Real gas confusion

[LetsGo352]

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I'm reading the BR chem content review for "gases and gas laws" and when I get to 'real gases' I'm a little confused...

The formula for real gases is van der Waals equation:

(observed pressure + (an^2/V^2))(volume of container^-nb) = nRT

The book says this is the real gas equation...but isn't it the ideal gas equation? After all, the two terms on the left hand side in the equation actually equal ideal pressure and ideal volume, respectively.

Can someone walk me through this?

 

[RogueUnicorn]

yes, this does reduce down to the idea gas equation when a and b are both = 0 (i.e. point particles with no intermolecular attraction); however, in real gasses these corrective factors will explain deviations seen. if you didn't add these factors, then PV will not equal nRT, and then things would get bad. worlds would end.

 

[BellJS]

I'm reading the BR chem content review for "gases and gas laws" and when I get to 'real gases' I'm a little confused...

The formula for real gases is van der Waals equation:

(observed pressure + (an^2/V^2))(volume of container^-nb) = nRT

The book says this is the real gas equation...but isn't it the ideal gas equation? After all, the two terms on the left hand side in the equation actually equal ideal pressure and ideal volume, respectively.

Can someone walk me through this?

Basically, it's just saying that in reality, gases don't always behave ideally.

In other words: take a KNOWN amount of gas and put it into a container of known volume.

If you were to measure the pressure inside the container, it would NOT be exactly what the ideal gas law would predict the pressure would be via simply doing (P = nRT/V).

In fact, you would find the pressure you measure (observed or real pressure) is less than what the ideal gas law predicts. This is because the intermolecular forces of the gas molecules are attractive, counteracting pressure. Essentially, this was neglected in the formulations of the ideal gas law (if you go back you can find it was one of the assumptions for the derivation).

Now about volume:

If we use the same scenario above, you must also take into consideration that the ideal gas law assumes that the ENTIRE container is available for the gas to move in. This is not realistically true because the gas molecules present within the container are not without volume. Therefore, the real volume is actually the volume of the container minus the volume of the gas MOLECULES you put into it (this is not to be confused with what we generally term "volume of gas" but actually refers to summing the volume of all the gas molecules and not counting the space between them). Just think about it in terms of empty space. Wherever a gas molecule exists, thats not empty space another molecule can occupy, so you have to subtract this to reflect that the available volume is actually less.

Eh maybe I didn't do such a great job with this explanation.

 

[LetsGo352]

Basically, it's just saying that in reality, gases don't always behave ideally.

In other words: take a KNOWN amount of gas and put it into a container of known volume.

If you were to measure the pressure inside the container, it would NOT be exactly what the ideal gas law would predict the pressure would be via simply doing (P = nRT/V).

In fact, you would find the pressure you measure (observed or real pressure) is less than what the ideal gas law predicts. This is because the intermolecular forces of the gas molecules are attractive, counteracting pressure. Essentially, this was neglected in the formulations of the ideal gas law (if you go back you can find it was one of the assumptions for the derivation).

Now about volume:

If we use the same scenario above, you must also take into consideration that the ideal gas law assumes that the ENTIRE container is available for the gas to move in. This is not realistically true because the gas molecules present within the container are not without volume. Therefore, the real volume is actually the volume of the container minus the volume of the gas MOLECULES you put into it (this is not to be confused with what we generally term "volume of gas" but actually refers to summing the volume of all the gas molecules and not counting the space between them). Just think about it in terms of empty space. Wherever a gas molecule exists, thats not empty space another molecule can occupy, so you have to subtract this to reflect that the available volume is actually less.

Eh maybe I didn't do such a great job with this explanation.

This makes sense to me. Real pressure < ideal pressure, obviously. But I was listening to EK audio osmosis and they were saying Real Volume > ideal volume......? How can that be? If volume is defined as the available space of the container and you take into account the volume of molecules for real volumes, that cant be true...

 

[RogueUnicorn]

real volume is > ideal volume because of the space occupied by the molecules themselves. a simple way to think about this is to say that there is to be an arbitrary distance between all gas molecules. if they suddenly occupy space, though, each molecule will have to move a bit farther apart from its neighbors to maintain that distance.

