Van Der Waals' Equation

[DrMattOglesby]

Is it considered a necessity that I memorize the Van Der Waals' equation?
it is used on the ideal gas law to correct deviations when temperature gets too low or pressure becomes too high...essentially when intermolecular forces arise.
wouldnt the MCAT supply this equation on the exam if it was needed to calculate a problem? especially since two variables in it need to be given for any particular problem.

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[iA-MD2013]

Is it considered a necessity that I memorize the Van Der Waals' equation?
it is used on the ideal gas law to correct deviations when temperature gets too low or pressure becomes too high...essentially when intermolecular forces arise.
wouldnt the MCAT supply this equation on the exam if it was needed to calculate a problem? especially since two variables in it need to be given for any particular problem.

ohhh no...but remember what happens to P and V when you deviate from ideal conditions.

 

[DrMattOglesby]

best approximate of ideal conditions are "Plow and Thigh"
that is when Pressure is low and Temperature is high =]
so...when i deviate from ideal, it means that pressure is high and temperature is low.
Makes sense, cause either of those two factors will create intermolecular forces.
Awwwh I LOVE it when things make sense--those "A-Ha!" effects are really making me addicted to this stuff!

 

[iA-MD2013]

best approximate of ideal conditions are "Plow and Thigh"
that is when Pressure is low and Temperature is high =]
so...when i deviate from ideal, it means that pressure is high and temperature is low.
Makes sense, cause either of those two factors will create intermolecular forces.
Awwwh I LOVE it when things make sense--those "A-Ha!" effects are really making me addicted to this stuff!

that is good Plow Thigh...
Also remember that the real pressure is greater than the calculated ideal pressure while the real volume is less than the calculated ideal volume. This you can see in the equation...

 

[physics junkie]

Well, you don't need to understand the equation but you do need to understand how the assumptions that go into PV=nRT make it different from a real gas.

The real volume is actually less than the calculated volume because molecules take up space. This becomes more apparently as the gas gets denser(when a gas is dense the volume of the box holding it is small so V is small and n is large since there are many particles).

The real pressure is actually smaller than the ideal pressure because there are attractive forces between molecules.

I would suspect if this shows up in the MCAT it would be with a graph asking you how a real gas deviates from an ideal gas or which graph best shows how a real gas' pressure/volume deviates from an ideal gas under certain conditions.

The equation itself looks kind of confusing since (P+an^2/V^2)(V-nb) doesn't really show you why you should increase the pressure term if you are looking at a real gas...to get an intuitive feel for why the a term is added you have to put the equation in the form P = nRT/(V-nb) - an^2/V^2...that bugged me for a while until I saw pressure in its more natural form.

 

[iA-MD2013]

The real pressure is actually smaller than the ideal pressure because there are attractive forces between molecules.

Doesn't the equation say that the real pressure is greater than the ideal pressure? But your explanation makes sense...

 

[DrMattOglesby]

without looking at the equation, i can say that it SHOULD account for the pressure being lower than ideal.
this is because real gases exert intermolecular forces on one another whereas ideal gases do not.
the intermolecular forces will essentially take gas molecules away from being able to randomly collide with one another and the walls of the container, thus reducing the pressure.
"my understanding...shes a not so good"--but maybe someone smarter can correct me later on =]

 

[bluemonkey]

Well, you don't need to understand the equation but you do need to understand how the assumptions that go into PV=nRT make it different from a real gas.

The real volume is actually less than the calculated volume because molecules take up space. This becomes more apparently as the gas gets denser(when a gas is dense the volume of the box holding it is small so V is small and n is large since there are many particles).

The real pressure is actually smaller than the ideal pressure because there are attractive forces between molecules.

I would suspect if this shows up in the MCAT it would be with a graph asking you how a real gas deviates from an ideal gas or which graph best shows how a real gas' pressure/volume deviates from an ideal gas under certain conditions.

The equation itself looks kind of confusing since (P+an^2/V^2)(V-nb) doesn't really show you why you should increase the pressure term if you are looking at a real gas...to get an intuitive feel for why the a term is added you have to put the equation in the form P = nRT/(V-nb) - an^2/V^2...that bugged me for a while until I saw pressure in its more natural form.

Actually, the real volume is higher because the particles themselves take up space, hence the addition of the nb term to the total volume. But, as you said, the attractive forces between molecules will lead to a decrease in volume...

