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# REAL GASES and COMPRESSIBILITY

last edited by 10 years, 3 months ago

REAL GASES.

We have seen how the formula PV=nRT describes the behavior of the “Ideal Gas”. However, this equation only attempts to describe how  real gases would behave “in a perfect world” (But in the “real world” gases are made up of real molecules and real atoms –and as we’ll see, this is why Real Gases act differently from Ideal Gases)…So in a sense, PV=nRT describes how any gas would behave if that gas were NOT made of real atoms and real molecules…as long as the Real Gas molecules of any gas remain far apart that gas behaves (mostly) like an Ideal Gas

This is the reason why Real Gases do not “follow” the Ideal Gas law PV=nRT.

As it turns out, Real Gases deviate from the Ideal Gas law the most when the molecules are close to each other…in turn, whatever P,V,T conditions bring gas molecules closest are also the P,V,T conditions that make that particular Real Gas deviate the most.

*So ask yourself, what P,V,T conditions make Real Gas molecules come together the most??

There are two ways to bring gas molecules together:

(1)   You can squeeze molecules together (compression) at a given Temperature.

(2)   You can cool the Real Gas molecules down so much that they don’t have the kinetic energy to push each other away.

So, as it turns out, if you want to make Real Gas molecules come close together, then you use a combination of (1) high pressure (squeezing together, compression) and (2) low temperature (slowing down molecules so they don’t really have the energy to bounce around and push each other away).

*But still, WHY does bringing Real Gas molecules closer and closer together make Real Gases act respectively less and less like an Ideal Gas??

*WHAT does bringing Real Gas molecules coming closer together have to do with deviating away from the formula PV=nRT??

Here’s the answer:..All Real Gas molecules have the ability to either repel OR attract another Real Gas molecule BUT only when the molecules are “close” together… These attractive & repulsive abilities of the molecules is what makes the Real Gas’s pressure either lower or higher compared to an Ideal Gas in the same situation (same moles, Temperature and Volume).

So when we are looking at this side by side comparison (Real vs. Ideal), keep in mind that we are keeping the Temperature, Volume and molarity the same and the only difference is the resulting Pressure.

*But wait a minute, If you have both Attractive forces and Repulsive forces, then WHY don’t the two forces just cancel out each other??

Well, there are two reasons for this:

(1)   First of all, the repulsive force is stronger than the attractive force, BUT

(2)   The attractive force is more important when the molecules are farther away from each other…when the molecules get closer and closer the repulsive force come into play more and more.

So generally, if the Real Gas molecules are a little bit far apart (several molecular diameters) they will want to interact (Vander walls forces; nucleus of Molecule A is Attracted to electron cloud of molecule B, and vise versa, Dipole-Dipole, ect.) and so their Real Gas behavior will be lower than the Ideal Gas, in the same situation…BUT if they are compressed (to about one molecular diameter or less) then there will be very strong repulsive force, and so the gas pressure will be greater than an Ideal Gas in the same situation.

Ah, but there’s a 3rd reason why Real Gases do not act like Ideal Gases as they are compressed:...Real Gas molecules are NOT points of infinite smallness, they are real matter (It becomes like putting 50 marbles in your pocket, they are already so close that they can’t get any closer, they need room in which to exist)…But at that point they are usually no longer gases anyhow (already turned to liquid or solid).

*Do you see what I mean??

Show me WHERE in the Formula PV=nRT do you find “Attractive” forces and “Repulsive” forces??

These are called “Intermolecular Forces”

[Insert Slide #26] [Insert Slide #27]

Slide 26 shows a fixed volume filled with a Real Gas ( This one is Ozone). The Gas molecules are condensed into a liquid form…It shows how that same volume of gas can be represented by that tiny amount of violet liquid (both contain the same amount of Ozone molecules!).

[Insert Slide #31, Intermolecular Forces]

As I mentioned above, the Intermolecular forces “Attractive” and “Repulsive” express themselves as Real variations in Pressure (as Compared to Ideal Gas in the same situation). These Real variations in Pressure can either be to have a Lower or Higher pressure (compared to what PV=nRT would predict).