 

[CaptainSSO]

real volume is > ideal volume because of the space occupied by the molecules themselves. a simple way to think about this is to say that there is to be an arbitrary distance between all gas molecules. if they suddenly occupy space, though, each molecule will have to move a bit farther apart from its neighbors to maintain that distance.

But a gas will fill up the dimensions of its container regardless of how far apart the actual molecules are. Now that he phrased it this way, I'm actually a little confused myself (never thought about it like this). For instance, if you have carbon dioxide in a 0.5 L bottle, the volume is 0.5 L, whether or not there is gas in the bottle at all. So I don't really understand how an ideal gas does not actually take up space, if the volume is accounted for via the size of the container?

 

[Morsetlis]

I never remembered a question about non-ideal gasses on the MCAT.

 

[RogueUnicorn]

But a gas will fill up the dimensions of its container regardless of how far apart the actual molecules are. Now that he phrased it this way, I'm actually a little confused myself (never thought about it like this). For instance, if you have carbon dioxide in a 0.5 L bottle, the volume is 0.5 L, whether or not there is gas in the bottle at all. So I don't really understand how an ideal gas does not actually take up space, if the volume is accounted for via the size of the container?

it's best to think of the parameters independently; in this scenario, a "real" gas in 0.5L vs an "ideal" gas held at that same constant volume would result in an increased pressure (ignoring the pressure effects of reality); or, to take the opposite view, at the same pressure (assuming there are no intermolecular forces, i.e. b=0) the volume of a real gas is greater than an ideal one

 

[LetsGo352]

it's best to think of the parameters independently; in this scenario, a "real" gas in 0.5L vs an "ideal" gas held at that same constant volume would result in an increased pressure (ignoring the pressure effects of reality); or, to take the opposite view, at the same pressure (assuming there are no intermolecular forces, i.e. b=0) the volume of a real gas is greater than an ideal one

The pressure is defined as the the collision of molecules against the wall, so if there are attractive forces (as is often the case with a real gas), then there would be less collision of molecules against the walls, which means there would be less pressure in a real gas. Which means there would be greater volume is a real gas, correct? I understand the fact that there is less pressure in a real gas, and that ultimately means more volume just based on the pressure-volume relationship. But beyond that, I don't understand why a real gas would have a greater volume. If the intermolecular forces are greater, the molecules are held tighter together, thus, one would assume there would be less volume...?

Also, when we are talking about volume, are we talking about the volume of the container or the volume of the gas itself? The volume of the container can't change so I'm pretty sure we're talking about the volume of the gas and if in a real gas, the molecules actually have volume so is that your reasoning for "greater volume in a real gas"? Thanks for the help.

 

[RogueUnicorn]

The pressure is defined as the the collision of molecules against the wall, so if there are attractive forces (as is often the case with a real gas), then there would be less collision of molecules against the walls, which means there would be less pressure in a real gas. Which means there would be greater volume is a real gas, correct? I understand the fact that there is less pressure in a real gas, and that ultimately means more volume just based on the pressure-volume relationship. But beyond that, I don't understand why a real gas would have a greater volume. If the intermolecular forces are greater, the molecules are held tighter together, thus, one would assume there would be less volume...?

again, the key here is to think of these terms INDEPENDENTLY. you are correct about the lower pressure in a real gas. let's just look at REAL pressure with IDEAL volume (i.e. point particles) at a given volume V, the pressure of a real gas is lower.

now let's look at volume. it is REAL volume (molecules take up space) with IDEAL pressure (no intermolecular attraction) for a given pressure P, the REAL gas will have a greater V, with my reduced down explanation a few posts above. let's pretent gas A is an ideal gas that is at 1atm in a sealed 1L vessel. if we suddenly turn this gas A into a gas with real molecular volume but no intermolecular attraction, the gas will still be contained in a sealed 1L vessel, so the pressure must go up. if it were in an expandable vessel like a syringe, the volume of the gas will increase, pushing the plunger of the syringe out, while maintaining a 1atm pressure.

volume of a gas is indeed dependent on the vessel. however, if you hold volume constant, pressure must change. if you hold pressure constant, volume must change. you are way overthinking this, i don't know how else to explain this, really. you might perhaps be confused by the fact that the "reality" of a gas has somewhat opposing effects - giving gas molecules a real volume means that at a given volume, the pressure the gas exerts goes up. on the other hand, real gasses also have intermolecular attraction, which, at a given volume, will exert a downward influence on pressure. how precisely, then, these two effects add up is precisely what the van der Waals equation of state is for, and it is depend on the a and b values.

