Yield and Purity

Transcript

0:00Introduction

Hello everyone! So, one small puzzle before we start. Imagine a product made in three steps, and at each step, one mole gives one mole. Step one has a yield of eighty percent, step two seventy five percent, and step three fifty percent. You start with one mole. How much product do you get at the end? Half a mole, because the weakest step is fifty percent? Or the average of the three, about sixty eight percent? Hmm. Hold on to your answer, okay? Today we learn yield and purity, and by the end of this lesson, you will know exactly. And look, these two ideas sit inside so many JEE stoichiometry numericals. So, let's begin.

0:45Percentage yield

So, first, yield. The balanced equation tells you how much product you should get. But tell me, in a real reaction, do you always get that full amount? No, not always! In our puzzle, the three steps gave only eighty, seventy five and fifty percent, right? So we compare two amounts. The amount the equation promises is the theoretical yield. The amount you actually get is the actual yield. Percentage yield equals actual yield, divided by theoretical yield, times one hundred. Write this down. Clear? Now one important question. If the question gives you two reactants, which one do you use to find the theoretical yield? The limiting reagent, exactly! Remember, the reactant that is used up first decides the amount of product. So the theoretical yield always comes from the limiting reagent, never from the reactant in excess. Many students slip here in the exam. Don't be one of them, okay?

1:46Percentage purity

Alright, next, purity. Often a JEE question gives you an impure sample. Part of its mass is the substance you want, and the rest is impurity. So, percentage purity equals the mass of pure substance, divided by the mass of the sample, times one hundred. Simple, right? Now think. When this impure sample reacts, where does the product come from? Only from the pure part, of course! In these questions the impurity does not react. So the product tells you about the pure substance only, not about the whole sample. That is the key idea. Got it? So the method is always the same. From the product, find the moles. From the moles, find the mass of pure substance. Then compare it with the mass of the sample. That's it, purity done.

2:37Many steps: multiply the yields

Now, back to our puzzle. We start with one mole, and each step turns one mole into one mole. So, is the overall yield the average of the three steps? Or just the weakest step? Let's not guess. Let's follow the moles, step by step. Step one gives eighty percent. One times zero point eight: zero point eight moles come out. Now look, step two does not start from one mole, right? It starts from only zero point eight. Seventy five percent of that: zero point eight times zero point seven five, that is zero point six moles. Step three: fifty percent of zero point six. Zero point three moles! Not half a mole, and not sixty eight percent. The overall yield is just thirty percent, even less than the weakest step. See, each step works only on what the step before it left behind! So, the rule. Write each step's yield as a fraction: y one, y two, y three, and so on. The overall yield is their product, y one times y two times y three. Here, zero point eight times zero point seven five times zero point five: zero point three, that is thirty percent. Never average the yields, and never take just the weakest one. Multiply them. With me?

4:00Example 1: percentage yield of ethene from ethanol

Now, example one. Forty six grams of ethanol is dehydrated to give twenty five point two grams of ethene. Find the percentage yield. Pause the video, and try it first. Done? Okay, let's check. First, the equation. Ethanol, C two H five O H, loses a water molecule and becomes ethene, C two H four, okay? One mole gives one mole. Now, the trap. Some students directly write twenty five point two over forty six, times one hundred. About fifty five percent, right? No, no, careful! Forty six grams is ethanol, the reactant. The theoretical yield must be a mass of ethene, the product. So, the molar mass of ethanol is forty six, which means forty six grams is exactly one mole. One mole of ethanol can give one mole of ethene, and that is twenty eight grams. This twenty eight grams is our theoretical yield. Actual over theoretical: twenty five point two over twenty eight, times one hundred. Ninety percent! Nice and clean.

5:14Example 2: mass of 80% pure limestone for 11.2 L of CO2

Now a harder one, JEE level. Read it with me. What mass of limestone, containing eighty percent calcium carbonate, must be heated to give, at STP, eleven point two litres of carbon dioxide? Pause and try. Hint: first find the mass of pure calcium carbonate. Done? Okay. On heating, calcium carbonate gives calcium oxide and carbon dioxide. One mole gives one mole, okay? At STP, one mole of gas takes up twenty two point four litres. So, eleven point two over twenty two point four: zero point five moles of carbon dioxide. So we need zero point five moles of pure calcium carbonate. Its molar mass is one hundred, so that is fifty grams of pure carbonate. Remember, only this pure part gives the gas. Now the trap. The limestone is eighty percent pure, so fifty times zero point eight, forty grams, right? No, wait! Think for a second. The sample has to be heavier than the pure carbonate inside it, doesn't it? Forty is less than fifty! The fifty grams of carbonate is only eighty percent of the limestone. So, limestone equals fifty divided by zero point eight. Sixty two point five grams. Quick check: eighty percent of sixty two point five is fifty grams. Absolutely correct. So remember, to find the mass of an impure sample, divide by the purity fraction, never multiply.

6:49Quick revision: yield, purity and multi-step yields

So, quick revision. Percentage yield is actual over theoretical, times one hundred, and the theoretical yield always comes from the limiting reagent. Percentage purity is pure mass over sample mass, times one hundred, and to find the sample, divide by the purity. And for many steps, multiply the fractional yields, never average them. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!