 

[iA-MD2013]

without looking at the equation, i can say that it SHOULD account for the pressure being lower than ideal.
this is because real gases exert intermolecular forces on one another whereas ideal gases do not.
the intermolecular forces will essentially take gas molecules away from being able to randomly collide with one another and the walls of the container, thus reducing the pressure.
"my understanding...shes a not so good"--but maybe someone smarter can correct me later on =]

That makes sense to me...But I have always been confuse with this because TPR has a different explanation than EK, so I drew my own conclusions from the equation. Now, I think I'm wrong...

 

[bluemonkey]

That makes sense to me...But I have always been confuse with this because TPR has a different explanation than EK, so I drew my own conclusions from the equation. Now, I think I'm wrong...

So take a look at the equation for a second:

Notice that when you solve for volume you end up adding nb to correct for the actual volume and if you solve for pressure, you subtract n^2a/V^2 because of the intermolecular forces between gas particles. At low pressures/high volumes and high temperatures, gases behave very ideally because they collide less frequently and when they do collide, they have sufficient kinetic energy to overcome intermolecular forces. When temperatures become low, however, attractive forces become significant thereby lowering the actual volume. Similarly, under moderately high pressures, the actual volume is lower than that predicted by the ideal gas law because of intermolecular forces. Once the pressure becomes extremely high, however, the actual volume is larger than what the ideal gas law predicts because you can only compress a gas so far (the gas particles themselves take up space). VDW used to give me an awful time until I really sat down and went over it many times...

 

[iA-MD2013]

So take a look at the equation for a second:

Notice that when you solve for volume you end up adding nb to correct for the actual volume and if you solve for pressure, you subtract n^2a/V^2 because of the intermolecular forces between gas particles. At low pressures/high volumes and high temperatures, gases behave very ideally because they collide less frequently and when they do collide, they have sufficient kinetic energy to overcome intermolecular forces. When temperatures become low, however, attractive forces become significant thereby lowering the actual volume. Similarly, under moderately high pressures, the actual volume is lower than that predicted by the ideal gas law because of intermolecular forces. Once the pressure becomes extremely high, however, the actual volume is larger than what the ideal gas law predicts because you can only compress a gas so far (the gas particles themselves take up space). VDW used to give me an awful time until I really sat down and went over it many times...

Thank you! But isn't your explanation (which makes sense) different than the equation which says that the real volume is always less than the calculated volume and the real pressure is always more than the calculated pressure?

 

[Vihsadas]

Understanding why the low pressure and the high temperature can give a good estimate of the ideal law is important. You should be able to extrapolate the effect of the other variables as well (what effect will increasing the container's volume have on the approximation of the ideal gas law all other things being equal?) If you understand why vanderwaals law is the way it is you should be able to figure that out as well without extra information.

(surreptitiously edited b/c I didn't read the specifics of the post I quoted.)

 

[physics junkie]

Actually, the real volume is higher because the particles themselves take up space, hence the addition of the nb term to the total volume. But, as you said, the attractive forces between molecules will lead to a decrease in volume...

I'm not trying to be mean but your answer is completely wrong and the original poster should avoid it if he is looking for clarification.

You seem to be confused as to what V means. It does not refer to the volume of the gas. In (V-nb) V refers to the volume of an empty container--nb refers to the volume of n molecules of gas. You have it backwards a bit. If you don't believe me think about PV=nRT for a bit. An assumption of the ideal gas equation is that molecules have no volume. How could you have a V term then? Only if V refers to the volume of the container. That is in fact what fluctuates with pressure--not the volume of the gas. To put it yet another way--solving for V like you did has no physical meaning. V is not a variable that fluctuates with nb. V is fixed--it's the volume of space available to the gas. Get what I'm saying? The only term that has physical meaning is (V-nb)...this refers to the unoccupied volume inside the container. This makes sense because if you think about having 1 mole of gas and shrinking the container that it is in the pressure is going to increase to infinity as the free volume inside the container goes to 0.

Yeah, it's kind of confusing since I made my explanation by solving for P...but the pressure of the gas DOES vary with density squared(n/V)^2 of the gas. That's why the quantity has physical meaning. If you look at another isolated constant like n and solved for that so you have n=some_garbage would get some messy equation about how n varies with the pressure, volume, and temperature. It would be useless/meaningless to try to interpret such an equation because we all know n is the number of gas molecules and we get to pick that and it stays constant for a closed system.

If you want more information wikipedia van der waals equation of state.

Notice that when you solve for volume you end up adding nb to correct for the actual volume and if you solve for pressure, you subtract n^2a/V^2 because of the intermolecular forces between gas particles. At low pressures/high volumes and high temperatures, gases behave very ideally because they collide less frequently and when they do collide, they have sufficient kinetic energy to overcome intermolecular forces.

