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## Physics library

### Unit 10: Lesson 1

Temperature, kinetic theory, and the ideal gas law- Thermodynamics part 1: Molecular theory of gases
- Thermodynamics part 2: Ideal gas law
- Thermodynamics part 3: Kelvin scale and Ideal gas law example
- Thermodynamics part 4: Moles and the ideal gas law
- Thermodynamics part 5: Molar ideal gas law problem
- What is the ideal gas law?
- The Maxwell–Boltzmann distribution
- What is the Maxwell-Boltzmann distribution?

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# Thermodynamics part 4: Moles and the ideal gas law

Sal explains the concept of a mole. Then he derives the molar version of the ideal gas law PV=nRT, where the gas constant R=831 J/molK. Created by Sal Khan.

## Want to join the conversation?

- Why did you use 8.31 J/mol K instead of 0.821 L atm/ mol K ?(6 votes)
- They're different values of the gas constant, it just depends on which units you're using.

8.31 J/mol K assumes you're in SI units, meaning you're using Pascals for pressure and meters^3 for volume.The joules unit comes from substituting F/A (aka Newtons per meter squared) in for the P (pascals) in PV=nRT.

After substitution, the units look like:

(Newtons/meters^2)(meters^3)= R (mols)(Kelvin)

So the remaining left side (Newtons x meters) becomes joules and R = joules/(mols x kelvin)

If you're using liters for volume and atm for pressure then you'd use the 0.0821 number you mentioned.(22 votes)

- This is actually a chapter in chemistry called states of matter.Where there's gas laws and stuff.And chem also has some chapter called thermodynamics.Whats the difference betweem the physics version and the chem one?(3 votes)
- Rather than thinking of the science as discrete sub-subjects as they are taught in school such as biology, chemistry, and physics, in the real world they are often all considered together as a whole, so thermodynamics is thermodynamics.

With that being said, you would probably focus on different aspects of thermodynamics in chemistry or physics classes. In the chemistry classes, you are more concerned with the states of matter as you mentioned, particularly the amount of energy required to change from one state to another. You look at the interactions between molecules in the condensed (liquid and solid) states, which give liquids and solids their properties. You also consider things such as change in enthalpy(delta H), entropy(delta S), and free energy (delta G) because these all shed light on EVERY chemical reaction (that is, every chemical reaction has a delta G,S, and H value). You can also look at equilibrium, as this is a thermodynamic property. Thermodynamics is one of the most important considerations of a chemical reaction.

In physics, you are more concerned with things such as cycles (adiabatic expansion/compression, isothermal and isobaric changes, etc.) and the efficiency of these process, as well as the theoretically most efficient process known as the carnot cycle. The treatment would probably be more mathematical.

They both, as you said, pay close attention to the behavior of gases. Gas behavior is quite complex. Depending on what the level of the class you are in, you might be introduced to the kinetic molecular theory of gas, which attempts to make some sense of the nature of gases. You will definitely look at ideal gas behavior (i.e. the ideal gas law) in both classes, as well as some common "reduced" forms of it such as Boyle's and Charles' laws. You might even get a glimpse of non ideal behavior.

In short, thermodynamics is one of the most fundamental subjects in nature, and is one of the most important in our attempt to understand the universe. Almost ALL natural phenomena can be looked at from a thermodynamic point of view, because it deals with the universal concept of energy.(27 votes)

- I'm wandering if temperatures of matter should have a reference point like velocity. From my understanding, the temperature of an substance is the average kinetic energy of it's molecules while the speed of the molecule is relative to a particular reference point (i.e the speed of the rotating earth). I hope my question is understood. :)(4 votes)
- Temperature, from what I know, is always measured as the kinetic energy of the molecules relative to the velocity of the center of mass of the body.