The X axis represents distance between two Real Gas molecules,

The Y axis represents the resulting potential energy in maintaining the distance X.

A) When two molecules are very very close, it is difficult to keep them together (and so the potential energy is very high),

B) And when two molecules are just a little bit far apart they are just close enough to experience some attractive force from each other (but not yet close enough to be repelled by each other), that is, the “dip” in the graph where attractions are dominant (“dominant” as in more significant than repulsion).

C) The point where the graph crosses the X axis is where Attractive forces exactly equal the repulsive forces (they “cancel each other out” in terms of pressure), (and just at that instant, Real gases appear to act like Ideal gases).

D) Notice that as the distance between two molecules increases more and more, the Real Gas looks more and more like an Ideal Gas (because it gets closer and closer to Y =“0” on the graph, and Ideal gases have Zero Attractive/Repulsive forces, and therefore Zero intermolecular potential energy).

*And WHEN do you have distance increasing more and more?? At high Temperature and Low pressure!

-- Summary --

Ideal Gas is represented by PV=nRT, but Real Gases are not really represented by PV=nRT because the resulting P (after you plug in for n,T,V) is that it is usually either higher or lower than the P of the Ideal Gas (That deviation, in terms of of potential energy between the Real Gas molecules is represented by slide #31).

When Real Gas molecules are a little bit far apart, they are attracted to each other, and the resulting Real Pressure is lower than Ideal Pressure (Ideal Gas in the same situation).

When Real Gas molecules are really close together (High pressure, Low temperature), their electron clouds repel each other, and the resulting Real Pressure is higher than an Ideal Pressure (Ideal gas in the same situation).

When Real Gas molecules are really far apart, they are attracted to each other, the resulting Real Pressure almost the same as Ideal Pressure (Ideal Gas in the same situation).

COMPRESSIBILITY

*Wouldn’t it be convenient to be able to express Real Gas behavior as a RATIO in terms of how many times it’s Volume deviates from Ideal Gas volume (using the same n, T and P)??

For example, if an Ideal Gas predicts 1.0 Liter, but my real gas (using the same values for n, T, P) gives 1.1 Liter, I could just divide my Real Gas Volume by my Ideal Gas Volume, and the resulting number would tell me  by how many times my Real Gas deviates from the Ideal Gas. And because we are using one mole for both the Real and Ideal gas we are using “Molar Volume”:

That equation would look like this: Z=Vm/Vm0

Vm = molar volume of the Real Gas,

Vm0 = molar volume of the Ideal Gas.

[Insert Slide #33]

Now, remember I said Z=Vm/Vm0 is a ratio between how a Real Gas behaves (in terms of its volume, per mole) and how an Ideal Gas would behave (in terms of its volume, per mole)?

[Insert Slide #35]

This suggests that when Real Gas behaves like an Ideal gas, you would get a value of  “1” or close to “1”.

*And WHEN do you get a Real Gas to act like an Ideal Gas?? When the molecules are far apart! …So Therefore we should get a value of “1” as we lower the pressure.

*And WHEN do you get a Real Gas to make a lower-than-Ideal Volume to accommodate the same amount of Pressure?? When Intermolecular Attractions are are at their highest!...and when is that?? When the Real Gas molecules are a little bit far apart!! And when are they a little bit far apart?? When the Pressure is not too high and not too low!...and so if you look at the graph you have a “dip” for Real gases like C2H2 and CH4 at about 200 atm….Hey! look at Hydrogen Gas! It does NOT “dip” this is because the Cloud of H2 does NOT really intermolecular attractions!

*And When do you get a Real Gas to make a Higher-than-Ideal Volume to accommodate the same amount of Pressure of an Ideal Gas?? When the Molecules are very very close together! And when are molecules very very close together? When you have High pressure!...This is the reason that at 600-800 atm the extra volume needed  to accommodate the same amount of pressure used in an Ideal Gas just sky rockets to about 1.8 times as much!

