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### Course: 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 5: Molar ideal gas law problem

Sal uses the molar version of the ideal gas law to solve for the number of moles in a gas. He also shows how to convert this answer into number of molecules using Avogadro's number. Created by Sal Khan.

## Want to join the conversation?

- At3:48, Sal wrote m for mole. Is this standard/allowed? Or will people confuse this with Meters?(5 votes)
- This is not standard, always use "mole" or it's abbreviation "mol"(18 votes)

- What exactly is the 'triple point' of water? i was told that it is a temperature where all the three forms of water can coexist in equilibrium... i dont really get it..(5 votes)
- Take a vessel with a lid and throw in a piece of ice, pour some water on and blow some water vapour in it then close the lid.

Now: in every second the following happens

1a) a portion of the ice will melt

1b) a portion of the water will freeze

2a) a portion of the water will evaporate

2b) a portion of the vapor will condense

It is the funny property of the triple point that the value of 1a is exactly equal to the value of 1b. And the value of 2a is exactly equal to the value of 2b. That means the mass of ice, water and vapour stays the same.

(That explanation is a bit of a simplification, but I hope you get the point)(18 votes)

- What are Bars?(5 votes)
- A unit of pressure where 1 bar is the pressure at sea level.(5 votes)

- What are Bars? you said it at the very end.(2 votes)
- A bar is a unit of pressure about the same a one atmosphere.(7 votes)

- I do not understand the dimensional analysis of the formula PV=nRT. N/m squared . m cubed = moles. J/mol/K . K

When everything is worked out, you get Joules on both sides of the equation. So, if you solve for n, you get no units. However, the unit of n is moles. How is this possible?(3 votes)- since a mole is a ratio (or simply a number), when you do dimensional analysis, you must not get a dimension for 'mole'. If you do, and you are not wrong, then dimensional analysis must be wrong !(2 votes)

- Does this mean that there will be the same amount of molecules in the balloon no matter what gas is in the balloon? For example, if the gas in the balloon was Hydrogen, not Helium, would the molecule count still be the same (1.26*10^21)? (considering the pressure, temperature and volume is the same)(2 votes)
- Yes, A direct application of what is classically called the Avogadro's Law, Note, if it were oxygen, there would be the same number of
**molecule**and twice the number of atoms.(2 votes)

- What's the difference between atom and molecule?(1 vote)
- Atoms combine together to form a molecule. Atom is the smallest particle of a matter which doesn't show any of the matters characters. Whereas Molecules have some characteristics of the matter :)(3 votes)

- I assume that the 5 Pa of the balloon is gauge pressure. So shouldn't he be using absolute pressure? I.e. add 1 atm, or 101,325 Pa to the 5 Pa?(1 vote)
- This is an excellent point. Sal is emphatic about how important Kelvin absolute temperatures are, but he neglects to mention that these proportions in the ideal gas law (PV=nET) only work for absolute pressure, not gauge pressure. The example is correct for 5 Pa of absolute pressure, but that is a ridiculously low pressure for any "balloon" except one surrounded by a vacuum. Atmospheric pressure is about twenty thousand times 5 Pa, so a corresponding example at the same temperature and volume near atmospheric pressure would represent about twenty thousand times as many helium atoms.(4 votes)

- when he says moles does he mean molecules? im confused(1 vote)
- No, moles are a unit of measure used in chemistry and physics. A mole is a number, like a dozen or a score, but way, way, way bigger.

