The Mole and the Avogadro Constant

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. I have four small bottles on my table. Each one holds exactly one gram: hydrogen gas, helium, oxygen gas, and methane. Same mass in every bottle. So, same number of atoms in every bottle? Or does methane win, because every methane molecule has five atoms? By the end of this video, you will answer this in ten seconds. And look, this is not a small topic. In JEE chemistry, almost every numerical starts with one step: convert to moles. So, let's begin.

0:40One mole: a fixed count of particles

So, first question. What is a mole? Is it a mass, or is it a number? Yes, it is a count! Just like a dozen always means twelve things, one mole always means one fixed number of particles. One mole is the amount of substance that contains exactly N A elementary entities, okay? And what is this N A? It is the Avogadro constant: six point zero two two one four zero seven six, times ten to the power twenty three. Not about this number, exactly this number. Oh, ten to the power twenty three, that is a huge count, right? Now, entities of what? Anything you can count: atoms, molecules, ions, electrons, or formula units. So always say a mole of what: one mole of atoms, or one mole of molecules. Clear? And in problems, you don't need all those digits. The wavy equals sign on screen means approximately: six point zero two two times ten to the power twenty three is enough. You will use this number again and again, so make it your friend, okay?

1:48Molar mass: same number, new unit

Alright, next. If one mole is a count, how much does one mole weigh? The mass of one mole, in grams, is called the molar mass, capital M, okay? Its unit is grams per mole: the g mol to the power minus one you see on screen. And here is the beautiful part. The molar mass in grams per mole is numerically equal to the atomic or molecular mass in atomic mass units, the little u on screen. Same number, only the unit changes. Really simple. So tell me. One water molecule has a molecular mass of eighteen atomic mass units. What is the mass of one mole of water? Eighteen grams, yes! Exactly. So the molar mass of water is eighteen grams per mole. But careful: eighteen atomic mass units is the mass of one molecule, and eighteen grams is the mass of one mole of molecules. Don't mix the units in the exam, okay?

2:45The mole map: everything goes through n

Now, the most useful picture in this chapter: the mole map. Look at the circle in the middle. That is small n, the number of moles. Mass, particles and gas volume all sit around it, and every conversion between them passes through n, right? So the mole is the hub. From mass: n equals m divided by capital M, the mass in grams divided by the molar mass. Going back is just the reverse: multiply by the molar mass. See the two arrows on the left? From particles: n equals capital N divided by N A, okay? Capital N is the number of particles, and N A is the Avogadro constant. And for a gas: n equals V gas divided by V m, where V m is the molar volume of the gas, the volume of one mole. Three formulas, one hub. Got it?

3:38Molar volume: read the conditions

Now, a question many students get wrong. One mole of any gas: is its volume always twenty two point four litres? Look, it depends on the conditions! Twenty two point four litres is the molar volume at zero degree Celsius and one atmosphere, okay? At zero degree Celsius and one bar, the molar volume is twenty two point seven litres. That is the current IUPAC standard, okay? And at twenty five degree Celsius and one atmosphere, it is about twenty four point five litres. Different conditions, different molar volume. So which one do you use? Use twenty two point four litres, unless the question says otherwise. But always read the conditions written in the question first. Clear?

4:27Topper's trick: convert to moles first

Now a trick that toppers use in every numerical. Always convert to moles first. Given a mass? Divide by the molar mass, and you have moles. Then from moles, go anywhere on the map: particles, gas volume, or back to mass. Always pass through the hub, okay? Alright, now a trap. One mole of oxygen gas, O two. How many atoms is that? Six point zero two two times ten to the power twenty three, right? No, no, careful! That number counts molecules, and each O two molecule has two oxygen atoms. So to count atoms, multiply the moles of molecules by the number of that atom per molecule. See the arrow going down on the right of the map? Times atoms per molecule. So one mole of O two gives two moles of oxygen atoms. Remember this step, because our bottle puzzle needs exactly this.

5:25Example 1: moles and molecules in 36 g of water

Now, example one. How many moles, and how many molecules, are there in thirty six grams of water? Pause the video, and try it first. Done? Okay, let's check. Topper's trick: convert to moles first. The molar mass of water is eighteen grams per mole. So n equals thirty six divided by eighteen: two moles. That's it! Now the molecules. Capital N equals n times N A: two times six point zero two two times ten to the power twenty three. Two times six point zero two two is twelve point zero four four. So that is twelve point zero four four times ten to the power twenty three, which is one point two zero four times ten to the power twenty four. About one point two times ten to the power twenty four molecules. And watch the power of ten: when the number crosses ten, the power goes up by one, okay?

6:22Example 2: which 1 g sample has the most atoms

Now, remember our four bottles? Let's finish the puzzle. Which contains the most atoms: one gram of hydrogen gas, one gram of helium, one gram of oxygen gas, or one gram of methane? Pause and try. Hint: convert to moles first, then count the atoms. See, many students say: methane has five atoms in each molecule, the most of all. So methane wins, right? No, no, careful! This is the JEE trap. More atoms per molecule does not mean more atoms per gram. Hydrogen first. The molar mass of H two is two grams per mole, so one gram is half a mole of molecules. Each molecule has two atoms. Half times two: one mole of atoms. Helium: molar mass four, so one gram is one fourth of a mole. Helium gas is made of single atoms, so that is simply one fourth mole of atoms. Oxygen: molar mass thirty two, so one gram is one thirty second of a mole of molecules. Times two atoms each: one sixteenth mole of atoms. Very small, right? And methane, C H four: molar mass sixteen, so one sixteenth of a mole of molecules. Times five atoms each: five sixteenths mole of atoms. Now compare: one, versus one fourth, one sixteenth, and five sixteenths. Hydrogen wins, by a long way! Methane only comes second. Puzzle solved: compare moles of atoms, not atoms per molecule. Hydrogen atoms are the lightest, so one gram of hydrogen holds the most atoms. Ten seconds, just as I promised! Really easy, once you count in moles.

8:08Quick revision: the mole, NA and the mole map

So, quick revision. One mole is N A entities, six point zero two two times ten to the power twenty three, and always say a mole of what. The mole map: n equals m by capital M, equals capital N by N A, equals V gas by V m, with twenty two point four litres unless told otherwise. And the topper's trick: convert to moles first, and for atoms, multiply by atoms per molecule. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!