[Insert slide #34]

Now, sometimes we just want to express the basic Idea of  Z=Vm/Vm0 in a different way. We can just plug into this formula (exchange 1/Vm0 for  P/RT ) into the formula Z=Vm/Vm0…the result would be Z= (PVm/RT) It’s still the SAME basic formula, just using different variables.

[Insert Slide #36]

Have you noticed that we have been making comparisons by saying things like “Increase Pressure while keeping Temperature the same” and stuff like that?

Well, we have a vocabulary to say “keeping something (T, or V or P) the same”:

Keep T the same = Isothermic

Keep P the same = Isobaric

Keep V the same = Isochoric

Slide 36 shows a graph (you can cut into slices like a Loaf of Bread). Let’s say you wanted to know the curve for how Pressure changes according to volume for a specific T (cut it like a loaf of bread at THAT Temperature, and you will get the curve you want!!).

That specific T is an Isotherm.

What if you wanted to see how a Pressure changes according to Temperature?? Just cut it like a loaf of bread at a specific Volume!!…

That specific V is an Isochore.

What if you wanted to see how steady changes in Temperature produces corresponding changes in Volume?? Just cut it like a loaf of bread at a specific Pressure!!

That specific P is an Isobar.

[Insert Slide #37]

This slide looks confusing, but it’s not trust me.

All it is,  is just slide 36, but looking at slide 36 so that the axis formed by Pressure plane and Volume plane is pointing at your eye.

The different lines are just Different specific Ts (the different Isotherms).

Notice that the higher the Temperature T, the higher Pressure P it will produce for the same Volume.

REAL GASES.

We have seen how the formula PV=nRT describes the behavior of the “Ideal Gas”. However, this equation only attempts to describe how  real gases would behave “in a perfect world” (But in the “real world” gases are made up of real molecules and real atoms –and as we’ll see, this is why Real Gases act differently from Ideal Gases)…So in a sense, PV=nRT describes how any gas would behave if that gas were NOT made of real atoms and real molecules…as long as the Real Gas molecules of any gas remain far apart that gas behaves (mostly) like an Ideal Gas

This is the reason why Real Gases do not “follow” the Ideal Gas law PV=nRT.

As it turns out, Real Gases deviate from the Ideal Gas law the most when the molecules are close to each other…in turn, whatever P,V,T conditions bring gas molecules closest are also the P,V,T conditions that make that particular Real Gas deviate the most.

*So ask yourself, what P,V,T conditions make Real Gas molecules come together the most??

There are two ways to bring gas molecules together:

(1)   You can squeeze molecules together (compression) at a given Temperature.

(2)   You can cool the Real Gas molecules down so much that they don’t have the kinetic energy to push each other away.

So, as it turns out, if you want to make Real Gas molecules come close together, then you use a combination of (1) high pressure (squeezing together, compression) and (2) low temperature (slowing down molecules so they don’t really have the energy to bounce around and push each other away).

*But still, WHY does bringing Real Gas molecules closer and closer together make Real Gases act respectively less and less like an Ideal Gas??

*WHAT does bringing Real Gas molecules coming closer together have to do with deviating away from the formula PV=nRT??

Here’s the answer:..All Real Gas molecules have the ability to either repel OR attract another Real Gas molecule BUT only when the molecules are “close” together… These attractive & repulsive abilities of the molecules is what makes the Real Gas’s pressure either lower or higher compared to an Ideal Gas in the same situation (same moles, Temperature and Volume).

So when we are looking at this side by side comparison (Real vs. Ideal), keep in mind that we are keeping the Temperature, Volume and molarity the same and the only difference is the resulting Pressure.

*But wait a minute, If you have both Attractive forces and Repulsive forces, then WHY don’t the two forces just cancel out each other??

Well, there are two reasons for this:

(1)   First of all, the repulsive force is stronger than the attractive force, BUT

(2)   The attractive force is more important when the molecules are farther away from each other…when the molecules get closer and closer the repulsive force come into play more and more.

So generally, if the Real Gas molecules are a little bit far apart (several molecular diameters) they will want to interact (Vander walls forces; nucleus of Molecule A is Attracted to electron cloud of molecule B, and vise versa, Dipole-Dipole, ect.) and so their Real Gas behavior will be lower than the Ideal Gas, in the same situation…BUT if they are compressed (to about one molecular diameter or less) then there will be very strong repulsive force, and so the gas pressure will be greater than an Ideal Gas in the same situation.

