Minimum Molar Mass

Transcript

0:00Introduction

Hello everyone! Let's start with one small puzzle. Haemoglobin, yes, the haemoglobin in your blood, is a giant molecule. Nobody can put one single molecule on a balance and weigh it. But a chemist gives you just one fact: haemoglobin is zero point three four percent iron by mass. That's it. From this one tiny number, can you tell how heavy the whole molecule is? Sounds impossible, right? Today we will see how much one small percentage can tell us. And in JEE, questions on proteins, enzymes and chlorophyll are all built on this one idea: the minimum molar mass. So, let's begin.

0:42Why minimum? Atoms come whole

So, let's think like a chemist. Haemoglobin contains iron, so every molecule of it has some iron, right? Now tell me, can one molecule hold half an iron atom? No, never! Atoms come whole. So, if a compound contains an element at all, each molecule has at least one atom of it. One, or two, or more, but never less than one, okay? And this one simple fact is the whole idea of today's lesson. Now let's put it into an equation. Say the element is x percent of the compound by mass, its atomic mass is capital A, and each molecule has k atoms of it. Let the molar mass of the compound be capital M, okay? Then the mass fraction of the element, x by one hundred, equals k times A, divided by M, clear? On the left, the element's share as a fraction. On the right, the mass of its atoms, out of the whole. Now the key question. If nobody tells us k, what is the smallest value it can take? Yes, one! At least one atom, remember? And more atoms means a heavier molecule, so the smallest k gives the smallest M, okay? So, put k equal to one, and rearrange. M min, the M with the little word min written below it, equals capital A times one hundred, divided by x, okay? This is the minimum molar mass. The compound cannot be lighter than this. Got it?

2:14Know the atom count? Multiply by k

Alright, now suppose the question also tells you that each molecule has two atoms of that element, okay? Same percentage. Will the molecule be heavier, or lighter? Heavier, exactly! Twice as heavy. The same x percent now has to hold two whole atoms, so the whole molecule must weigh twice as much. In general, with k atoms per molecule, M equals k times M min. So the plan is: find M min, then multiply by k. Simple as that. Now one JEE trap, and many students fall for it. In this formula, x stands for the percentage. So you first change x percent into a fraction, divide it by one hundred, and then put it in, right? No, no, careful! Look at the formula again. That times one hundred on top is already doing the percent job, okay? So x is just the plain number written before the percent sign. If you also divide x by a hundred, you divide twice, and your answer comes out a hundred times too big. So, pick one way. Either use the formula, with times one hundred and the plain number x. Or use the fraction form, x by one hundred, equal to k times A, divided by M, okay? Never both. Clear?

3:35Topper's trick: smaller percent, heavier molecule

Now a quick trick that toppers use to check their answers. Look where x sits in the formula: at the bottom of the fraction, okay? So if x gets smaller, what happens to M min? Yes, it gets bigger! The double arrow on screen means implies, or simply, so. Smaller x, so a bigger M min. With me? So, a tiny percentage of the element means a very heavy molecule. Remember our haemoglobin, with just zero point three four percent iron? So expect a really big answer there. And if a tiny percentage ever gives you a small molar mass, stop and recheck.

4:13Example 1: molar mass of chlorophyll from 2.72% Mg

Alright, time for the first example. Chlorophyll contains two point seven two percent magnesium, and one magnesium atom per molecule. Find its molar mass. The atomic mass of magnesium is twenty four point three. Pause the video, and try it first. Done? Okay, let's check. First, how many magnesium atoms are there in one molecule? Just one, the question says so. That is the one M g atom on screen, M g for magnesium. So k is one, and the molar mass is exactly the minimum molar mass, okay? Now the formula. Capital A is twenty four point three, and x is two point seven two, the plain number. No dividing by a hundred, remember the trap? Twenty four point three times one hundred is two thousand four hundred and thirty. Now divide that by two point seven two. That gives about eight hundred and ninety three grams per mole. The wavy equals sign on screen means approximately. Nice and clean. One atom, one formula, and done.

5:21Example 2: molar mass of haemoglobin with 4 Fe atoms

Now a harder one, JEE pattern, and it is our puzzle from the start. Haemoglobin contains zero point three four percent iron by mass, and each molecule contains four iron atoms. Find the molar mass of haemoglobin. Iron is fifty six. Pause the video and try it. Now, here is what many students do. Iron is fifty six, x is zero point three four, so the answer is fifty six times one hundred, divided by zero point three four, right? No, no, careful! That is only the minimum, for one iron atom per molecule. Each molecule has four iron atoms, so we must count all four. This time, let's use the fraction form. The mass fraction of F e, that is iron: zero point three four percent, as a fraction, is zero point zero zero three four, okay? The mass fraction equals k times A, divided by M, okay? So, four times fifty six, divided by M, equals zero point zero zero three four. And four times fifty six is two hundred and twenty four. So, M equals two hundred and twenty four, divided by zero point zero zero three four. That is about sixty five thousand nine hundred grams per mole. And see, we used the fraction, so we did not multiply by one hundred again. One way only, remember? Or, about six point six times ten to the power four grams per mole. And there it is, our puzzle is solved! One tiny percentage, plus the count of iron atoms, gave us the mass of a giant molecule. And it is a really big number, just as our topper's trick said. If your answer came out four times smaller, you forgot the four iron atoms, right?

7:13Quick revision: minimum molar mass and the k-atom rule

So, quick revision. Every molecule has at least one atom of the element, so M min equals capital A times one hundred, divided by x, okay? If each molecule has k such atoms, multiply: M equals k times M min. And watch the percent: use times one hundred with the plain number, or use the fraction, but never both. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!