If in your referential the body is moving, the temperature is the same, but you also have to consider the body's kinetic energy ( K = 1/2 mv^2), which has nothing to due with its temperature.(2 votes)

- what is meant by "6 followed by roughly 230's of molecules" at1:50?(2 votes)
- Well, a mole of any element is equal to 6.022*10^23 atoms. So, if we ignore .022, it means roughly 6*10^23 atoms. This means that there are roughly '6 followed by 23 zeroes(6000.....)' atoms. That's what Sal meant at1:50.

Hope this helps :)(4 votes)

- p1v1 / t1 = p2v2 / t2 ....this works only for ideal gas?(1 vote)
- Yes, only for ideal gases! For ideal gases you make two conventions. First convention: The molecules have no volume. Second convention: The molecules don't attract each other. We do these conventions to make our life easier and study simpler systems.

For real gases you should study about Van der Waals equation for real gases.(3 votes)

- is it possible to boiling water at room temperatur(2 votes)
- Yes it is.. Provided the the atmospheric pressure is reduced..

its even possible at 10*C(2 votes)

- Why do we have to convert to kelvins in the equations given in the video?(2 votes)
- Because Kelvin is the unit of temperature. The celsius scale is problematic because "0" doesn't correspond to zero of anything, it's just a label given to a temperature where water freezes. In the Kelvin scale, 0 really means zero thermal energy.(1 vote)

- I was wondering if temperatures of matter should have a reference point like velocity. From what I understand, the temperature of a substance is the average kinetic energy of its molecules while the speed of the molecule is relative to a particular reference point. I saw someone else asked this but I didnt understand the answer they were given(2 votes)
- Sal,I did not understand how is pv=nrt?(1 vote)
- It comes from pv=KNT , where N is number of molecules and K is some constant, T-temperature in Kelvins.

pv=nRT , here we have small n , and it means , how many mols we have 1 mol=6,022 * 10^23 beacuse if we write in N it will be a huge number and its easier with mol mass. And R is gas constant that applies to any gas. I hope this helps , and if I am wrong , someone please rewrite.

We got R from Boltzman constant * Avogardo number(1 vote)

- At8:35, Sal told that we got a relation between p,v,R,t,n and he told that in the relation n is no.of molecules but he clearly wrote it is no.of moles , so which one is correct the no.of molecules or moles?(1 vote)
- a mole is a number, so n is the number of molecules, measured in units of moles.(2 votes)

