Ideal Solutions

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle first. Pour some benzene into toluene. They mix completely, on their own. But touch the flask: it does not warm up, and it does not cool down. Practically no heat comes out, and no heat goes in. So no energy is released. Then why do they mix at all? What is pushing them together? Strange, right? Today we find that hidden push, and meet the simplest kind of solution: the ideal solution. This idea comes up often in JEE, so let's begin.

0:36What makes a solution ideal?

So, what is an ideal solution? It is a solution that obeys Raoult's law, from the last chapter: p A equals x A times p A nought. p A, with the small A written below, is the partial vapour pressure of A, and x A is its mole fraction in the liquid, okay? The small circle on top, read as nought, means the pure liquid. Right? But an ideal solution obeys it completely: for every component, at every composition, and at every temperature, the capital T on screen. Look at the graph, plotted against the mole fraction of A: p A, p B and the total pressure, capital P, are all straight lines, from pure B right across to pure A, okay? Now think. In the solution, a molecule of A now has some B molecules around it. When will it escape just as easily as it did from the pure liquid? When the B molecules hold it exactly as strongly as its old A neighbours did! So the condition is: the attraction between A and B equals the attraction between A and A, and between B and B, okay? The short dash between two letters just means the attraction between them. Got it?

1:50Mixing an ideal solution: four signs

Now, let's mix the two liquids. The attractions are the same before and after mixing, right? So will any heat be given out, or taken in? None at all! Delta mix H equals zero. The little triangle is delta, meaning the change, and mix, written small below it, means on mixing. So delta mix H is the enthalpy change on mixing. Okay? And the same for volume. Delta mix V equals zero. The molecules pack just as they did in the pure liquids, so the volumes simply add. With me? Now, a classic trap. Delta H is zero, delta V is zero. So ideal means nothing changes, and delta S is zero too, right? No, no, careful! Delta mix S is greater than zero. Once mixed, the molecules have many more ways of arranging themselves. So the entropy increases. Right? Now, Gibbs energy. Since delta mix H is zero, delta mix G is just minus T times delta mix S, okay? T is positive, delta mix S is positive, so delta mix G is less than zero: negative. So the mixing happens on its own. That is the hidden push from our puzzle: not energy, but entropy! Clear?

3:13Nearly ideal pairs

So, which real mixtures behave like this? Benzene plus toluene, and n hexane plus n heptane. The small n before the name means the normal, straight chain form. Okay? Then, bromoethane plus chloroethane, and chlorobenzene plus bromobenzene. These are nearly ideal: very close, but not perfect. Got it? Now look at each pair carefully. What do the two partners have in common? Yes, exactly! They are alike: similar size, similar structure, and similar polarity. So the attractions between unlike molecules are almost the same as between like ones. With me?

3:53Entropy and Gibbs energy of mixing

Now, how much does the entropy increase? For ideal mixing, delta mix S equals minus n R, times the sum of x i l n x i. The big Greek letter sigma means add up over every component, the small i written below is just a label for each component, and l n is the natural log. Okay? Here, n is the total number of moles, R is the gas constant, and x i is the mole fraction of component i. Remember, these formulas are for ideal mixing only. Clear? Now, a quick check. Every mole fraction in a mixture is less than one. So is l n x i positive or negative? Negative, yes! The log of a number less than one is negative. The double arrow means implies. So the sum is negative, and the minus sign in front makes delta mix S positive. Never drop that minus sign, or you get a negative entropy of mixing. Right? And delta mix G equals minus T delta mix S, which is n R T times the sum of x i l n x i, with T in kelvin. That sum is negative, so delta mix G is negative, just as we said. Got it?

5:07Example 1: which pairs form nearly ideal solutions

Alright, example one. Which of these form nearly ideal solutions? Option A, benzene plus toluene. Option B, water plus ethanol. Option C, n hexane plus n heptane. And option D, acetone plus chloroform. Pause the video, and try it first. Done? Okay, let's check. Benzene and toluene, hexane and heptane: in each pair, the molecules are alike in size and forces. So both are nearly ideal. Right? Now, water plus ethanol, and acetone plus chloroform. Many students tick these as well. Are they nearly ideal? No, no, careful! Both involve hydrogen bonding, and that hydrogen bonding changes when the liquids mix. So the attractions between unlike molecules are no longer the same as between like ones: not ideal. With me? So the answer is options A and C, clear?

6:07Example 2: entropy and Gibbs energy of mixing

Now a harder one, example two, and it settles our puzzle with numbers. One mole of benzene is mixed with one mole of toluene at three hundred kelvin. Treat the solution as ideal. Find delta mix S and delta mix G, okay? On screen, m o l is moles, and capital K is kelvin. Pause the video and try it. Hint: find the total moles first. Done? Okay, let's check. The total number of moles, n, is two moles. One mole out of two for each liquid, so x benzene and x toluene are both one half. With me? Now the formula; delta S here is short for delta mix S, right? Delta S equals minus two R, times, in brackets, one half l n one half, plus one half l n one half. The two halves add up to l n one half, and minus l n one half is l n two. So delta S equals two R l n two. Clear? Put in R as eight point three one four, and l n two as zero point six nine three. Two times eight point three one four times zero point six nine three is about eleven point five; the wavy equals sign means approximately. J K to the power minus one means joules per kelvin. Positive, as it must be. Right? Now the Gibbs energy. Delta H is zero here, remember? So how do we get delta G? Yes, delta G equals minus T delta S! So, minus three hundred times eleven point five three joules. We keep one more digit here, eleven point five three, so the rounding does not creep into the answer. Got it? That is minus three thousand four hundred and fifty nine joules: about minus three point four six kilojoules, the k J on screen. Negative! So benzene and toluene mix on their own, with zero heat change. Puzzle solved: entropy did it! With me?

8:13Quick revision: four signs of mixing for an ideal solution

So, quick revision. An ideal solution obeys Raoult's law fully, because the attractions between unlike molecules equal those between like ones. On mixing, delta H and delta V are zero, delta S is positive, and delta G is negative. And it is entropy that drives the mixing. Now go and try the practice problems on this page. All the best!