[orgo814]

Dealing with a question that says the van der waals equation contains a term representing molecular size (assuming b). It asks for the approximate magnitude of this term. The choices are 10^-6 cm^3/mol, 1 cm^3/mol, 10^-3 cm^3/mol, and 10^3 cm^3/mol.

The answer is 1 cm^3/mol. I'm not sure how they got to this and would appreciate any help you could give. Thanks

[Yggdrasil]

What would you say is the typical radius of an atom?  Based on that answer, and the fact that volume ~ radius ^3, figure out the typical volume of a gas molecule then multiply that quantity by Avogadro's number to get vol / mol.

[orgo814]

That's kind of my issue I don't know what radius of atom is since I figured it differed depending on the element

[Borek]

That's kind of my issue I don't know what radius of atom is since I figured it differed depending on the element

While they are different for different atoms, they are all of the same order.

Actually if you don't remember what is the order of magnitude of atom radii (and you definitely should IMHO), you can try to estimate the parameter from another approach. In water molecules touch each other, so it is not difficult to estimate their sizes just from the water density (and I suppose that's something you do remember).

But I don't like the question. That is - I like the question, I don't like the answers given to choose from. b is not much better than one of the other numbers given.

[orgo814]

Yes water density is approx 1 g/mL but I still don't know the approximate atomic radii which is what I need to solve the problem

[sjb]

Yes water density is approx 1 g/mL but I still don't know the approximate atomic radii which is what I need to solve the problem

OK,so roughly how many atoms are there in a ml?

[mjc123]

Since the answers are in cm³/mol, you are over-complicating. The molar volume of water is 18cm³/mol. So while some of this is no doubt space between the molecules, it suggests a figure for molecular volume of the order of 10 cm³/mol - rather bigger than the suggested answer, but perhaps they are thinking of e.g. helium.

[orgo814]

They are not telling me any atom so I can't just assume Helium.

[Borek]

Question is about order of magnitude, doesn't matter what atom you choose.

[orgo814]

So... 10^-10 would be acceptable radius?

[mjc123]

Not without units.