Gen Chem - Kinetic Molecular Theory Confusion

[slinquii]

I'm looking over the gas phase content for the MCAT

I'm not sure what the take-home message is for the kinetic molecular theory of gases. Also, I'm stuck on how they got the equation:

NA(Avogadro's number) x (1/2mu^2) = 3/2RT

Why does the book say that (mass x Avogadro's number) = molar mass??

If you have 32g O2 and you multiply it by 6.022x10^23, you obviously don't come up with 16g/mol. What the heck am I missing??

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[laczlacylaci]

For the KMT:
remember that
1) matter is made of atoms and molecules (related to avo#)
2) particles are constantly in motion (kinetic energy)
3) they interact with each other (attraction, repulsion [potential energy]
4) v increases with temp.
5) energy is transferred upon collision with each other.

To understand Avogadro's #, its important to look at its units. atoms or molecules/moles
I'm not sure what your book said, maybe it would be useful if you posted a picture of the (Mass x Avo#)=molar mass
Instead of remembering formulas, its important to just understand that
grams->moles(uses molar mass) [32g*(1mol/16g)=2mol]
moles->molecules or atoms (uses avo#) [2mol*(6E23molecules or atoms/mol)=12E23 molecules or atoms
Just make sure you have your units lined up in your dimensional analysis.

 

[aldol16]

I'm not sure what the take-home message is for the kinetic molecular theory of gases. Also, I'm stuck on how they got the equation:

The idea is that molecules collide with each other and their container and this gives rise to various properties of gases, including diffusion, effusion, and pressure. In statistical mechanics, one can actually go through and derive the ideal gas law using this theory but that's beyond the scope of the MCAT.

NA(Avogadro's number) x (1/2mu^2) = 3/2RT

Why does the book say that (mass x Avogadro's number) = molar mass??

If you have 32g O2 and you multiply it by 6.022x10^23, you obviously don't come up with 16g/mol. What the heck am I missing??

When you're doing statistical mechanics, it's always important to keep in mind when you're talking about one molecule versus a mole of molecules. In many statistical mechanics equations, you're talking about a single molecule - that is, the kinetic energy of a single molecule is (1/2)*m*v^2. However, when you want to scale that up to macroscopic quantities like R, you have to realize that (1/2)*m*v^2 refers to Joules per molecule. To scale that up, you have to do dimensional analysis and to do that, you have to multiply by a conversion factor: Joules/molecule*molecules/mole = Joules/mole. That's why you're multiplying by Avogadro's number. In this case, you're not referring to molar mass.