Mixed Problems: Set 1 (Mole Concept, Composition and Formulae)

Transcript

0:00Introduction

Hello everyone! Let's warm up with one small puzzle before we start. Three bags are kept on a table. The first has half a mole of ozone. The second has one point two into ten to the power twenty three molecules of sulphur dioxide. And the third has eleven point two litres of carbon dioxide, at STP, okay? Which bag is the heaviest? Tricky, right? Three different units: moles, molecules and litres. This is exactly how JEE Main mixes things up. Today we solve a mixed set on the mole concept, composition and formulae, and by the end, you will crack this puzzle in one or two minutes, the way the exam wants. So, let's begin.

0:46Tool 1: everything goes through moles

So, the first tool, and the most important one. Whatever the question gives you, molecules, grams or litres, first change it into moles. From molecules, divide by N A, the Avogadro constant, six point zero two two into ten to the power twenty three, okay? Try this one from our set. Find the mass of three point zero one one into ten to the power twenty two molecules of sulphuric acid, H two S O four. First, how many moles is that? Look, three point zero one one is exactly half of six point zero two two, and the power is one less, ten to the twenty two. So it is half of one tenth of a mole: zero point zero five mole. Perfect! Now moles to mass: multiply by the molar mass. Sulphuric acid is ninety eight grams per mole, so zero point zero five times ninety eight gives four point nine grams. Two lines, done. Clear?

1:46Tool 2: count inside the formula

Alright, the second tool: counting particles inside a formula. How many moles of oxygen atoms are present in zero point two mole of aluminium sulphate? First tell me: how many oxygen atoms sit in one formula unit? Twelve, exactly! Each sulphate has four oxygens, and the three outside the bracket multiplies everything inside. Three times four, twelve. Students who forget the bracket write four, and lose the marks, okay? So zero point two mole of the salt has zero point two times twelve, that is two point four moles of oxygen atoms. Simple as that. Now a twist. How many protons are present in zero point one mole of ammonium ions, N H four plus? Nitrogen brings seven protons, and each hydrogen brings one. But the ion has a plus charge, so one proton less, right? Ten? No, no, careful! This is the JEE trap. The charge changes the electrons, not the protons. So the protons per ion are seven plus four, eleven, okay? Then zero point one mole times eleven is one point one moles of protons, that is one point one times N A, okay? Multiply by the Avogadro constant, and you get six point six two into ten to the power twenty three. Got it?

3:11Tool 3: percentage composition, both ways

Now composition. Find the percentage of sulphur in hypo, sodium thiosulphate with five waters, to the nearest integer. Its molar mass, M on the screen, is two hundred and forty eight. See, the two forty eight already includes the five water molecules. Water of crystallisation counts! So, what goes on top? The mass of sulphur in one mole: two sulphur atoms, sixty four grams. Sixty four over two forty eight, times hundred, gives twenty five point eight percent. To the nearest integer, twenty six, exactly how JEE Main asks it in numerical questions. Now turn it around. Here is a protein with zero point five six percent iron, and two iron atoms in every molecule. Find its molar mass. Same formula, just run backwards. Can you see how? Yes, exactly! Here is the topper's trick. The iron in one mole is two times fifty six, one hundred and twelve grams, and that is zero point five six percent of M, the molar mass. So M equals two times fifty six times hundred, over zero point five six: twenty thousand grams per mole. The answer box wants it as something into ten to the power three, so you enter twenty. And notice the two. Forget it, and your answer is only half. With me?

4:34Example 1: greatest mass of O3, SO2 or CO2

Now, remember our three bags? Let's finish them. Half a mole of ozone, one point two into ten to the power twenty three molecules of sulphur dioxide, or eleven point two litres of carbon dioxide at STP, okay? Which has the greatest mass? Use tool one: everything into moles first. Pause the video, and try it. Done? Okay, let's check. Ozone is already in moles, so nothing to convert. O three is forty eight grams per mole, so half a mole is twenty four grams. Sulphur dioxide: one point two into ten to the twenty three, divided by the Avogadro constant, is about zero point two mole. Times sixty four, that is twelve point eight grams. The heavy sulphur did not help, did it? Too few molecules. Now carbon dioxide. One mole of gas at STP fills twenty two point four litres, so eleven point two litres is half a mole. Same moles as the ozone, so the same mass, twenty four grams, right? No, no! Equal moles do not mean equal mass. Carbon dioxide is forty four grams per mole, so half a mole is twenty two grams. Moles are a count, okay? The mass depends on the molar mass. So the winner is half a mole of ozone, at twenty four grams. Twenty four, twelve point eight, twenty two. Puzzle solved, and in under two minutes!

6:04Example 2: water molecules in hydrated Na2SO4

Now a harder one, JEE level. Hydrated sodium sulphate, with x water molecules per formula unit, loses fifty five point nine percent of its mass on complete dehydration. Find x. Pause and try. Hint: think what exactly is lost on heating. Done? Okay, let's check. On heating, only water leaves, so the mass lost is the water. One formula unit carries x waters, that is eighteen x grams per mole. And sodium sulphate itself is one hundred and forty two. So eighteen x over one forty two equals zero point five five nine, right? No, no, careful! Fifty five point nine percent of which mass? Of the starting mass, the whole hydrate! So the bottom is one forty two plus eighteen x. Eighteen x, over one forty two plus eighteen x, equals zero point five five nine. Same lesson as hypo: water of crystallisation counts in the molar mass. Now cross multiply, and bring the x terms together. Eighteen x, times one minus zero point five five nine, equals zero point five five nine times one forty two. That is eighteen x times zero point four four one, equals about seventy nine point four. So x comes out as ten. Quick check: one eighty over three twenty two is zero point five five nine. Absolutely correct! The formula has ten waters, and the answer is ten.

7:39Quick revision: moles, atom counts and percent

So, quick revision. One: everything goes through moles, whether the question gives particles, grams or litres. Two: count carefully inside the formula, and remember, a charge changes the electrons, not the protons. Three: for percentages, the part over the whole molar mass, times hundred, and the water of crystallisation always counts. Now go and try the four practice problems on this page. Give each one two minutes, like the real exam. You will do great. All the best!