The Principle of Atom Conservation and Mixtures

Transcript

0:00Introduction

Hello everyone! Let's start with one small puzzle. I give you one point eight four grams of a white powder. It is a mixture of two carbonates, calcium carbonate and magnesium carbonate. I heat it strongly, and only zero point nine six grams of residue is left. Now tell me: how much calcium carbonate was in that powder? Hmm, two unknowns, and we only weighed it twice. Can we really find both? Yes, we can! Today we learn two tools: the principle of atom conservation, POAC for short, and the topper's trick for mixtures. And look, this mixture question is a classic JEE pattern. So, let's begin.

0:44POAC: atoms are conserved

So, start with a simple question. In a reaction, the molecules change, right? But can an atom simply vanish? Or appear from nowhere? No, it cannot. Atoms are conserved in a reaction. Every atom you start with is still there at the end, maybe sitting in a different species. This is the principle of atom conservation, and we call it POAC for short, okay? Now let's turn it into a formula. Pick any one element, say oxygen. Now look at every species that contains oxygen. For each species, multiply its moles by the number of oxygen atoms in one unit of it, and then add. That big sigma sign on screen is just the symbol for add them all up, okay? And POAC says: this sum is the same before the reaction and after the reaction. Atoms in equals atoms out.

1:40POAC in action: skip the balancing

Clear? Alright, let's use it. Potassium chlorate, the formula on screen, is heated, and it gives oxygen gas. All its oxygen comes out as oxygen gas. Now count oxygen atoms. One unit of potassium chlorate has three oxygen atoms. One oxygen molecule has two. So, small n means moles. Now tell me: is n of potassium chlorate equal to n of oxygen gas? Many students write exactly that. No, no, careful! This is the JEE trap. POAC counts atoms, not molecules. Oxygen atoms before: three times the moles of potassium chlorate. Oxygen atoms after: two times the moles of oxygen gas. So, three n of potassium chlorate equals two n of oxygen. Look, we never wrote the balanced equation! Straight to the answer. One more. Pyrite, F e S two, is roasted, and all its sulphur ends up in sulphuric acid. Quick, how many sulphur atoms in one pyrite unit? Two, yes! And each sulphuric acid has one. So, two times the moles of pyrite equals the moles of sulphuric acid. That's it! We did not need any equation at all. So here is the rule. When only one element links a reactant to a product, you can skip the balancing. Just apply POAC on that one element. Got it?

3:12Topper's trick: two equations for a mixture

Now, mixtures. You get a mixture of two substances, and you must find how much of each. Two unknowns, right? So how many equations do you need? Two, exactly! Equation one comes from the total mass. Call one component x grams. Then the other one is the total minus x. Okay? Equation two comes from whatever the question has measured. So think, what can a question actually measure in the lab? Yes, it may be the mass of residue left after heating, the gas evolved, or a precipitate. And to write this second equation, POAC links each component to what was measured. Two unknowns, two equations, and the problem is solved. That's the whole trick. And see, this is exactly how we will crack our puzzle in a few minutes. With me?

4:03Example 1: mass of P4O10 from 6.2 g of white phosphorus

Now, example one. What mass of P four O ten is obtained by burning six point two grams of white phosphorus, P four? The atomic mass of phosphorus is thirty one. Pause the video, and try it first. Done? Okay, let's check. Many students divide six point two by thirty one, get zero point two, and write zero point two moles of P four O ten. Right? Oh no! Zero point two moles of what? Of phosphorus atoms, not of P four molecules! White phosphorus is P four, four atoms in one molecule. So its molar mass is four times thirty one, one hundred and twenty four. Six point two over one hundred and twenty four: zero point zero five moles of P four. Now POAC on phosphorus. Before: four times the moles of P four. After: four times the moles of P four O ten. The fours cancel. So, zero point zero five moles of P four O ten. Its molar mass? Four times thirty one, plus ten times sixteen: two hundred and eighty four. Mass equals zero point zero five times two hundred and eighty four. Fourteen point two grams. And see, no balanced equation anywhere. Nice and simple. Got it?

5:29Example 2: CaCO3 and MgCO3 mixture from the residue mass

So, remember our puzzle from the start? Let's finish it. Read it with me. The mixture of calcium carbonate and magnesium carbonate weighs one point eight four grams. It is heated strongly, and leaves zero point nine six grams of residue, calcium oxide plus magnesium oxide. Find the composition of the mixture. Magnesium is twenty four, and calcium is forty. Pause and try. Hint: two unknowns, so two equations. Done? Okay, let's check. Some students see zero point nine six grams of residue and think: that is all calcium oxide, right? No, no, careful! Magnesium carbonate also leaves a residue, magnesium oxide. The zero point nine six grams is both oxides together. So, equation one, the total mass. Let calcium carbonate be x grams. Then magnesium carbonate is one point eight four minus x grams. Now POAC, to link each carbonate to its oxide. The arrow on screen means changes into. All the calcium in calcium carbonate ends up in calcium oxide, mole for mole. Calcium carbonate has molar mass one hundred, and calcium oxide fifty six. Same idea for magnesium: magnesium carbonate is eighty four, and magnesium oxide is forty, okay? Equation two, the residue. Fifty six by one hundred of x, plus forty by eighty four of one point eight four minus x, equals zero point nine six. Clear? Open the bracket. Zero point five six x, plus zero point eight seven six two, minus zero point four seven six two x, equals zero point nine six. Move the constant across, and the double arrow means so: zero point zero eight three eight x equals zero point zero eight three eight. So x is one point zero zero grams. One gram of calcium carbonate, and one point eight four minus one, that is zero point eight four grams of magnesium carbonate. Quick check. One gram of calcium carbonate gives zero point five six grams of calcium oxide. Zero point eight four grams of magnesium carbonate gives zero point four zero grams of magnesium oxide. Together, zero point nine six grams. Absolutely correct! See, that was our puzzle: two unknowns, two weighings, two equations, solved.

8:00Quick revision: POAC and two equations for mixtures

So, quick revision. POAC: for any element, moles times atoms per species is the same before and after the reaction. When one element links a reactant to a product, skip the balancing, and use POAC on that element. And for a two component mixture, write one equation for the total mass, and one for what you measure. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!