Percentage Composition

Transcript

0:00Introduction

Hello everyone! First, one small puzzle before we start. You have one tonne of haematite, an iron ore. And eighty percent of this ore is iron oxide, F E two O three. So, how much iron can you actually take out of it? Eight hundred kilograms, right? Eighty percent of one thousand. Hmm. Are you sure? Hold on to that answer. By the end of this video, you will see why so many students get this wrong. And look, this idea, percentage composition, is the very first step of this whole chapter on empirical and molecular formulae, and JEE keeps coming back to it. So, let's begin.

0:42Mass percentage of an element

So, let's start with a simple question. You have a compound, made of a few elements. What part of its mass comes from one particular element? Well, think of it like your test marks: your score, divided by the total, times a hundred. Same idea here. The element's share of the mass, divided by the whole mass, times a hundred. So here is the formula. Write it down. Percentage of an element equals the number of atoms of that element, times its atomic mass, divided by the molar mass of the compound, and then times a hundred. On top, the element's share. At the bottom, the whole compound. Clear? Alright, let's try it on urea, a fertiliser that farmers use for its nitrogen. Look at its formula on screen: C O, then N H two inside a bracket, with a two outside the bracket. Now tell me, how many nitrogen atoms are there? Only one? No, no, careful! That little two outside the bracket doubles everything inside it. So, two nitrogen atoms, and two times two, that is four hydrogen atoms. Now the molar mass, capital M on screen: carbon twelve, plus oxygen sixteen, plus two times fourteen for nitrogen, plus four times one for hydrogen. Sixty. Nice and simple. Nitrogen's share is two times fourteen, that is twenty eight. Twenty eight over sixty, times a hundred: forty six point seven percent. And if you had put only one nitrogen on top? Fourteen over sixty: twenty three point three percent, just half the real answer. That is the trap. Always count the atoms from the subscripts, and from the brackets too. Got it?

2:30From percent to grams, and a free check

So, what can we do with this percentage? Percent means per hundred, right? So in every hundred grams of urea, forty six point seven grams is nitrogen. And for any mass, m grams of the compound, the mass of the element is m times the percentage, divided by a hundred, okay? This one line turns a percentage into real grams, or real kilograms. Now one more question. Suppose you find the percentage of every element in a compound, and then add them all. What should you get? Yes, a hundred! Exactly. Every bit of the compound's mass belongs to one of its elements, so all the percentages add up to a hundred, okay? And this gives you a topper's trick, completely free. After any calculation, add your percentages. If you get a hundred, or very close to it because of rounding, you are safe. If not, go back and count your atoms again.

3:26Example 1: percentage of C, H and O in ethanol

Right, time for the first example. Find the percentage of each element in ethanol, C two H five O H, okay? Carbon is twelve, hydrogen one, and oxygen sixteen. Pause the video, and try it first. Done? Okay, let's check. First, the molar mass. And for that, how many hydrogen atoms are there in ethanol? Five? No, no, look again! There is one more hydrogen hiding in the O H at the end, see? So, five plus one: six hydrogens. Two carbons at twelve each, that is twenty four. Six hydrogens at one each, that is six. And one oxygen, sixteen. Twenty four plus six plus sixteen: so M, the molar mass, is forty six. Now carbon. Its share is twenty four. Twenty four over forty six, times a hundred: fifty two point one seven percent. Hydrogen: six over forty six, times a hundred. Thirteen point zero four percent. And if you had counted only five hydrogens, both the top and the bottom of this fraction would be wrong, right? And oxygen: sixteen over forty six, times a hundred. Thirty four point seven eight percent. Now, our topper's check. Fifty two point one seven, plus thirteen point zero four, plus thirty four point seven eight. Ninety nine point nine nine. The tiny gap is just rounding, so it is a hundred. Absolutely correct! With me?

5:01Example 2: iron from one tonne of 80% haematite ore

Now a harder one, JEE style. And look, this is our puzzle from the start. Haematite ore contains eighty percent F E two O three. What mass of iron can be extracted from one tonne of the ore? Iron is fifty six, and oxygen sixteen. Pause the video and try it. Hint: read every word of the question carefully. Done? Okay, let's check. Eighty percent of one thousand kilograms is eight hundred. So, eight hundred kilograms of iron, right? No, no, careful! This is the JEE trap. Read it again. Eighty percent of the ore is F E two O three, not iron. So, one tonne is one thousand kilograms, and eighty over a hundred of it is eight hundred kilograms. But that is the mass of iron oxide in the ore. The iron is still locked inside it, right? So now we need the percentage of iron in F E two O three. First, the molar mass, M of F E two O three: two irons at fifty six each, plus three oxygens at sixteen each. One hundred and twelve plus forty eight: one hundred and sixty. Now tell me, what goes on top of the fraction: fifty six, or one hundred and twelve? Yes, one hundred and twelve! Two iron atoms, so two times fifty six. One hundred and twelve over one hundred and sixty, times a hundred: seventy percent. Put only fifty six on top, and you get half the answer. The same trap as urea, remember? Last step, our formula from before: mass of the element equals the mass of the compound, times the percentage over a hundred. Eight hundred kilograms, times seventy over a hundred: five hundred and sixty kilograms. So, from one tonne of ore, you get only five hundred and sixty kilograms of iron. Not eight hundred! Puzzle solved. Just a percentage of a percentage, that is the whole trick.

7:05Quick revision: mass percent formula and the 100% check

So, quick revision. Percentage of an element: number of atoms times atomic mass, over the molar mass, times a hundred. Mass of the element in any sample: the sample's mass, times the percentage, over a hundred. And count every atom, brackets included, then check that your percentages add up to a hundred. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!