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Every chemistry textbook I have ever seen defines intensive and extensive properties the same way: Intensive properties are those which do not depend on how much matter is present, while extensive properties do. I came across a question while looking through sample FE exam questions for which my understanding of these properties by this definition failed. The gist of my question really just revolves around pressure and volume in largely compressible substances (i.e., gases).

It seems that, when considering a gaseous substance, these definitions are not robust enough:

  • Volume can be shown to be independent of the amount of material present by simply compressing the gas.
  • Density can be shown to be dependent on the amount of material present by keeping a fixed volume and simply adding more gas molecules.

While I have heard the convincing argument that we should simply consider smaller subsets of the original to determine intensiveness and extensiveness (for instance, if I consider half of the container instead, the volume halves from $V_0$ to $\frac{1}{2}V_0$ and the density remains constant at $\rho$), this doesn't help me to identify why the conventional definition remains in use with what seems like flawed implications. Can anyone help to clarify this?

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    $\begingroup$ Just a general question, since I am very new here: Why was my question edited? Certain parts of what I said (salutation, "this is my first question", etc. - other additional information) were removed. I am confused by this, since I added it for a reason. Is there a convention of which I am not aware? I would prefer if these things are stated, rather than done without my knowledge, so that I can improve. $\endgroup$ – Martensite May 7 '15 at 15:39
  • $\begingroup$ You can always rollback :) $\endgroup$ – Freddy May 7 '15 at 15:40
  • $\begingroup$ I don't think I know what that means! I'm still coming to grips with the layout and functionality of the site. I'm a long-term reader but have only just made an account. $\endgroup$ – Martensite May 7 '15 at 15:43
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    $\begingroup$ Welcome to the Chemistry.SE. You should take the Tour and also have a look at Help Center . Though i din't see your original post, I think the edit was made to keep your question to the point and remove things irrelevant(Salutation). You can always Rollback or reject edit if you think it removes valuable information. You can also read posts in Meta about this. Also this $\endgroup$ – Gowtham May 7 '15 at 15:55
  • $\begingroup$ Welcome to StackExchange @Martensite! A horrid place where we suspend users, remove their accounts, give them thousands of downvotes and etc. :P SE is a little different from anywhere else. It's not totally a forum. The co-founders wanted Stack Overflow and subsequently Stack Exchange to be repositories of knowledge, sheer Q & A, with no noise. That's why there are strict rules here, like for example, salutations are discouraged. You'll get used to this, sooner or later. :) $\endgroup$ – M.A.R. May 7 '15 at 16:32
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To give you a more clear explanation of the definition of these properties, it's more easy to remember them this way :

-Extensive properties are those which *are additive * ( mass, volume ) for example 1 L + 1 L = 2 L. On the other hand, intensive properties are not additive ( temperature, pressure, concentration ) for example 2 mol/L + 3 mol/ L does not give you a 5 mol/L solution. These are properties which don't change at any circumstance.

Some other thing to be considered : The ratio of two extensive properties, gives us an intensive property. For example density= mass/volume. Since it is a ratio it will always be the same regardless of how much of a sample is measured.

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  • $\begingroup$ While I do understand your answer and think it is helpful, I don't think it helps to explain why the definition which is typically presented in chemistry textbooks is still valid. Simply saying that an extensive property "depends on the amount of matter present" would imply that density is extensive. For this reason I am wondering less about a correct way to interpret it and more about why the definition that discusses the amount of mass is the standard one when it seems to fail in the case of density. $\endgroup$ – Martensite May 7 '15 at 15:41
  • $\begingroup$ Also, you say that intensive properties are not additive, but pressure is an intensive property, and if I take 2 mol of a gas at a particular pressure and add another 2 mol of gas that is at the same pressure, the total pressure (i.e., the sum of the partial pressures) is the additive sum of their individual pressures. How does that fit into this definition? $\endgroup$ – Martensite May 7 '15 at 15:47
  • $\begingroup$ I edited my answer for your density question, moles do not define the pressure ! 2 mmHg and 2 mmHg are not equal to 4 mmHg. $\endgroup$ – Ndrina Limani May 7 '15 at 15:49
  • $\begingroup$ I am confused by your answer. After reviewing my chemistry textbook, it states very clearly that if I combine two gases, each with a partial pressure of 2 mmHg, the total pressure is unequivocally 4 mmHg. Am I misunderstanding your point? $\endgroup$ – Martensite May 7 '15 at 15:51
  • $\begingroup$ Well it is UNequivocally, that's what I also said. You may probably have troubles because some other factors you must clearify such as Dalton's law and Rault's law. $\endgroup$ – Ndrina Limani May 7 '15 at 15:55

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