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### Course: Physics library>Unit 10

Lesson 1: Temperature, kinetic theory, and the ideal gas law

# 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?

• At , Sal wrote m for mole. Is this standard/allowed? Or will people confuse this with Meters?
• This is not standard, always use "mole" or it's abbreviation "mol"
• 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..
• 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)
• What are Bars?
• A unit of pressure where 1 bar is the pressure at sea level.
• What are Bars? you said it at the very end.
• A bar is a unit of pressure about the same a one atmosphere.
• 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?
• 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 !
• 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)
• 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.
• 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 :)
• 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.