## Video transcript

Before I continue, I want to
introduce you to what might be an unfamiliar concept, although
if you've taken chemistry, you might know a
little bit about it-- it's called a mole. This isn't the thing that grows
on your face with the hair in it, or the animal that
digs in your backyard, although those are also
called moles. We're talking about the
SI unit called a mole. A mole is just a number. It's like saying a mole of
something means a certain number of something, just like
a dozen-- it's like saying that a dozen eggs is 12 eggs. Just like that, a mole would
be 6-- I always forget the exact number, but it's 6.023,
or something of that nature. You could look it up--
I think it's 6.023 times 10 to the twentieth. Let me look up the exact number,
just because I think that 23 I'm misremembering. The mole is 6.022 times 10 to
the 23 of something, so it's a very number of something. Normally, we don't deal in moles
of eggs-- I don't think there has been a mole of eggs
ever produced in the history of the universe. 10 to the 23 is a very, very,
very large number. Where is it useful? A mole is useful for counting
atoms, and so what is a mole of atoms or molecules? What's that many molecules? It's 6 followed by roughly 23
0's of molecules-- a very, very big number. What's interesting about a mole
is that when I have a mole of something, its mass--
let's say its mass in grams. A mole of carbon: its mass in
grams is going to be equal to-- so if I have this many
carbon molecules, its mass in grams is x grams. It'll have a
mass of x grams, where x is the atomic mass number of an
atom of carbon, although if I was talking about a mole of a
molecule, I would figure out the atomic mass of the
entire molecule. What's an atomic mass number? Let me see if I can do a Web
search on a periodic table. I'm showing you what I do here,
and it's not fancy. Let me go to Google, and let's
look up periodic table, and let's see if we can
find a good one-- this one looks good. If we go to carbon, which is
right here, we see that its atomic number is 6, and
that's the number of protons that it has. The atomic mass number-- it's
the mass of the entire atom. And just so you know-- we're
delving into a little bit of chemistry here-- but most of
the mass of an atom is the protons and the neutrons. The neutrons and the protons
weigh roughly the same thing, and then the electrons are
much, much, much smaller. If you factor in the mass of the
protons and the neutrons, you pretty much have the
mass of the particle. Just a little more chemistry
here is that although on average most of the most of
the atoms have roughly the same number of protons and
neutrons-- some don't. Some, you could have a carbon
atom that has seven neutrons, another one with five, another
one with six, and those are actually all called isotopes,
and I won't go into all of that-- they're just
the same atom with different numbers of neutrons. In general, the atomic mass is
equal to the mass of the protons and the neutrons, and
they tend to be equal. So if the atomic number
is 6, the atomic mass tends to be 12. So why is this useful? We can say if we have niobium--
let's say I have a mole of niobium. If we look here on the periodic
table, it has an atomic mass number of 41, and
its average atomic mass-- if we were to average all of the
isotopes based on the weighting of how they exist
in nature-- it's 92.9, so roughly 93. It's actually a little bit more
than double its atomic number, but let's say 93. If we had a mole of niobium--
if we had 6.022 times 10 to the 23 of niobium, it would
have a mass of 92 grams. That's pretty easy-- look
at any element. Let's say chromium: we see its
atomic mass number is roughly 52, and we see that there. If I have a mole of it-- if I
have roughly 6 times 10 the 23 three of it, that much will
have a mass of 52 grams. That's how we think
about a mole. If I tell you I have a mole of
something, I'm also telling you how many of that molecule
I have, and I'm also telling you what the mass of that mole
that quantity will be, assuming that you
have a periodic table in front of you. With that said, and with that
out of the way, let's make some more progress with
our thermodynamics. We said in the last several
videos that pressure times volume is somehow
proportional-- let's call that K. And this is an arbitrary number,
it's not some special constant-- to the total kinetic
energy of a system. We also said that that is
roughly proportional-- that's another constant-- times the
number of molecules we have times the temperature, because
temperature we viewed as kinetic energy per molecule. In general, we could also say
that this is proportional to this, which is proportional to
this, that pressure times volume is proportional. We'll use R, because you'll see
where that's coming from in a second. It's proportional, it's equal
to some constant times the number of molecules n. Here I just take the absolute
numbers-- if I had five molecules, I'd put a five here,
but now this n, I'm counting in moles. If this n is 1, that means that
I have 6.022 times 10 to the 23 molecules. One mole equals 6.022 times 10
to the 23, so I'm just saying that this is another way to
write the number of molecules, and then that's times
temperature. Then if we rearrange
it-- PV equals nRT. We have a relationship, that
if I know the pressure, the volume, and the number of
molecules, I can figure out the temperature, or if I know
the number of molecules, the temperature, and the pressure,
I can figure out the volume, assuming I know what R is. I'm about to tell you
what that is. R is called the universal gas
constant, and it is R is 8.31 joules per mole-Kelvin. That kind of tells you what
you need in this formula. This should end up being
joules, so if you have pressure in pascals and volume
in meters cubed, you'll end up with joules there. This should be in moles--
this is 8.31 joules per mole-Kelvin. And then this, as we always
said, should be in Kelvin. Honestly, if you just memorize
two things in all of thermodynamics, you'll probably
be able to do 95% of problems, but you actually
should have the intuition of how they work. Just remember that PV over T
is equal to a constant, or that if you change them, they
relate to each other in that they all equal a constant, so
P1 times V1 divided by T1 is equal to P2 times V2
divided by T2. You also should just need to
memorize PV is equal to nRT, where R is equal to 8.31
joules per mole Kelvin. I know you might not have a
lot of intuition of this formula yet, because I haven't
used it, but I'm going to do that in the next video. These are literally the two
most important things you should know in thermodynamics,
and hopefully you have a little intuition at this point
of what they mean. See you soon.