Ah, but there’s a 3rd reason why Real Gases do not act like Ideal Gases as they are compressed:...Real Gas molecules are NOT points of infinite smallness, they are real matter (It becomes like putting 50 marbles in your pocket, they are already so close that they can’t get any closer, they need room in which to exist)…But at that point they are usually no longer gases anyhow (already turned to liquid or solid).

*Do you see what I mean??

Show me WHERE in the Formula PV=nRT do you find “Attractive” forces and “Repulsive” forces??

These are called “Intermolecular Forces”

[Insert Slide #26] [Insert Slide #27]

Slide 26 shows a fixed volume filled with a Real Gas ( This one is Ozone). The Gas molecules are condensed into a liquid form…It shows how that same volume of gas can be represented by that tiny amount of violet liquid (both contain the same amount of Ozone molecules!).

[Insert Slide #31, Intermolecular Forces]

As I mentioned above, the Intermolecular forces “Attractive” and “Repulsive” express themselves as Real variations in Pressure (as Compared to Ideal Gas in the same situation). These Real variations in Pressure can either be to have a Lower or Higher pressure (compared to what PV=nRT would predict).

The X axis represents distance between two Real Gas molecules,

The Y axis represents the resulting potential energy in maintaining the distance X.

A) When two molecules are very very close, it is difficult to keep them together (and so the potential energy is very high),

B) And when two molecules are just a little bit far apart they are just close enough to experience some attractive force from each other (but not yet close enough to be repelled by each other), that is, the “dip” in the graph where attractions are dominant (“dominant” as in more significant than repulsion).

C) The point where the graph crosses the X axis is where Attractive forces exactly equal the repulsive forces (they “cancel each other out” in terms of pressure), (and just at that instant, Real gases appear to act like Ideal gases).

D) Notice that as the distance between two molecules increases more and more, the Real Gas looks more and more like an Ideal Gas (because it gets closer and closer to Y =“0” on the graph, and Ideal gases have Zero Attractive/Repulsive forces, and therefore Zero intermolecular potential energy).

*And WHEN do you have distance increasing more and more?? At high Temperature and Low pressure!

-- Summary --

Ideal Gas is represented by PV=nRT, but Real Gases are not really represented by PV=nRT because the resulting P (after you plug in for n,T,V) is that it is usually either higher or lower than the P of the Ideal Gas (That deviation, in terms of of potential energy between the Real Gas molecules is represented by slide #31).

When Real Gas molecules are a little bit far apart, they are attracted to each other, and the resulting Real Pressure is lower than Ideal Pressure (Ideal Gas in the same situation).

When Real Gas molecules are really close together (High pressure, Low temperature), their electron clouds repel each other, and the resulting Real Pressure is higher than an Ideal Pressure (Ideal gas in the same situation).

When Real Gas molecules are really far apart, they are attracted to each other, the resulting Real Pressure almost the same as Ideal Pressure (Ideal Gas in the same situation).

COMPRESSIBILITY

*Wouldn’t it be convenient to be able to express Real Gas behavior as a RATIO in terms of how many times it’s Volume deviates from Ideal Gas volume (using the same n, T and P)??

For example, if an Ideal Gas predicts 1.0 Liter, but my real gas (using the same values for n, T, P) gives 1.1 Liter, I could just divide my Real Gas Volume by my Ideal Gas Volume, and the resulting number would tell me  by how many times my Real Gas deviates from the Ideal Gas. And because we are using one mole for both the Real and Ideal gas we are using “Molar Volume”:

That equation would look like this: Z=Vm/Vm0

Vm = molar volume of the Real Gas,

Vm0 = molar volume of the Ideal Gas.

[Insert Slide #33]

Now, remember I said Z=Vm/Vm0 is a ratio between how a Real Gas behaves (in terms of its volume, per mole) and how an Ideal Gas would behave (in terms of its volume, per mole)?