 

[Vanguard23]

This makes sense to me. Real pressure < ideal pressure, obviously. But I was listening to EK audio osmosis and they were saying Real Volume > ideal volume......? How can that be? If volume is defined as the available space of the container and you take into account the volume of molecules for real volumes, that cant be true...

Real volume is greater than ideal because the atoms actually take up volume; volume that is neglected in the ideal gas law.
Pressure is lower because there are intermolecular forces attracting the molecules. Sort of like if you were to run around a room filled with people. You have a certain momentum. Now imagine these *******s start pulling on you, messing your groove up. Your momentum drops because your velocity is being lowered by all those *******s.
Same way for the pressure, which is determined by the momentum of particles hitting the sides of a container. It's lowered by the attractive forces.

 

[bigballer27]

real volume is > ideal volume because of the space occupied by the molecules themselves. a simple way to think about this is to say that there is to be an arbitrary distance between all gas molecules. if they suddenly occupy space, though, each molecule will have to move a bit farther apart from its neighbors to maintain that distance.

i searched for this thread b/c my TPR book and EK are conflicting

tpr says: "Therefore, in reality, the actual volume and pressure for a real gas are less than those values obtained from applying the ideal gas law to that gas. That is, Preal<Pideal because real gases do experience intermolecular forces, reducing collision with the walls of the container. And Vreal<Videal because real gases do have volume that reduces the effective volume of the container (since the molecules take up space, there is less space in the container for all the other particles to occupy).

can someone explain what is REALLY going on?!?

 

[Geekchick921]

Bigballer, one of them must be wrong. Are you sure you're reading it right?

P real < P ideal due to intermolecular forces between particles of real gas.
V real > V ideal due to volume of particles of real gas.

Check out the Van Der Waals equation, and we can see that is the case.

Ideal gas law: PV = nRT
Van der Waals: (observed pressure + (an^2/V^2))(volume of container^-nb) = nRT

So to make the observed pressure comparable to the ideal pressure, we have to add the (an^2/V^2) equation to make up for the IM forces that decrease the real/observed pressure. And to make the observed volume comparable to the ideal volume, we have to subtract the volume of the particles of the real gas: nb (number of moles * volume of a mole of the particles).

 

[Nefertiri]

i searched for this thread b/c my TPR book and EK are conflicting

tpr says: "Therefore, in reality, the actual volume and pressure for a real gas are less than those values obtained from applying the ideal gas law to that gas. That is, Preal<Pideal because real gases do experience intermolecular forces, reducing collision with the walls of the container. And Vreal<Videal because real gases do have volume that reduces the effective volume of the container (since the molecules take up space, there is less space in the container for all the other particles to occupy).

can someone explain what is REALLY going on?!?

For a Real gas the pressure is less than for an Ideal gas.Since real gas molecules actually stick together, the force that the individual gas molecules strike the container with is less and thus the pressure (Force/Area) on the container due to each molecule is less.

For a Real gas the volume of gas in the container is greater than for an Ideal gas since real gas molecules have Real volume, unlike Ideal gas molecules which have no volume leaving more unoccupied volume(i.e. effective volume) in the container.

 

[LetsGo352]

Bigballer, one of them must be wrong. Are you sure you're reading it right?

P real < P ideal due to intermolecular forces between particles of real gas.
V real > V ideal due to volume of particles of real gas.

Check out the Van Der Waals equation, and we can see that is the case.

Ideal gas law: PV = nRT
Van der Waals: (observed pressure + (an^2/V^2))(volume of container^-nb) = nRT

So to make the observed pressure comparable to the ideal pressure, we have to add the (an^2/V^2) equation to make up for the IM forces that decrease the real/observed pressure. And to make the observed volume comparable to the ideal volume, we have to subtract the volume of the particles of the real gas: nb (number of moles * volume of a mole of the particles).

I haven't understood this concept for about two months now and my MCAT is on Saturday, but you cleared this up for me real well. Nice explanation.

 

[Geekchick921]

Aww, thanks! Good luck this weekend!

