Mole Fraction

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Take a bottle of ethanol and water, labelled forty six percent ethanol, by mass. Forty six percent, that is almost half, right? So tell me: out of all the molecules in that bottle, are almost half of them ethanol molecules? Most students say, yes, obviously. But look, the true answer is very different, and by the end of this video, you will find it yourself. And this is not a small topic. In JEE, mole fraction comes back again and again, especially when you convert one concentration term into another. So, let's begin.

0:41Mole fraction: a share of the moles

So, a solution has two parts. Let me call them A and B, okay? B is the solute, the thing we dissolve, and A is the solvent, like water. Now, if I want to know what share of the solution is B, what should I count? Grams? Or molecules? Yes, molecules! And in chemistry, we count molecules in moles, right? So the first job is always the same: change every mass into moles. n equals mass divided by molar mass. Clear? Now the definition. The mole fraction of B is written as small x, with B below it. x B equals n B, divided by n A plus n B, okay? Moles of B, divided by the total moles in the solution. And that is the whole formula. It is simply the share of the moles that B holds. Alright, and the mole fraction of A? Same idea, just swap the top: x A equals n A, divided by the same total, n A plus n B, okay? Now tell me. If I add x A and x B, what do I get? One! Exactly. Both have the same bottom, so the tops add up to n A plus n B, over n A plus n B, and that is one. So x A plus x B equals one, always. And notice: it is moles divided by moles, so a mole fraction has no unit. It is just a fraction. And this gives us the topper's trick. When a question has two substances, never calculate both mole fractions from scratch. Find one, and the other is simply one minus that. x A equals one minus x B, okay? Quick and easy.

2:28Heat it up: does the mole fraction change?

So, now a question that JEE loves to ask. I take this solution, and I heat it. Does the mole fraction change? Look at the formula again. What is inside it? Only moles. There is no volume anywhere, right? When you heat the solution, its volume may change, but the number of moles of A and of B stays exactly the same. Same moles, so the same mole fraction. So, mole fraction does not depend on temperature. Got it? And the same is true for mass percent, and for molality, which you will meet very soon. Mass percent uses only masses, and molality uses moles and the mass of the solvent. No volume in either, so they do not change with T, the temperature you see on screen, okay? But molarity, which also comes in the next lesson, uses the volume of the solution. And the volume changes with temperature, so molarity changes. This is a favourite JEE trap: which of these changes when the solution is heated? Only the one with a volume in it, molarity. Clear?

3:34Example 1: mole fraction of ethanol in water

Alright, our first example. Find the mole fraction of ethanol in a solution of forty six grams of ethanol and thirty six grams of water. Pause the video, and try it first. Done? Okay, let's check. Many students straight away write forty six, divided by forty six plus thirty six. Easy, right? No, no, careful! Those are grams. That gives the share of the mass, not the share of the moles. Mole fraction needs moles, remember? So, first, the moles of ethanol. Ethanol is C two H five O H, and its molar mass is forty six. Forty six grams divided by forty six: exactly one mole. Now water, H two O, molar mass eighteen. Thirty six divided by eighteen: two moles. Look, there are fewer grams of water than of ethanol, but more moles of water! Water molecules are light, so each gram holds more of them. So, the mole fraction of ethanol equals one, divided by one plus two. One third, that is zero point three three three. With me? And the mole fraction of water? Don't calculate it again. Use the trick: one minus one third, which is two thirds. And we are done.

4:56Example 2: mole fraction in 46% w/w ethanol

Now the harder one, and look, this is our puzzle from the start. Find the mole fraction of ethanol in forty six percent aqueous ethanol, w by w. Here, w by w means by mass, okay? Pause the video and try it. Done? Okay, let's check. Forty six percent ethanol, so the mole fraction is zero point four six, right? No, no, careful! That is a share of the mass, not a share of the moles. We must change to moles first, just like before. But how much solution do we have? The question gives no mass at all. Here is the topper's trick: with a percent by mass, simply take one hundred grams of solution. Then forty six percent becomes just forty six grams of ethanol. Nice and easy. Now, how many grams of water are there in this solution? Fifty four grams, not one hundred! The hundred grams is the whole solution, ethanol plus water, right? So the water is one hundred minus forty six, fifty four grams. Honestly, so many students put a hundred grams of water here. Don't do that! Now the moles. Ethanol: forty six divided by forty six, one mole. Water: fifty four divided by eighteen, three moles. So, the mole fraction of ethanol equals one, divided by one plus three. One fourth, zero point two five. And now our puzzle is solved! By mass, the bottle is almost half ethanol. But for every one ethanol molecule, there are three water molecules, so only one molecule in four is ethanol. The light water molecules pack many more of themselves into each gram. Got it?

6:45Quick revision: moles not grams, sum is 1

So, quick revision. Mole fraction is the moles of B over the total moles, so always change grams into moles first. x A plus x B equals one, so find one, and the other comes free. And there are only moles in it, no volume, so temperature does not change it. Now go and try the two practice problems on this page. You will find them easy, I promise. All the best!