Ok, first error is gases collide less frequently at high temperatures. They collide more frequently at high temperatures because they have more kinetic energy and are thus traveling at higher velocities. I'm confused about what you think about gases needing kinetic energy to overcome intermolecular forces(implying the forces are repulsive) and then saying the forces are attractive one line later. The gases are exerting forces on eachother pulling eachother together so kinetic energy has nothing to overcome in that sense. Your confusion about the volume leads you to quite a few problems in your understanding of the VDW equation.

When temperatures become low, however, attractive forces become significant thereby lowering the actual volume.

This is flat out wrong. Volume is not a function of temperature--pressure is. A gas doesn't take up more volume when it's heated up. It simply has more kinetic energy and thus more pressure.

Similarly, under moderately high pressures, the actual volume is lower than that predicted by the ideal gas law because of intermolecular forces.

Wrong, this is just fundamentally confusing what is fluctuating. Volume does not fluctuate with pressure since you are talking about the volume of a container minus the volume of the gas. The pressure of the gas fluctuates with volume. Think about it. Under low volume there is high pressure and thus greater density. Since the pressure term adjustment is a(n/V)^2 you can see that it adjusts to the density of the gas. The more dense the gas the more attractive intermolecular forces at play so the greater the negative pressure deviation from an ideal gas described by PV=nRT.

Once the pressure becomes extremely high, however, the actual volume is larger than what the ideal gas law predicts because you can only compress a gas so far (the gas particles themselves take up space).

Not true for reasons already stated.

VDW used to give me an awful time until I really sat down and went over it many times...

Van der waals deviations aren't confusing conceptually but understanding the equation is confusing. It requires a lot of thinking about what the details are and what is being held constant and what is not constant.

Edit: Vihsadas, can you read both our explanations and reevaluate your opinion. I thought bluemonkey's post looked good and was just a different formulation of my own thoughts until I thought about it and realized that I think he's wrong.

 

[tncekm]

Man, all this confusing talk...

I just like to remember it the simple way: ideal molecules don't have electrostatic interactions and take up no volume.

If there are no molecular interactions then all of the mechanical energy is in the form of Kinetic Energy which contributes to the pressure because the KE provides the energy for the molecules to slam against their container; real molecules lose KE to PE so they have less KE to slam the container walls. In addition, since there is no molecular volume the calculated volume will actually be less than it would if we included the volume of the molecules.

And in PV=nRT for MCAT purposes either P or V is changing, so one of them is fixed.

I think that's all we need to know for the MCAT!

 

[bluemonkey]

Yes, I did manage to mix up more vs. less collisions with increasing temperature. No, I am not confusing the volume of gas particles with the volume of the system. Thank you for your reference to wikipedia, but I don't need to run to wikipedia to fact-check everything. All of what I mentioned about intermolecular forces vs. KE, moderate high pressure & extreme high-pressure is true. As far as temperature vs. volume, I guess Charles' law doesn't apply in your universe. I seem to recall something about temperature and volume being directly related, but apparently Charles was wrong...

Thank you for your diatribe. I think my intelligence just dropped by a considerable margin...

 

[physics junkie]

Doesn't the equation say that the real pressure is greater than the ideal pressure? But your explanation makes sense...

No, the equation doesn't say the real pressure is greater than the ideal pressure. You have to read my clarification that I posted later to understand. If you still have questions I can write up a full explanation of the VDW from my perspective.

Thank you! But isn't your explanation (which makes sense) different than the equation which says that the real volume is always less than the calculated volume and the real pressure is always more than the calculated pressure?

The real volume is always less than the calculated volume using PV=nRT. The real pressure is always less than the calculated pressure using PV=nRT. The equation doesn't look like it--but it's true and I showed in my first post how to look at it to see this. The analagous argument for V fails because the volume of the container doesn't fluctuate depending on properties of the gas.

 

[bluemonkey]

I'm not trying to be mean but your answer is completely wrong and the original poster should avoid it if he is looking for clarification.