 

[bigballer27]

Bigballer, one of them must be wrong. Are you sure you're reading it right?

P real < P ideal due to intermolecular forces between particles of real gas.
V real > V ideal due to volume of particles of real gas.

Check out the Van Der Waals equation, and we can see that is the case.

Ideal gas law: PV = nRT
Van der Waals: (observed pressure + (an^2/V^2))(volume of container^-nb) = nRT

So to make the observed pressure comparable to the ideal pressure, we have to add the (an^2/V^2) equation to make up for the IM forces that decrease the real/observed pressure. And to make the observed volume comparable to the ideal volume, we have to subtract the volume of the particles of the real gas: nb (number of moles * volume of a mole of the particles).

GC i quoted it straight out of my princeton gchem book.

but what you're saying does make sense, but where did you get that equation from i dont get it (or what the variables on the exponents stand for)

 

[Geekchick921]

GC i quoted it straight out of my princeton gchem book.

but what you're saying does make sense, but where did you get that equation from i dont get it (or what the variables on the exponents stand for)

That's just the Van der Waals equation, but here's what the variables are.

(observed pressure + (an^2/V^2))(volume of container-nb) = nRT
(Note, I had volume of container^-nb) before, but that ^ should NOT be in there, it's just (Volume - nb).

a = a constant that gives the amount of IM force the particles act on each other.

n = number of moles of gas

V = Volume

b = a constant that gives the volume occupied by a mole of the particles.

Remember, the Van der Waals equation and the Ideal Gas Law are really the same thing.

Van der Waals Equation: (observed pressure + (an^2/V^2))(volume of container-nb) = nRT
Ideal Gas Law: PV = nRT

(observed pressure + (an^2/V^2)) = Ideal P
(observed volume-nb) = Ideal V

a & b are specific to a given gas. a is in J*m^3/moles^2... don't ask me how they arrived at this, but the units will cancel. B is given in m^3/mole.

So we have real pressure PLUS the a(n^2/V^2) equation, which will account for the IM forces between the particles of a real gas. Since a Joule is a Newton*meter, J*m^3/moles^2 is equal to N*m^4/moles^2. Moles^2 will cancel out with the n^2 variable, and V^2 in the denominator will cancel out the m^4 and we'll be left with N/m^2, which is the same as a pascal. So we ADD that to the real pressure to give us the equivalent of the ideal pressure.

That might be confusing, but it helps me. If I get lost, sometimes making sure the units are right keeps me on track.

We also have the real volume, but we need to subtract the volume of the actual particles to make it comparable to the volume of an ideal gas, whose particles do not take up space. This one is much more self-explanatory. We take the observed volume, and SUBTRACT (moles*(m^3/mole), and we know what the volume of this gas would be if it were ideal and its particles didn't occupy volume.

Did I make it better or worse?

 

[dingyibvs]

Bigballer, one of them must be wrong. Are you sure you're reading it right?

P real < P ideal due to intermolecular forces between particles of real gas.
V real > V ideal due to volume of particles of real gas.

Check out the Van Der Waals equation, and we can see that is the case.

Ideal gas law: PV = nRT
Van der Waals: (observed pressure + (an^2/V^2))(volume of container^-nb) = nRT

So to make the observed pressure comparable to the ideal pressure, we have to add the (an^2/V^2) equation to make up for the IM forces that decrease the real/observed pressure. And to make the observed volume comparable to the ideal volume, we have to subtract the volume of the particles of the real gas: nb (number of moles * volume of a mole of the particles).

While that is true for most cases, it is not true for all cases. For gases under high pressure, their volume reduces dramatically and thus inter-molecule distances also reduce dramatically. Due to the molecules being so much closer, the effect of intermolecular attraction becomes GREATER than the effect of the fact that real gases have volume. Therefore, for gases under high pressure, Vreal < Videal.

In other words, Vreal is not always greater than Videal.

 

[GASPER20]

P real < P ideal
V of gas real > V of gas ideal
V of container real < V of container ideal

is there anything else i'm missing in this thread?

 

[dingyibvs]

P real < P ideal
V of gas real > V of gas ideal
V of container real < V of container ideal

is there anything else i'm missing in this thread?

1)There's nothing about V container.

2) V of gas real < V of gas ideal when the pressure is high.