[galpinj]

I'll get right to it,

I was reading about exceptions to the ideal gas law and it got me thinking about how we measure volume. Wen we measure a solid or liquid, we look at the volume that  substance takes up. However, when we measure a gas (via ideal gas law), we look at the total volume of the container. One is a measure of the amount of a substance while the other is a measure of "space" (and in fact ignores the volume taken up by the substance!). It seems to me that the definition of volume is very different for a  gas than it is for solids and liquids, so how do we compensate for this difference?

I think that the differences are reconciled through the gas constant (0.0821 L-atm/mole-K), but I'm not really sure.

Please share your thoughts and help me better understand this.

[Arkcon]

I think you're close to the real question,but you may no see it.  Query:What formula is the gas constant used for?

[AWK]

I was reading about exceptions to the ideal gas law and it got me thinking about how we measure volume

The ideal gas law is the approximation hence discusion about exceptions has no sense.

I think that the differences are reconciled through the gas constant (0.0821 L-atm/mole-K), but I'm not really sure

The value of gas contsant in these unit is different (0.082057338 - usually approximated to 0.08206 for calculation with 3 significant digits)

One is a measure of the amount of a substance while the other is a measure of "space" (and in fact ignores the volume taken up by the substance!)

Vant der Waals law uses also own volume of molecules but but this is still the approximation, though better (and much complicated calculations).

[mjc123]

There is no difference. The volume is the amount of space occupied by the substance - that is, which the molecules permeate. It is, if you like, the region of space which, if you impinge on it, you will experience a pressure from the substance. In no case is it equal to the volume of the molecules (which itself is mostly empty space). It's just that there's a lot less space between the molecules in a solid or liquid than a gas. In fact, in the van der Waals equation in the term (V-b) you subtract the volume of the molecules from the total volume - it is the space between the molecules that behaves more like V in the ideal gas law.

[galpinj]

There is no difference. The volume is the amount of space occupied by the substance - that is, which the molecules permeate. It is, if you like, the region of space which, if you impinge on it, you will experience a pressure from the substance. In no case is it equal to the volume of the molecules (which itself is mostly empty space). It's just that there's a lot less space between the molecules in a solid or liquid than a gas. In fact, in the van der Waals equation in the term (V-b) you subtract the volume of the molecules from the total volume - it is the space between the molecules that behaves more like V in the ideal gas law.

That mostly makes sense, but then why don't we remove the volume of the molecules from the total volume in liquids or solids? Obviously they take up more "space" than the gas molecules do, and yet we are only concerned with the volume of gas molecules when looking at the volume of a gas (i.e. Van Der Waals Equation). The fact that they are treated so differently makes me think that the concept of volume for the two are fundamentally different!

[galpinj]

I think you're close to the real question,but you may no see it.  Query:What formula is the gas constant used for?

Gas constant is used in both the ideal gas law and Van Der Waals Equation.

[galpinj]

Hi everyone,

I'm having some trouble understanding a sentence in a textbook I'm reading, and was hoping someone could help clarify it for me.

The book I was reading last night stated the following: "To underscore the concept that gases behave more ideally at higher temperatures, if we increase the temperature of the system for any gas, the first term in the van der Waals equation approaches the pressure of the ideal gas while the second term remains unchanged"

This doesn't really make sense to me. If the system is held at constant volume, then I can see how increasing temperature will increase pressure and reduce the impact of (an^2/V^2), thus making the first term "approach the pressure of the ideal gas"; However, I don't understand why the second term (I think "second term" refers to (V-nb)) has to remain unchanged! If the pressure of the system was held constant, then obviously the volume would increase and become more ideal!

On the one hand, it makes conceptual sense that, in a constant volume container, increasing temperature will not affect volume (the same amount of space and molecules are present, although moving about faster); however, I still contend that volume would increase if pressure was held constant (PV = T).

What is the book trying to say? What am I missing here? Does temperature really only affect pressure and not volume?

Thank you everyone!

[mjc123]

why don't we remove the volume of the molecules from the total volume in liquids or solids?

Because the space between them doesn't behave even approximately like an ideal gas, so it's not useful.
In a van der Waals gas it is the corrected volume (after subtraction of the volume of the molecules) that behaves approximately like an ideal gas, ie PV ≈ nRT. But the actual volume occupied by the gas is still the total volume, including the volume of the molecules.

[mjc123]

I think they must be assuming constant volume. (Check again if they said that.) At constant pressure, V will increase, so nb will become smaller in comparison. But still the pressure correction will decrease faster, because of the 1/V² dependence.

[Arkcon]

I hope no one minds, I've merged two threads, the concepts are similar enough, and the answers to one may help for another one.