Set 2

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle before we start. Here is a reaction with delta G naught equal to minus ten kilojoules per mole. Negative! So any mixture of it must react forward, right? Most students say yes, straight away. But there is a mixture of this very reaction that reacts backward! How can that be? Today we solve the last four problems of Set two, all on Gibbs energy, and this puzzle is one of them. Problems like these come up often in JEE Main, so let's begin.

0:36Warm-up: two one-liners from Set 2

So, first, two quick warm-ups. Delta H is plus ninety kilojoules, and delta S is plus one hundred and twenty joules per kelvin. The little triangle is the Greek letter delta, meaning change in; H is enthalpy and S is entropy. Here J is joules and K is kelvin, and the small minus one on the K means per kelvin. Now, above what temperature is this reaction spontaneous? Think Gibbs energy. At constant temperature T and pressure P, a reaction is spontaneous when delta G is less than zero; the sign on screen means less than. And delta G equals delta H minus T delta S, okay? Both delta H and delta S are positive, so delta G turns negative only when T is greater than delta H over delta S, as you see on screen. But careful with the units! Delta S is in joules per kelvin, so write ninety kilojoules as ninety thousand joules. Ninety thousand over one hundred and twenty: seven hundred and fifty kelvin. Right? Next one. Delta G is minus three hundred kilojoules, at constant temperature and pressure. What is the most electrical work this reaction can do? Three hundred kilojoules, yes! Minus delta G is the maximum useful work, the non-expansion work, that a process can do at constant temperature and pressure, like the electrical work of a cell. So just flip the sign. Clear?

2:04Delta G, Q and K: which way does it go?

Now, the other two problems need one more tool. Delta G equals delta G naught, plus R T times the natural log of Q, okay? The small circle on top, read naught, means standard: every substance in its standard state. R is the gas constant, T is the temperature in kelvin, l n is the natural log, and Q is the reaction quotient of the mixture at this moment. With me? Now look at the graph. Capital G, the Gibbs energy of the mixture, goes up, and the extent of reaction goes across, from pure reactants to pure products. At constant temperature and pressure, the mixture always moves downhill and settles at the lowest point, this orange dot: the equilibrium. And the orange arrow is delta r G naught, small r for reaction: the gap between pure reactants and pure products. Right? So, at the bottom of the curve, delta G is zero, and Q equals K, the equilibrium constant. The notes beside the graph say the same thing. Okay? Now put these into the first line: zero equals delta G naught, plus R T times the natural log of K, since delta G is zero and Q equals K there. So delta G naught equals minus R T times the natural log of K: the third line. Change to log to base ten, and that is minus two point three zero three R T log K, right? Now, the direction. If Q is less than K, the mixture sits to the left of the bottom. Delta G is negative, so it moves forward, downhill. Got it? And if Q is greater than K, the mixture sits to the right of the bottom. Now delta G is positive, so it moves backward: the reverse reaction is the spontaneous one. Clear? Now a quick one for you. Take R as eight point three one four, in joules per kelvin per mole. What is two point three zero three R T at two hundred and ninety eight kelvin? Five point seven one kilojoules per mole, correct! Mol to the minus one means per mole. Here is a topper's shortcut: learn this number, it saves time. But careful, it works only at two hundred and ninety eight kelvin, okay?

4:16Example 1: delta G naught from K = 0.001 at 300 K

Now, Example one. K is one point zero times ten to the power minus three, at three hundred kelvin. Find delta G naught. Pause the video, and try it first. Done? Okay, let's check. K is given, so we use delta G naught equals minus two point three zero three R T log K, right? First, log of one point zero times ten to the power minus three is simply minus three. Okay? Now, can we use our shortcut, five point seven one kilojoules per mole? No, no, careful! That number is only for two hundred and ninety eight kelvin, and here T is three hundred kelvin. So use R equal to eight point three one four joules per kelvin per mole. Delta G naught equals minus two point three zero three, times eight point three one four, times three hundred, times minus three, in joules per mole. With me? Minus times minus is plus. So delta G naught is about plus seventeen thousand two hundred and thirty two joules per mole; the wavy equals sign means approximately. Divide by one thousand: about plus seventeen point two kilojoules per mole. Got it? And a quick check. K is less than one, so delta G naught must be positive. It is. Perfect!

5:36Example 2: negative delta G naught, yet it runs backward

And now, Example two, our puzzle from the start. Here is a reaction with delta G naught equal to minus ten point zero kilojoules per mole, at two hundred and ninety eight kelvin. In which direction does a mixture with Q equal to one hundred react? Pause the video, and try it first. Done? Okay, let's check. Delta G naught is negative, so the reaction goes forward, right? No, no, careful! This is the trap. Delta G naught is about the standard state, and it only fixes the value of K, the equilibrium constant. The direction of this mixture comes from the sign of delta G, not delta G naught. Clear? So, write delta G equals delta G naught, plus two point three zero three R T log Q, with log to base ten. Same formula as before. Okay? Here the temperature is two hundred and ninety eight kelvin, so now our shortcut works: five point seven one kilojoules per mole. And log of one hundred is two. Right? Substitute: minus ten point zero, plus five point seven one times two. That is minus ten point zero, plus eleven point four two. With me? So delta G is about plus one point four kilojoules per mole, and the sign at the end means greater than zero. Positive! So, which way does this mixture react? Backward, exactly! Delta G is positive, so Q is greater than K, and the reverse reaction is spontaneous. Puzzle solved! Remember, a negative delta G naught only fixes the value of K, the equilibrium constant. This mixture has Q even bigger than K, so it reacts backward, down to equilibrium. Got it?

7:23Quick revision: spontaneity, delta G naught, direction

So, quick revision. At constant temperature and pressure, spontaneous means delta G less than zero, and change kilojoules to joules before dividing delta H by delta S, always. Delta G naught equals minus two point three zero three R T log K, and K less than one gives a positive delta G naught. The direction of a mixture is the sign of delta G, which uses Q; Q greater than K means backward. And five point seven one kilojoules per mole works only at two hundred and ninety eight kelvin. Now open Set two, start your clock, give it twenty five minutes, and try all fifteen problems on this page before you look at the solutions. You can do this. All the best!