[Insert Slide #35]

This suggests that when Real Gas behaves like an Ideal gas, you would get a value of  “1” or close to “1”.

*And WHEN do you get a Real Gas to act like an Ideal Gas?? When the molecules are far apart! …So Therefore we should get a value of “1” as we lower the pressure.

*And WHEN do you get a Real Gas to make a lower-than-Ideal Volume to accommodate the same amount of Pressure?? When Intermolecular Attractions are are at their highest!...and when is that?? When the Real Gas molecules are a little bit far apart!! And when are they a little bit far apart?? When the Pressure is not too high and not too low!...and so if you look at the graph you have a “dip” for Real gases like C2H2 and CH4 at about 200 atm….Hey! look at Hydrogen Gas! It does NOT “dip” this is because the Cloud of H2 does NOT really intermolecular attractions!

*And When do you get a Real Gas to make a Higher-than-Ideal Volume to accommodate the same amount of Pressure of an Ideal Gas?? When the Molecules are very very close together! And when are molecules very very close together? When you have High pressure!...This is the reason that at 600-800 atm the extra volume needed  to accommodate the same amount of pressure used in an Ideal Gas just sky rockets to about 1.8 times as much!

[Insert slide #34]

Now, sometimes we just want to express the basic Idea of  Z=Vm/Vm0 in a different way. We can just plug into this formula (exchange 1/Vm0 for  P/RT ) into the formula Z=Vm/Vm0…the result would be Z= (PVm/RT) It’s still the SAME basic formula, just using different variables.

[Insert Slide #36]

Have you noticed that we have been making comparisons by saying things like “Increase Pressure while keeping Temperature the same” and stuff like that?

Well, we have a vocabulary to say “keeping something (T, or V or P) the same”:

Keep T the same = Isothermic

Keep P the same = Isobaric

Keep V the same = Isochoric

Slide 36 shows a graph (you can cut into slices like a Loaf of Bread). Let’s say you wanted to know the curve for how Pressure changes according to volume for a specific T (cut it like a loaf of bread at THAT Temperature, and you will get the curve you want!!).

That specific T is an Isotherm.

What if you wanted to see how a Pressure changes according to Temperature?? Just cut it like a loaf of bread at a specific Volume!!…

That specific V is an Isochore.

What if you wanted to see how steady changes in Temperature produces corresponding changes in Volume?? Just cut it like a loaf of bread at a specific Pressure!!

That specific P is an Isobar.

[Insert Slide #37]

This slide looks confusing, but it’s not trust me.

All it is,  is just slide 36, but looking at slide 36 so that the axis formed by Pressure plane and Volume plane is pointing at your eye.

The different lines are just Different specific Ts (the different Isotherms).

Notice that the higher the Temperature T, the higher Pressure P it will produce for the same Volume.

REAL GASES.

We have seen how the formula PV=nRT describes the behavior of the “Ideal Gas”. However, this equation only attempts to describe how  real gases would behave “in a perfect world” (But in the “real world” gases are made up of real molecules and real atoms –and as we’ll see, this is why Real Gases act differently from Ideal Gases)…So in a sense, PV=nRT describes how any gas would behave if that gas were NOT made of real atoms and real molecules…as long as the Real Gas molecules of any gas remain far apart that gas behaves (mostly) like an Ideal Gas

This is the reason why Real Gases do not “follow” the Ideal Gas law PV=nRT.

As it turns out, Real Gases deviate from the Ideal Gas law the most when the molecules are close to each other…in turn, whatever P,V,T conditions bring gas molecules closest are also the P,V,T conditions that make that particular Real Gas deviate the most.

*So ask yourself, what P,V,T conditions make Real Gas molecules come together the most??

There are two ways to bring gas molecules together:

(1)   You can squeeze molecules together (compression) at a given Temperature.

(2)   You can cool the Real Gas molecules down so much that they don’t have the kinetic energy to push each other away.

So, as it turns out, if you want to make Real Gas molecules come close together, then you use a combination of (1) high pressure (squeezing together, compression) and (2) low temperature (slowing down molecules so they don’t really have the energy to bounce around and push each other away).