You seem to be confused as to what V means. It does not refer to the volume of the gas. In (V-nb) V refers to the volume of an empty container--nb refers to the volume of n molecules of gas. You have it backwards a bit. If you don't believe me think about PV=nRT for a bit. An assumption of the ideal gas equation is that molecules have no volume. How could you have a V term then? Only if V refers to the volume of the container. That is in fact what fluctuates with pressure--not the volume of the gas. To put it yet another way--solving for V like you did has no physical meaning. V is not a variable that fluctuates with nb. V is fixed--it's the volume of space available to the gas. Get what I'm saying? The only term that has physical meaning is (V-nb)...this refers to the unoccupied volume inside the container. This makes sense because if you think about having 1 mole of gas and shrinking the container that it is in the pressure is going to increase to infinity as the free volume inside the container goes to 0.

Yeah, it's kind of confusing since I made my explanation by solving for P...but the pressure of the gas DOES vary with density squared(n/V)^2 of the gas. That's why the quantity has physical meaning. If you look at another isolated constant like n and solved for that so you have n=some_garbage would get some messy equation about how n varies with the pressure, volume, and temperature. It would be useless/meaningless to try to interpret such an equation because we all know n is the number of gas molecules and we get to pick that and it stays constant for a closed system.

If you want more information wikipedia van der waals equation of state.



Ok, first error is gases collide less frequently at high temperatures. They collide more frequently at high temperatures because they have more kinetic energy and are thus traveling at higher velocities. I'm confused about what you think about gases needing kinetic energy to overcome intermolecular forces(implying the forces are repulsive) and then saying the forces are attractive one line later. The gases are exerting forces on eachother pulling eachother together so kinetic energy has nothing to overcome in that sense. Your confusion about the volume leads you to quite a few problems in your understanding of the VDW equation.



This is flat out wrong. Volume is not a function of temperature--pressure is. A gas doesn't take up more volume when it's heated up. It simply has more kinetic energy and thus more pressure.



Wrong, this is just fundamentally confusing what is fluctuating. Volume does not fluctuate with pressure since you are talking about the volume of a container minus the volume of the gas. The pressure of the gas fluctuates with volume. Think about it. Under low volume there is high pressure and thus greater density. Since the pressure term adjustment is a(n/V)^2 you can see that it adjusts to the density of the gas. The more dense the gas the more attractive intermolecular forces at play so the greater the negative pressure deviation from an ideal gas described by PV=nRT.


Not true for reasons already stated.



Van der waals deviations aren't confusing conceptually but understanding the equation is confusing. It requires a lot of thinking about what the details are and what is being held constant and what is not constant.

Edit: Vihsadas, can you read both our explanations and reevaluate your opinion. I thought bluemonkey's post looked good and was just a different formulation of my own thoughts until I thought about it and realized that I think he's wrong.

Furthermore, there is a conversion from attractive to repulsive forces as particles get closer to one another. Or perhaps you don't remember the switch from dipole-dipole to electrostatic repulsion...

 

[bluemonkey]

The real volume is always less than the calculated volume using PV=nRT. The real pressure is always less than the calculated pressure using PV=nRT. The equation doesn't look like it--but it's true and I showed in my first post how to look at it to see this. The analagous argument for V fails because the volume of the container doesn't fluctuate depending on properties of the gas.

REALLY??? What are you talking about??? That is completely false. PV=nRT calculations would give you an infinitely decreasing volume with an infinitely increasing pressure. This is totally bogus!!! You cannot infinitely compress gas particles. THEY TAKE UP SPACE.

 

[tncekm]

The real volume is always less than the calculated volume using PV=nRT.

No, not according to the texts I've been reviewing and this link: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.html

 

[iA-MD2013]

No, the equation doesn't say the real pressure is greater than the ideal pressure. You have to read my clarification that I posted later to understand. If you still have questions I can write up a full explanation of the VDW from my perspective.

The real volume is always less than the calculated volume using PV=nRT. The real pressure is always less than the calculated pressure using PV=nRT. The equation doesn't look like it--but it's true and I showed in my first post how to look at it to see this. The analagous argument for V fails because the volume of the container doesn't fluctuate depending on properties of the gas.

I see...that makes sense now. Thank you!

 

[iA-MD2013]

No, not according to the texts I've been reviewing and this link: http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.html

I saw that website, too. But TPR agrees with phys junkie. I just don't know anymore.

 

[bluemonkey]

I saw that website, too. But TPR agrees with phys junkie. I just don't know anymore.

Take a second to think about this. If you compress a gas, eventually the particles are butting up against one another and you cannot compress them any further (unless fusion is going to occur). Most equations that we use are extremely useful for making predictions, but most don't apply to every situation in the real world, eg extremely high pressures for gases vs. volumes.

 

[tncekm]

I saw that website, too. But TPR agrees with phys junkie. I just don't know anymore.

