Percentage Composition from a Formula

Transcript

0:00Introduction

Hello everyone! Let us start with a small puzzle. Aspirin, the familiar tablet, has eight hydrogen atoms in every molecule, but only four oxygen atoms. That is twice as many hydrogen atoms as oxygen atoms. So hydrogen must make up more of its mass than oxygen, right? Hmm, keep your answer in mind; we will test it in Example one. Today we learn how to find the percentage of each element in a compound, straight from its formula. It is a short calculation, and in JEE it often sits inside a bigger question on organic analysis. So, let's begin.

0:38Percentage of an element

So, here is the one formula for today. The percentage of an element equals the number of its atoms, times its atomic mass, over the molar mass of the compound, times one hundred. The sign before the word element is the per cent sign, the cross means times, and the brackets just keep each quantity together. The long line in the middle is a fraction bar, so we read it as over. Okay? Now let me ask you this. Why do we multiply by the number of atoms? Why not just put the atomic mass on top? Because every atom of that element adds its own mass, yes, exactly! So the top of the fraction is the total mass of that element in one mole of the compound. The small m o l on screen is short for mole. Right? And the bottom is the molar mass, which we call capital M, the sum of the masses of all the atoms in the formula. So the fraction is simply the part of the mass that belongs to our element, and the times one hundred turns that part into a percentage. Clear? For today we need only four atomic masses: carbon twelve, hydrogen one, nitrogen fourteen, and oxygen sixteen. Keep them at your fingertips. Got it?

1:49Reaction given? The chemistry decides the formula

Now, in JEE, the formula is often not handed to you. The question describes a reaction, or a sequence of reactions, and then asks for a percentage in the product. So tell me, whose formula goes into our percentage formula: the starting compound's, or the product's? Yes, the product's formula, of course! So step one is to use the chemistry to find the final product. This is the real chemistry part of the question. Right? Step two is to write its molecular formula, count the atoms carefully, and add up the molar mass. With me? And step three is to put the numbers in our formula. Once the formula of the product is right, the arithmetic is routine. So step one is where you must be most careful. Okay?

2:36Example 1: percentage composition of aspirin C9H8O4

Now, Example one, and it is our puzzle from the start. Find the percentage composition of aspirin, C nine H eight O four. The small numbers written low after each symbol are subscripts, and they count the atoms: nine carbons, eight hydrogens and four oxygens in one molecule. Percentage composition means the percentage of every element in it. Pause the video and try it first. Done? Okay, let's check. First, the molar mass. Nine carbons times twelve, plus eight hydrogens times one, plus four oxygens times sixteen. That is one hundred and eight, plus eight, plus sixty four, which gives one hundred and eighty. Got it? Now carbon. The atomic mass of carbon is twelve, so carbon is twelve over one hundred and eighty, right? No, no, wait, that is the trap! There are nine carbon atoms, so the top is nine times twelve, which is one hundred and eight. One hundred and eight over one hundred and eighty, times one hundred, gives sixty point zero per cent. Clear? Next, hydrogen. Eight hydrogen atoms times one gives eight. Eight over one hundred and eighty, times one hundred, gives four point four four per cent. Right? And oxygen. Four times sixteen is sixty four, and sixty four over one hundred and eighty, times one hundred, gives thirty five point six per cent. Now our puzzle. Eight hydrogen atoms give only four point four four per cent, while just four oxygen atoms give thirty five point six per cent. And why is that? Because each oxygen atom is about sixteen times as heavy as a hydrogen atom. Counting atoms is not counting mass. So that is the mystery solved, see? Finally, a quick check. Sixty point zero, plus four point four four, plus thirty five point six, is about one hundred; the wavy equals sign means approximately, because we rounded each value. If your percentages do not add up to about one hundred, something has gone wrong. With me?

4:48Example 2: percent nitrogen in aniline made from benzene

Now Example two, a harder one, JEE style. Benzene is nitrated, and the product is reduced with S n slash H C l, which means tin with hydrochloric acid. Find the percentage of nitrogen in the final product. Pause the video and try it first. Done? Okay, let's check. Step one, the chemistry. Nitration of benzene gives nitrobenzene. Then tin and hydrochloric acid reduce the nitro group to an amino group, and we get aniline. The arrows on screen mean gives, and the words above them say what we did. So the final product is aniline, not nitrobenzene; stopping one step early is the trap here. Right? Now step two, the formula. Aniline is C six H five N H two: a benzene ring with five hydrogens left on it, and an N H two group. So how many hydrogen atoms does aniline have in total? Seven, correct! Five on the ring, plus two on the nitrogen. So aniline is C six H seven N, and that is our formula. Oh no, careful here: if you count only five hydrogens, the molar mass comes out wrong. Okay? Now the molar mass. Six carbons times twelve, plus seven hydrogens times one, plus fourteen for the one nitrogen. Seventy two, plus seven, plus fourteen, gives ninety three. Clear? And step three, the routine part. There is only one nitrogen atom, so just fourteen on top. Per cent nitrogen equals fourteen over ninety three, times one hundred, which gives fifteen point one per cent. See? The chemistry did the real work, and the arithmetic was quick.

6:39Quick revision: mass percent formula and the atoms trap

So, quick revision. The percentage of an element equals the number of its atoms times its atomic mass, over the molar mass, times one hundred. Count the atoms carefully, and remember that more atoms need not mean more mass. And when a reaction is given, find the final product's formula first; after that, the arithmetic is routine. Now go and try the practice problems on this page. You will do well. All the best!