Sal has a vid on the mole and avogadro's number.(3 votes)

- Wouldn't the pressure inside the balloon have to be equal to the atmospheric pressure (roughly 100 kPa), for the shape of the balloon to stable?(2 votes)

## Video transcript

I told you that the two most
important things you should know in thermodynamics that will
get you most of your way through most exams is that the
pressure times the volume is equal to a constant, and that
the pressure times the volume divided by the temperatures
is equal to a constant. They all change such that the
initial pressure times the volume divided by the initial
temperature is equal to the final pressure times volume
divided by the final temperature. Assuming that you're not
changing the energy of the system, and we'll do
more on that later. The other thing you should
remember is that pressure times volume is equal
to n, where n is the number of moles. Mole is a number like dozen, but
mole is a huge number-- 6 times 10 to the 23 times R. R was the universal gas
constant-- that's 8.31 joules per mole Kelvin times
the temperature. Remember, just to be safe,
always convert to Kelvin first. Let's see if we can do a problem
that I can make up on the fly of this situation. Let's say I have a balloon, and
the volume of the balloon is 1 meter cubed, so this
is a big balloon. That's fairly large, if you
imagine a cubic meter. The volume is a cubic meter, and
let's say the pressure is equal to 5 pascals, and that's
newtons per meter squared. And let's say we're at a
reasonably warm temperature, so temperature is equal to 20
degrees Celsius, and let's say that balloon is filled helium. My question to you is, how many
molecules of helium do I have in the balloon? Let's just substitute
into the equation. We have pressure, which is 5--
and I'll actually write the units, I never do it, but you
should, and you should always do it on an exam-- 5
newtons per meter squared times the volume. 1 meter cubed is equal to my
number of moles, n, times the universal gas constant, 8.31
joules per mole Kelvin, times temperature. Remember, and I can't repeat
this enough, always convert the temperature to Kelvin--
so whatever our Celsius temperature is, add 273. Add 273 to that, and
you get 293 Kelvin. So I get 5 times 1, and meters
square, meters cubed cancels out and just becomes a meter. Newton meter is joules. 5 joules is equal to
n moles times 8.31 joules per mole Kelvin. This Kelvin and this Kelvin
cancel out, so 8.31 times 293 is equal to 2,434.83
joules per mole. To get to the number of moles,
we just divide both sides of this equation by that. And the units should work
out, so you get 5. So n is equal to 5 joules
times 1 over 2,434.83. Since we're dividing by this,
this flips; moles per joule. This joule cancels out with this
joule, so we just have to divide 5 by this, and we'll
get the number of moles. Let's take the inverse of what
I had there times 5, and so I get 0.002 moles. So this equals 0.0021 moles. That might seem like a small
number to you, but let's figure out how many
molecules that is. Let me make some space free,
so I can write Avogadro's number down. Did I even say what Avogadro's
number is? Avogadro's number is the number
of molecules per mole-- it's that number. So, number Avogadro is equal
to 6.022 times 10 to the 23 molecules per mole. The top is molecules, and the
bottom is moles-- I know you can't read that. I have 0.0021 moles, so how
many molecules do I have? I just multiply that 0.0021
times how many moles per molecule-- because this is
moles-- times Avogadro's number, which is molecules
per mole. That's molecules, this is
moles-- maybe I should write the whole thing-- so then the
moles cancel out, and Avogadro's number is 6.022 times
10 to the 23-- let's just remember that--
and let's just multiply that times 0.0021. It equals 0.0126 times 10
to the 23 molecules. This is 0.0126. That's the same thing as 1.26
times 0.01, and then of course times 10 to the 23. What's 0.01? That's 10 to the negative 2--
10 to the negative 1 is 0.1, so this 10 to the negative 2. Then we get 1.26-- 10 to the
negative 2, times 10 to the negative 3, and we add the
exponents times 10 to the 21. It's roughly 1.26, and then
another 19 zeroes-- or roughly 1 followed by 21 zeroes-- is how
many molecules of, in this case, helium we had
in the balloon. It's not too difficult. The hard part is really just
remembering Avogadro's number, remembering the universal gas
constant is 8.31 joules per mole Kelvin, remembering
to always convert your temperature to Kelvin, and then
just making sure all your units match up. Sometimes that might be tricky:
they might give volume in liters, and you have to--
especially in this case-- convert it to meters cubed
before you do it. They might give pressure,
atmospheres, or bars, and you should know the conversion, and
convert it to pascals or newtons per meter squared. Other than that, it's just
substituting and just doing the hairy math and the
scientific notation. Hopefully, that was vaguely
clarifying. See you in the next video.