In TPR they're talking about volume available for other gases to occupy in the situation where there is a fixed container.

I believe there is an argument here about how much space, for example, a mole of real gas would occupy at standard conditions versus how much space the ideal gas would occupy at standard conditions.

I guess its probably good to know both!

 

[physics junkie]

Yes, I did manage to mix up more vs. less collisions with increasing temperature. No, I am not confusing the volume of gas particles with the volume of the system. Thank you for your reference to wikipedia, but I don't need to run to wikipedia to fact-check everything. All of what I mentioned about intermolecular forces vs. KE, moderate high pressure & extreme high-pressure is true. As far as temperature vs. volume, I guess Charles' law doesn't apply in your universe. I seem to recall something about temperature and volume being directly related, but apparently Charles was wrong...

Thank you for your diatribe. I think my intelligence just dropped by a considerable margin...

*shrug*

Way to take it personally and not understand why you can't solve for V and make sense of it. I could care less if you want to dig your head in the sand but don't defend all my criticisms of your argument with "I'm right and too smart for wikipedia." You're just confusing everyone.

Amusingly enough I didn't criticize any of your situations with moderate-high pressure or extreme high-pressure or any crap like that because I couldn't think of any clearcut arguments to either support or criticize you and didn't think it necessary to analyze everything you say. I just pointed out flaws in your reasoning as I saw them. You haven't defended any criticism of your arguments so don't convince yourself that you did. If Vihasdas or you provide arguments telling me that I'm wrong then I'll eat my words--until then...

 

[physics junkie]

REALLY??? What are you talking about??? That is completely false. PV=nRT calculations would give you an infinitely decreasing volume with an infinitely increasing pressure. This is totally bogus!!! You cannot infinitely compress gas particles. THEY TAKE UP SPACE.

Dude, it's a model based on classical mechanics that was developed before the advent of quantum mechanics. Of course it's not going to be accurate in the limits. I was just explaining to you why V can't refer to the volume of the gas and has to refer to the volume of the container. I didn't expect you or anyone else to take it literally. It is just an easy proof by contradiction to show you that V refers to the volume of the container, nb refers to the volume of the gas. You said "Actually, the real volume is higher because the particles themselves take up space," and that's wrong. What "real volume" are you referring to then? What variable is it? Or how could I construct it mathematically?

No offense but my physics and math background is pretty damn strong compared to your own. I'm on my third quantum mechanics class and have taken statistical mechanics. I know how forces vary between attractive and repulsive but overall the force adjustment in the van der waals equations says that gases tend to have an attractive force between them as compared to their ideal conception. This isn't debatable stuff. You said the gas needs kinetic energy to overcome intermolecular forces...to do what? Bond into one molecule? That has nothing to do with PV=nRT so I don't even know why you'd mention it!

I'm going to read your purdue chem article to see if you're just not understanding me or if purdue is wrong. If I think purdue is wrong I'll ask my statistical mechanics professor tomorrow.

 

[DrMattOglesby]

If Vihasdas or you provide arguments telling me that I'm wrong then I'll eat my words--until then...

i wish i had the power to convince you that you were wrong.
but, 1) i dont think im smart enough, and 2) my mind-control powers are not that matured yet.

anyhow, think of it like this; you are walking away with a DAMN good understanding of Van Der Waals' equation now. I generally dont condone arguing on the internet, but this looks like a good exercise in critical thinking to say the least. Its like a prep for the verbal reasoning section =]

and btw. I am sticking with "Plow and Thigh" to understand ALL of these arguments.

 

[Vihsadas]

Oh man, I don't think that I have time to go through what everyone said, but the heart of the misunderstanding seems to be based in two things:

1) misinterpretation of what is said (thought not being accurately reflected in words)
2) Confusion about which variables are being held constant. As I'm sure all of you know, you can't work through ideal gas law problems or vander waals problems without first specifying which variables are being held constant. There is P,V and T, and they are all interdependent.

I must study. Good luck guys...You guys might try to be a bit more diplomatic in the phrasing of your posts. Noone's done anything wrong, but phrasing things nicer just makes for nicer conversation.

For the MCATers: Just make sure that you refer to your texts, and really think about what each term means. Also make sure you have clearly defined the artificial constraints given in each problem before you look at the problem. i.e., Which of pressure, temperature, and volume are allowed to vary and which are held constant? When I keep either pressure, temperature or volume constant how does that affect the two variables that are not constant when I vary one of them?

Let's try not to get into a 'my brain is bigger' pissing contest. Noone wins. haha.

