Positive and Negative Deviations

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle first. Mix fifty millilitres of one liquid with fifty millilitres of another. How much solution do you get? One hundred millilitres, obviously, right? But suppose you measure only ninety seven, and the flask even warms up! Where did three millilitres go? Today's topic answers it: positive and negative deviations from Raoult's law, which come up often in JEE, okay? So, let's begin!

0:30Raoult's law: the ideal straight lines

So, first a quick recall. For two volatile liquids, A and B, mixed together, Raoult's law says: p A equals x A times p A nought. p with the subscript A is the partial vapour pressure of A, x with the subscript A is its mole fraction in the liquid, and the small circle on top, read as nought, means the pure liquid. The same works for B, with its own mole fraction and pure pressure. With me? On the graphs, the axis runs from x A equals zero to x A equals one, and the dashed straight lines are these Raoult's law values. Now, a solution sits exactly on those dashed lines only when the attraction between A and B equals the attractions of A with A, and of B with B, as the little dash between two letters shows. Then the solution is ideal. Right? But real mixtures are often not that perfect. In a non-ideal solution, the attraction between A and B is either weaker, or stronger. Then the real pressures, the solid curves, move off the dashed lines: left graph, positive deviation; right graph, negative.

1:42Positive deviation: weaker A–B attractions

Clear? Weaker first. Here, the attraction between A and B is weaker than within each pure liquid. So in the mixture, each molecule is held less tightly. With me? Held less tightly, the molecules escape more easily into the vapour. So p A is greater than x A times p A nought; the pointed sign means greater than. More than Raoult's law predicts, okay? The same happens for B, so the total, capital P, also comes out higher. On the left graph, the thick curve marked capital P bulges above its dashed line. Above the line: a positive deviation. Right? Now think about energy. To mix, we break stronger attractions within each liquid, and form only weaker ones between the two. So, is heat absorbed, or released? Absorbed, correct! So delta H mix, the enthalpy change on mixing, is greater than zero. The capital Greek delta means change, and the small word mix written below it means on mixing. The heat is taken in, so the mixture cools down. Got it? Now the volume. Weakly held molecules sit a little farther apart, so delta V mix, the volume change on mixing, is also greater than zero: the volume increases. Clear?

3:01Negative deviation: stronger A–B attractions

Now the opposite case. Here the attraction between A and B is stronger than in the pure liquids, very often because of new hydrogen bonds, written H bonds on screen. Okay? So tell me: the molecules are held more tightly. Does capital P go above the Raoult line, or below it? Below, yes! Held more tightly, the molecules escape less easily. On the right graph, the thick curve, capital P, sags below the dashed line: a negative deviation. Clear? And everything else flips. Stronger attractions form, so heat is released, and the mixture warms: delta H mix is less than zero; the sign now points the other way, and means less than. They also pull the molecules closer, so delta V mix is less than zero too. Warming up and losing volume: just like our puzzle! With me?

3:54Which mixtures go which way?

Now, the real mixtures. These lists are worth learning. Positive deviation: ethanol with water, ethanol with acetone, and acetone with C S two, carbon disulphide. The plus sign simply means mixed with, okay? Also ethanol with cyclohexane, and C C l four, carbon tetrachloride, with chloroform. In each one, mixing weakens the attractions the pure liquids had. Right? Negative deviation: acetone with chloroform, phenol with aniline, and acetic acid with pyridine. Clear? And two acids with water: HNO three, nitric acid, and H C l, hydrochloric acid. In all of these, the two kinds of molecules attract each other more strongly than in the pure liquids. Got it?

4:42The hydrogen-bond trap

Now, the classic trap. Water and ethanol both form hydrogen bonds. So mixing them means more hydrogen bonding, and that implies, the double arrow, a negative deviation, right? No, no, careful! Ethanol gets in between and breaks some hydrogen bonds of water, and some of its own too. Weaker attractions overall, so ethanol and water shows a positive deviation. Don't forget this one, okay? Now acetone with chloroform. Here, mixing makes a brand new hydrogen bond. On screen, C l three C, dash, H is chloroform. The three dots are the new hydrogen bond, from its hydrogen to the oxygen of acetone, the O double bond C with two C H three groups. Stronger attractions: negative deviation. So don't just ask whether hydrogen bonds exist; ask whether mixing breaks them or makes new ones. Right?

5:39Topper's trick: know one sign, know them all

Now a topper's trick. Positive deviation: capital P above Raoult, delta H mix and delta V mix greater than zero, and the mixture cools. All on the plus side, okay? Negative deviation: capital P below Raoult, delta H mix and delta V mix less than zero, and the mixture warms. All on the minus side. In JEE problems, these signs go together, so know any one, and you know them all! That's it!

6:09Example 1: 50 mL + 50 mL gives 97 mL, which deviation

Now, our puzzle. Mixing fifty millilitres of liquid X with fifty millilitres of liquid Y gives ninety seven millilitres of solution, and the temperature rises; m L means millilitres. What deviation is expected? Pause the video, and try it first. Done? Okay, let's check. Fifty plus fifty is one hundred, but we got only ninety seven: less, as the sign shows. So delta V mix is less than zero. Right? The temperature rises, so heat is released: delta H mix is less than zero. With me? Both negative, so by our topper's trick, the arrow on screen: negative deviation! Puzzle solved. X and Y attract each other more strongly than in the pure liquids, so the molecules pull closer, three millilitres seem to vanish, and heat comes out. Got it?

7:04Example 2: 95 vs Raoult 80 mm Hg, deviation and heat sign

Now a harder one. For a solution of A and B, p A nought is one hundred and p B nought is sixty millimetres of mercury, m m H g. x A is zero point five, and the measured vapour pressure is ninety five. What type of deviation is this? Is the mixing endothermic or exothermic? Pause the video, and try it. Done? Alright. Ninety five lies between sixty and one hundred, so it looks normal. So the solution is ideal, right? No, no, wait! Lying between them is not enough. Compare with Raoult's law at this exact composition. x B is one minus zero point five: zero point five. So capital P from Raoult is zero point five times one hundred, plus zero point five times sixty. Okay? That is fifty plus thirty: eighty millimetres of mercury. But the measured value is ninety five. So, which deviation is this? Positive deviation, yes! Ninety five is greater than eighty: higher than Raoult's law predicts. Clear? Now the mixing. Positive deviation means delta H mix is greater than zero: heat is absorbed, so the mixing is endothermic. One sign, and the whole answer follows. That's it!

8:26Quick revision: signs of mixing H and V, key examples

So, quick revision. Positive deviation: weaker attractions, capital P above the Raoult line, delta H mix and delta V mix greater than zero. Negative deviation: stronger attractions, capital P below, and both less than zero. And remember: ethanol and water, positive; acetone and chloroform, negative. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!