# V(real) vs. V(ideal)

#### bluesTank

##### Zombie
10+ Year Member
5+ Year Member
Hey everyone, havin a problem with EK not matching up to my Princeton Review book on gases.

EK says that an real gas volume is greater then a ideal volume
PR says the other way around

from the Van Der Waals equation, you have (V-nb) so it seems like it would be lower, so im guessing PR is right.

Is the correct?

#### killinsound

##### Full Member
10+ Year Member
From the Van Der Waals equation if (V - nb), then b would be some value which means V would be larger than predicted by the ideal gas law.

Just say N, T, and (P + a blah blah) are constant. If b = zero, then they would just be equal, but if b was an actual value you would get nRT/P + bn to be equal to your V value.

EK is right. You can also think that the ideal gas law assumes that the gases themselves do not take up their own volume. Well, in real life they do, so real volume would increase.

What exactly does PR say? It sounds as though they are not assuming STP.

#### bluesTank

##### Zombie
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Quoted from PR:

"That is, P(real) < P(ideal) because real gases do experience intermolecular forces, reducing collisions with the walls of the container. And V(real) < V(ideal) because molecules of real gases DO have volume which reduces the effective volume of the container"

#### mc4435

##### Full Member
10+ Year Member
Quoted from PR:

"That is, P(real) < P(ideal) because real gases do experience intermolecular forces, reducing collisions with the walls of the container. And V(real) < V(ideal) because molecules of real gases DO have volume which reduces the effective volume of the container"

My PR chem teacher said that TPR book is wrong, it's an error.

#### ssh18

##### Member
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so just to make sure,

Preal<Pideal
Vreal>Videal?

I had a question about this too as I was going over the gas material today.

#### dochoov

##### Intercalating Death Disk
10+ Year Member
do we need to know the van der walls equation for the MCAT?

#### HippocratesX

##### Member
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EK says we don't need to memorize the van der waals equation, but you should understand what the equation means and how to apply it. Basically, they will not give you a calculation to perform, unless they give you the equation, but...u should know that Vreal > Videal and Preal < Pideal.

Quoting from EK, "Since molecules of a real gas DO have volume, their volume must be added to the ideal volume. Thus Vreal > Videal (where Videal is calculated from PV=nRT). Second, molecules in a real gas do exhibit forces on eachother and those forces are attractive when the molecules are far apart. Since the predominant intermolecular forces in a gas are attractive, gas molecules are pulled inward toward the center of the gas, and slow before colliding with the container walls. Having been slightly slowed, they strike the container wall with less force than predicted by the kinetic molecular theory. Thus a real gas exerts LESS PRESSURE than predicted by the ideal gas law. Preal < Pideal (where Pideal is calculated from PV = nRT).

So for the van der waals equation, [P + a(n/V)^2](V -nb) = nRT, a and b are constants for specific gases. b is a measure of the actual volume occupied by one mole of gas. a reflects the strength of intermolecular attraction (ie..pressure).

#### MrDocNYU

##### Member
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15+ Year Member
My PR chem teacher said that TPR book is wrong, it's an error.

your teacher is wrong.

#### inthemiddle

##### New Member
10+ Year Member
Quoted from PR:

"That is, P(real) < P(ideal) because real gases do experience intermolecular forces, reducing collisions with the walls of the container. And V(real) < V(ideal) because molecules of real gases DO have volume which reduces the effective volume of the container"

I think they're talking about effective volume of the container. So, since real gases do take up volume, the volume of "air" (non-gas particles) in the container is lower.

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