I really must go study.

 

[Kaustikos]

The real pressure is actually smaller than the ideal pressure because there are attractive forces between molecules.

The equation itself looks kind of confusing since (P+an^2/V^2)(V-nb) doesn't really show you why you should increase the pressure term if you are looking at a real gas...to get an intuitive feel for why the a term is added you have to put the equation in the form P = nRT/(V-nb) - an^2/V^2...that bugged me for a while until I saw pressure in its more natural form.

The pressure statement makes sense, since you HAVE to take into account the attractive forces that molecules exhibit in real situations. It would make sense that the pressure would decrease, not to mention the lower kinetic energy that was mentioned. But it still makes no sense because the whole paranthesis ordeal basically says that (P + an^2/V^2) = Preal. Which would imply it's always larger, unless the constant were negative. The real volume being lower works according to that way of thinking. Putting it into the P = nRT/(V-nb) - a(n*v)^2 only solves for the ideal gas, not real.

I get it, conceptually, but it makes no sense to think that way from the formula. It seems that with pressure, you would have an increased real pressure and a decreased volume (volume available).

And thanks for the clarification about the Volume, it absolutely abolishes any confusion I had about that term.

 

[physics junkie]

The pressure statement makes sense, since you HAVE to take into account the attractive forces that molecules exhibit in real situations. It would make sense that the pressure would decrease, not to mention the lower kinetic energy that was mentioned. But it still makes no sense because the whole paranthesis ordeal basically says that (P + an^2/V^2) = Preal. Which would imply it's always larger, unless the constant were negative. The real volume being lower works according to that way of thinking. Putting it into the P = nRT/(V-nb) - a(n*v)^2 only solves for the ideal gas, not real.

I get it, conceptually, but it makes no sense to think that way from the formula. It seems that with pressure, you would have an increased real pressure and a decreased volume (volume available).

And thanks for the clarification about the Volume, it absolutely abolishes any confusion I had about that term.

What I'm about to write is definitely beyond the scope of the MCAT but it is pretty cool and I hope you take the time to read it and understand it.

Ok, there is a subtle difference between the words "real" and "observed" so I'm going to be very cautious about how I use the two terms. Since you seem to be clear about volume I'm going to refer to V-nB as the "actual volume."

The equation is NOT saying (P + an^2/V^2) = P_observed. It actually says (P+an^2/V^2) = P_calculated. You probably think its contradictory that I say that and also say (V-nb) = V-observed but you have to understand that the variable V stands for the same quantity in both equations but the variable P stands for different quantities in the two equations.

In the VDW equation you have to think of 'P' alone as the observed pressure and (V-nb) as the actual volume where V is the ideal calculated volume of an empty container. So V in the ideal gas law equation and V in the van der waals equation refer to the same quantity: the volume of the box. However, P in the ideal gas equation refers to the calculated pressure whereas P in the van der waals equation refers to the observed(or actual) pressure.

You might be making the mistake of trying to look at P=(nRT)/(V-nB) and then subtracting a term -an^2/V^2 to see what the difference is. The problem with your logic here is subtle and conceptual. When you're looking at P=(nRT)/(V-nb) you are talking about the calculated P for which you have not taken into account attractive molecular forces. When you subtract -an^2/V^2 and get the equation P=(nRT)/(V-nb) - an^2/V^2 notice that we are no longer talking about the same calculated P--we have now just defined a new P--the observed P. It's easier to see that we're not talking about the same variable P in both equations if you realize that the real P can only have 1 value--not two. You can actually put the equation P=(nRT)/(V-nb) - an^2/V^2 in words as Observed_Pressure = Calculated_pressure - correction_factor.

So then you can see in the actual van der waal's equation (P+an^2/V^2) is actually the term that describes the calculated pressure! So at the VDW equation says calculated-pressure*actual_volume=nRT. I know it looks really ****ing bizarre but you gotta hear me out on why it is this way. After you're done reading this you're probably going to need to read it 2 more times for it to sink in but once you get it you will know a piece of information that is very, very gratifying to finally understand.

Now I'm going to explain to you a situation now where it is physically intuitive to think of (P+an^2/V^2) as the calculated pressure in the van der waals equation.

First thing you gotta realize is nRT has units of joules which means it is equivalent to the energy of the system. That means that the pressure of a system is equal to the energy density(energy per unit volume) of the system!

Instead of looking at the VDW equation as a set of relations between variables let's think of it another way--as a way to define the relation between pressure and energy density.