*But still, WHY does bringing Real Gas molecules closer and closer together make Real Gases act respectively less and less like an Ideal Gas??

*WHAT does bringing Real Gas molecules coming closer together have to do with deviating away from the formula PV=nRT??

Here’s the answer:..All Real Gas molecules have the ability to either repel OR attract another Real Gas molecule BUT only when the molecules are “close” together… These attractive & repulsive abilities of the molecules is what makes the Real Gas’s pressure either lower or higher compared to an Ideal Gas in the same situation (same moles, Temperature and Volume).

So when we are looking at this side by side comparison (Real vs. Ideal), keep in mind that we are keeping the Temperature, Volume and molarity the same and the only difference is the resulting Pressure.

*But wait a minute, If you have both Attractive forces and Repulsive forces, then WHY don’t the two forces just cancel out each other??

Well, there are two reasons for this:

(1)   First of all, the repulsive force is stronger than the attractive force, BUT

(2)   The attractive force is more important when the molecules are farther away from each other…when the molecules get closer and closer the repulsive force come into play more and more.

So generally, if the Real Gas molecules are a little bit far apart (several molecular diameters) they will want to interact (Vander walls forces; nucleus of Molecule A is Attracted to electron cloud of molecule B, and vise versa, Dipole-Dipole, ect.) and so their Real Gas behavior will be lower than the Ideal Gas, in the same situation…BUT if they are compressed (to about one molecular diameter or less) then there will be very strong repulsive force, and so the gas pressure will be greater than an Ideal Gas in the same situation.

Ah, but there’s a 3rd reason why Real Gases do not act like Ideal Gases as they are compressed:...Real Gas molecules are NOT points of infinite smallness, they are real matter (It becomes like putting 50 marbles in your pocket, they are already so close that they can’t get any closer, they need room in which to exist)…But at that point they are usually no longer gases anyhow (already turned to liquid or solid).

*Do you see what I mean??

Show me WHERE in the Formula PV=nRT do you find “Attractive” forces and “Repulsive” forces??

These are called “Intermolecular Forces”

[Insert Slide #26] [Insert Slide #27]

Slide 26 shows a fixed volume filled with a Real Gas ( This one is Ozone). The Gas molecules are condensed into a liquid form…It shows how that same volume of gas can be represented by that tiny amount of violet liquid (both contain the same amount of Ozone molecules!).

[Insert Slide #31, Intermolecular Forces]

As I mentioned above, the Intermolecular forces “Attractive” and “Repulsive” express themselves as Real variations in Pressure (as Compared to Ideal Gas in the same situation). These Real variations in Pressure can either be to have a Lower or Higher pressure (compared to what PV=nRT would predict).

The X axis represents distance between two Real Gas molecules,

The Y axis represents the resulting potential energy in maintaining the distance X.

A) When two molecules are very very close, it is difficult to keep them together (and so the potential energy is very high),

B) And when two molecules are just a little bit far apart they are just close enough to experience some attractive force from each other (but not yet close enough to be repelled by each other), that is, the “dip” in the graph where attractions are dominant (“dominant” as in more significant than repulsion).

C) The point where the graph crosses the X axis is where Attractive forces exactly equal the repulsive forces (they “cancel each other out” in terms of pressure), (and just at that instant, Real gases appear to act like Ideal gases).

D) Notice that as the distance between two molecules increases more and more, the Real Gas looks more and more like an Ideal Gas (because it gets closer and closer to Y =“0” on the graph, and Ideal gases have Zero Attractive/Repulsive forces, and therefore Zero intermolecular potential energy).

*And WHEN do you have distance increasing more and more?? At high Temperature and Low pressure!

-- Summary --

Ideal Gas is represented by PV=nRT, but Real Gases are not really represented by PV=nRT because the resulting P (after you plug in for n,T,V) is that it is usually either higher or lower than the P of the Ideal Gas (That deviation, in terms of of potential energy between the Real Gas molecules is represented by slide #31).

When Real Gas molecules are a little bit far apart, they are attracted to each other, and the resulting Real Pressure is lower than Ideal Pressure (Ideal Gas in the same situation).

