so we can see where your confusion(s) lie. Consider oxygen, with an atomic mass of 16 and a molecular (O2) mass of 32. How many moles are in 100g of oxygen gas?

[Aside: physicists prefer to say "mass" rather than "weight" in this context, because an object's weight is different on e.g. the moon versus the earth, whereas its mass is the same.]

S91005774
The approach as far as I know is to multiply the molecular mass for O2, 32, by the molar mass constant 1g/mol. This gives a molar mass for O2 of 32g/mol. Dividing the mass of the oxygen gas by its molar mass yields the number of moles, i.e. 100/32 moles = 3.125 moles.

What has confused me was the use of a dimensionless quantity for the molecular mass. This confused me because I expected a unit of mass.

Another confusing point is that the molar mass is not a mass, as the name suggests, but actually has units of mass/mole.

As I understand it now, the following definitions explain the conversion procedure as used in the above.

Definition 1: the molar mass of 12C := 12 g/mole.

Definition 2: the molecular mass of 12C := 12u.

Replacing the unit u by the units g/mole turns the molecular mass of 12C into its molar mass. Equivalently, if its molecular mass is given without the unit u, then one simply multiples by 1g/mole (called the molar mass constant). The same conversion procedure holds for other molecules.

I have further confidence in my current understanding because the above definitions combine to produce the correct value for u. Only one further definition is needed to demonstrate this:

Definition 3: there are N_A particles in a mole.

It then follows that: 12u x N_A/mole = 12 g/mole.

Hence: u = 1g/N_A. If one takes the known value for N_A this indeed gives u = 1.66E-24 g.

Thank you both. I feel that you've helped me navigate a part of physics which, for me at least, is unnecessarily confusing because of its terminology and units.