Now let's pretend we are lowly pre-meds in a physics lab with a particularly sadistic TA who hates teaching pre-meds who don't care about physics. He's prepared a lab apparatus where he has put n moles of hydrogen gas at a temperature T inside of a volume V. He tells you what n, V, R, T, and b are so you can calculate the energy density. He then asks you to find the energy density using a pressure gauge and your textbook. You realize immediately that kinetic-energy/volume is expressed in the form of pressure in a gas and decide to hook up a pressure gauge to the apparatus. To your surprise, the observed pressure is less than the total-energy/volume you calculated from nRT/(V-nb). Your TA, noticing you're struggling, then urges you to think critically and remember that on the average there are attractive forces in a gas. Suddenly, it clicks to you. Some of the energy in the gas is stored as potential energy between the gas molecules. When you looked at the pressure gauge you were only measuring the kinetic energy of the gas and ignoring the potential energy. By adding the an^2/V^2 term to the left side you get P_observed + an^2/V^2 = nRT/(V-nb). You have satisfied your TA now that you understand that measuring the pressure empirically will always give you a value of the energy density of the gas that is lower than the actual energy density. You further explain to him that the an^2/V^2 term is actually the potential energy density of the gas!

So you see there are plenty of ways of interpreting the VDW equation. First we looked at it as a statement about how to calculate the observed pressure from the calculated nRT/(V-nb) - an^2/V^2 term. Then we looked at it as a statement about how the energy density is distributed between the kinetic energy and potential energy of the gas. When you looked at in this second way you realized why the an^2/V^2 term is there and why the equation takes the form (observed_pressure + correction_factor)(actual volume)=nRT. It's all quite beautiful. It's a shame no one comes outright and says these things but it is a lot of fun to discover these things on your own. Of course, if you waste too much time doing stuff like this you'll end up with a low GPA and a high MCAT and a plane ticket to the caribbean like yours truly.

This purdue link seems to capture this viewpoint: chemed.chem.purdue.edu/genchem/history/vanderwaals.html

The molecule striking the wall does so at a velocity that is slightly less (determined by the size of the intermolecular forces) than it would without these forces. Or, the observed pressure is actually slightly less than the pressure would be without the intermolecular forces. To correct for this, a small positive pressure must be added to the observed pressure, hence the term with "a" in it is positive. This is illustrated in the figure below:

Let me know if you get it. I spent almost 45min typing this up so hopefully it helps.

 

[Kaustikos]

I understand it. I think I was just assuming that because this was the "Van Der Waals Equation", the paranthesised (??) terms equaled the real terms and that the individual P and V were the ideal and you were correcting for that.

But that's not even close to true. I just think I was confused along the way. Your post explains it perfectly and it does make sense. Pressure should be lower than ideal because of said forces and they say so in so many books. Excellent post. It wasn't beyond or over the top and well explained. Or I think so.

The only confusing thing was having to remember observed = real and calculated = ideal.

Thanks a lot.

 

[BerkReviewTeach]

Is it considered a necessity that I memorize the Van Der Waals' equation?
it is used on the ideal gas law to correct deviations when temperature gets too low or pressure becomes too high...essentially when intermolecular forces arise.
wouldnt the MCAT supply this equation on the exam if it was needed to calculate a problem? especially since two variables in it need to be given for any particular problem.

To answer your first question, it is highly likely that such an equation would be supplied, along with some a and b values for a few real gases. Keep in mind that the MCAT has several different authors, so there is never a 100% answer as to what will be on the exam, but they are typically very liberal in the information they present in passages.

Also, in light of the direction this thread has taken, I'd like to offer my two cents that this topic needs to be understood on a simplistic, conceptual level on par with first-year general chemistry. The previous references to quantum mechanics and statistical mechanics are irrelevant given that (1) the real gas equation is not rooted in quantum mechanics, (2) those classes are beyond the level of the MCAT, and most improtantly perhaps that (3) anyone who's taken those classes can confirm that they actually make you dumber rather than teach you much.

At the level you need, there are two basic considerations:

First: Real gas particles exert forces on one another, and although we generally consider these to be attractive in nature, the equation allows for the possibility that the particles may repel.

Second: Real gas particles have a definite size and are non-compressible.

Consider the VDW equation to be the ideal gas equation with corrections. If particles have attractive forces, then the gas can be thought of as one that would implode. By imploding, the particles have a tendency to collide with the walls less frequently, and thus exert a lower pressure than one would expect if they were ideal. Hence, the correction term is added to the observed P, to compensate for the drop in pressure from ideal behavior.