When Real Gas molecules are really close together (High pressure, Low temperature), their electron clouds repel each other, and the resulting Real Pressure is higher than an Ideal Pressure (Ideal gas in the same situation).

When Real Gas molecules are really far apart, they are attracted to each other, the resulting Real Pressure almost the same as Ideal Pressure (Ideal Gas in the same situation).

COMPRESSIBILITY

*Wouldn’t it be convenient to be able to express Real Gas behavior as a RATIO in terms of how many times it’s Volume deviates from Ideal Gas volume (using the same n, T and P)??

For example, if an Ideal Gas predicts 1.0 Liter, but my real gas (using the same values for n, T, P) gives 1.1 Liter, I could just divide my Real Gas Volume by my Ideal Gas Volume, and the resulting number would tell me  by how many times my Real Gas deviates from the Ideal Gas. And because we are using one mole for both the Real and Ideal gas we are using “Molar Volume”:

That equation would look like this: Z=Vm/Vm0

Vm = molar volume of the Real Gas,

Vm0 = molar volume of the Ideal Gas.

[Insert Slide #33]

Now, remember I said Z=Vm/Vm0 is a ratio between how a Real Gas behaves (in terms of its volume, per mole) and how an Ideal Gas would behave (in terms of its volume, per mole)?

[Insert Slide #35]

This suggests that when Real Gas behaves like an Ideal gas, you would get a value of  “1” or close to “1”.

*And WHEN do you get a Real Gas to act like an Ideal Gas?? When the molecules are far apart! …So Therefore we should get a value of “1” as we lower the pressure.

*And WHEN do you get a Real Gas to make a lower-than-Ideal Volume to accommodate the same amount of Pressure?? When Intermolecular Attractions are are at their highest!...and when is that?? When the Real Gas molecules are a little bit far apart!! And when are they a little bit far apart?? When the Pressure is not too high and not too low!...and so if you look at the graph you have a “dip” for Real gases like C2H2 and CH4 at about 200 atm….Hey! look at Hydrogen Gas! It does NOT “dip” this is because the Cloud of H2 does NOT really intermolecular attractions!

*And When do you get a Real Gas to make a Higher-than-Ideal Volume to accommodate the same amount of Pressure of an Ideal Gas?? When the Molecules are very very close together! And when are molecules very very close together? When you have High pressure!...This is the reason that at 600-800 atm the extra volume needed  to accommodate the same amount of pressure used in an Ideal Gas just sky rockets to about 1.8 times as much!

[Insert slide #34]

Now, sometimes we just want to express the basic Idea of  Z=Vm/Vm0 in a different way. We can just plug into this formula (exchange 1/Vm0 for  P/RT ) into the formula Z=Vm/Vm0…the result would be Z= (PVm/RT) It’s still the SAME basic formula, just using different variables.

[Insert Slide #36]

Have you noticed that we have been making comparisons by saying things like “Increase Pressure while keeping Temperature the same” and stuff like that?

Well, we have a vocabulary to say “keeping something (T, or V or P) the same”:

Keep T the same = Isothermic

Keep P the same = Isobaric

Keep V the same = Isochoric

Slide 36 shows a graph (you can cut into slices like a Loaf of Bread). Let’s say you wanted to know the curve for how Pressure changes according to volume for a specific T (cut it like a loaf of bread at THAT Temperature, and you will get the curve you want!!).

That specific T is an Isotherm.

What if you wanted to see how a Pressure changes according to Temperature?? Just cut it like a loaf of bread at a specific Volume!!…

That specific V is an Isochore.

What if you wanted to see how steady changes in Temperature produces corresponding changes in Volume?? Just cut it like a loaf of bread at a specific Pressure!!

That specific P is an Isobar.

[Insert Slide #37]

This slide looks confusing, but it’s not trust me.

All it is,  is just slide 36, but looking at slide 36 so that the axis formed by Pressure plane and Volume plane is pointing at your eye.

The different lines are just Different specific Ts (the different Isotherms).

Notice that the higher the Temperature T, the higher Pressure P it will produce for the same Volume.