Think of it as Pideal = Pobserved + a correction term. The correction term takes into account the degree of attraction (a value) and concentration (nexp2/Vexp2).

For volume, the open space that we consider to be available for a particle to move into (space that is not currently occupied by another particle) is thought of as the ideal volume.

Think of it as Videal = Vcontainer - space occupied by other particles. The correction term takes into account the size of the particles (b value) and the amount of particles .

The key to this topic on the MCAT is to keep it as simple as possible. If you can accurately answer the following few questions, you have a solid enough grasp to be good at the MCAT level.

(1) Which of the following gases would likely exhibit the greatest b value?
A. Methane
B. Carbon dioxide
C. Hydrogen
D. Dimethyl ether

(2) Which of the following gases would likely exhibit the smallest a value?
A. Helium
B. Chlorine
C. Ammonia
D. Sulfur dioxide

(3) How can it be explained that argon has a larger b value than hydrogen?
A. Argon is more polar than hydrogen
B. Argon is more electronegative than hydrogen
C. Argon has a significantly larger atomic radius than hydrogen
D. Hydrogen is a diatomic gas while argon is monatomic

(4) At extremely high pressures, the value of PV/nRT increases to a value greater than 1 for all gases. How can this be explained?
A. Gas atoms become smaller as the gas is compressed.
B. Temperature deviates from ideal behavior at elevated pressures.
C. The size of the particles becomes more significant than intermolecular forces.
D. Molecules experience greater induced dipoles as the mean free path decreases.

 

[DrMattOglesby]

The key to this topic on the MCAT is to keep it as simple as possible. If you can accurately answer the following few questions, you have a solid enough grasp to be good at the MCAT level.

(1) Which of the following gases would likely exhibit the greatest b value?
*I am looking for the molecule that takes up the most volume*
A. Methane
B. Carbon dioxide
C. Hydrogen
D. Dimethyl ether - occupies greatest volume

(2) Which of the following gases would likely exhibit the smallest a value?
*I am looking for the most unreactive species*
A. Helium - it is a noble gas and has little interaction with other gases
B. Chlorine
C. Ammonia
D. Sulfur dioxide

(3) How can it be explained that argon has a larger b value than hydrogen?
*I am looking for a reason to explain why argon takes up more volume than Hydrogen*
A. Argon is more polar than hydrogen
B. Argon is more electronegative than hydrogen
C. Argon has a significantly larger atomic radius than hydrogen
D. Hydrogen is a diatomic gas while argon is monatomic

(4) At extremely high pressures, the value of PV/nRT increases to a value greater than 1 for all gases. How can this be explained?
A. Gas atoms become smaller as the gas is compressed.
B. Temperature deviates from ideal behavior at elevated pressures.
C. The size of the particles becomes more significant than intermolecular forces.
D. Molecules experience greater induced dipoles as the mean free path decreases.

i PMd BerkReviewTeach and he explained #4 for me...but I'll let someone else try to tackle if it possible before i post Berk's explanation.

 

[iA-MD2013]

4. C?

 

[Kaustikos]

4. C?

That's what I figured. I hated the wording on those choices though.

 

[glknoyo]

I know it's an old thread, but this is the first hit when you google "SDN Van Der Waals Equation," and if anyone wants a quick easy way to look at this concept, here it is:

So we know (Pr+X)(Vr-Y) = nRT. But also PiVi = nRT! so then (Pr+X)(Vr-Y) = PiVi, so
Pi = Pr + X and Vi = Vr-Y. Therefore Pi - X = Pr and Vi + Y = Vr, and it follows that Pi < Pr and Vr > Vi.

 

[leathersofa]

Could someone explain why the answer is C for question 4. I thought it was C through POE but I dont understand why the size of the particles becomes more significant than IMFs?

 

[shklorg]

.

 

[Sergiy MSc]

Is it considered a necessity that I memorize the Van Der Waals' equation?
...essentially when intermolecular forces arise.

Hi, in my Institute they would also ask about concept of gas - liquid - crystall transformations that the Equation describes, and student's understanding of the critical temperature. To deeper understand, probably watching molecules behaviour could help - simulated, of cause , at a big scale - with/without intermolecular forces, at different temperatures. You will see them condensating and freezing, apply pressure by Piston and build graph P(V).

 

[Sergiy MSc]

If you have Android smartphone or tablet, the freeware 'Van der Waals gas' App is here - https://play.google.com/store/apps/details?id=gmailcom.koozy.app.vander