Degree of Dissociation

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Take some N two O four gas in a closed syringe, at one atmosphere. Twenty percent of it has broken up into N O two. Now I squeeze it, keeping the temperature the same, until only ten percent is broken up. How much pressure do I need? Half the breaking up, so double the pressure, two atmospheres? Sounds sensible, right? Keep that guess; we will check it at the end. In JEE, questions on degree of dissociation come up often. So, let's begin.

0:37What is the degree of dissociation?

So, what is the degree of dissociation? We write it with the Greek letter alpha, the symbol on screen. Alpha is the fraction of the initial moles that has dissociated, that is, broken up, at equilibrium. It is a fraction, not a percentage. Okay? For gases, the method is simple: start from one mole; m o l on screen is short for mole. If alpha of it breaks up, how much is left? One minus alpha moles, yes, exactly! The whole mole, minus the part that broke up. Right? Then find the total moles at equilibrium. Each partial pressure is the mole fraction, that gas's moles over the total, times capital P, okay? And capital P is the total pressure at equilibrium, not at the start. Students mix these up, so be careful. Clear?

1:29Type 1: A ⇌ B + C, as in PCl5

Now, three standard types. Type one, in the heading: A gives B plus C, one molecule breaking into two. Like phosphorus pentachloride, P C l five, the five written small below. It gives P C l three and chlorine, C l two; the two half arrows mean reversible. Start from one mole, and let alpha dissociate. What is the total number of moles? P C l five: one minus alpha. P C l three and chlorine: alpha each. Total: one plus alpha. Yes, exactly! One molecule became two. Right? Now the partial pressures: small p, with the formula written below it. For P C l five, one minus alpha over one plus alpha, times capital P; for each product, alpha over one plus alpha, times P again. Okay? Put these into K p, capital K with a small p below: the products multiplied, over the reactant. One P and one factor of one plus alpha cancel. So K p equals alpha squared P, over one minus alpha squared; the small two up top means squared. Write this down. Got it?

2:44Type 2: A ⇌ 2B, as in N2O4

Type two: A gives two B, one molecule giving two of the same kind. Dinitrogen tetroxide, N two O four, gives two N O two, nitrogen dioxide. One mole to start, and alpha dissociates. How many moles of N O two form? Alpha, right? No, no, careful! Each N two O four gives two N O two, so two alpha. Total: one minus alpha, plus two alpha, again one plus alpha. With me? The pressure of N O two gets squared in K p, and that two, squared, gives this four. So K p equals four alpha squared P, over one minus alpha squared. Drop the four, and your K p comes out four times too small. Clear?

3:31Type 3: 2A ⇌ B + C, as in HI

Type three: two A give B plus C, two molecules giving two. Two H I, hydrogen iodide, gives hydrogen, H two, and iodine, I two. Start from one mole of hydrogen iodide, and alpha dissociates. How much hydrogen forms? Alpha over two! Correct! Two H I make just one H two, so half of alpha, and the same for iodine. Total: one minus alpha, plus alpha over two, plus alpha over two: just one. The total does not change. Okay? So K p equals alpha squared, over four times the square of one minus alpha. And here K p equals K c, capital K with a small c, written with concentrations, because the moles of gas do not change. Right? Now look closely: no P, and no V, V for the volume. So for this type, changing the pressure or the volume does not change alpha at all. Questions do test this! Got it?

4:35Small α: a quick shortcut

Now, a shortcut. Suppose alpha is very small. Then what is one minus alpha squared? Almost exactly one! Very good! The wavy equals sign means approximately. So for type one, K p is about alpha squared P, and alpha is about the square root of K p over P, nice and simple. With me? This sign, like an open alpha, means proportional to. Alpha goes as one over root P: more pressure, smaller alpha. That fits Le Chatelier's principle: higher pressure pushes the equilibrium back towards fewer moles of gas. Okay? But is this shortcut always safe? No, no, wait! Take a course example. K p is one point six four atmospheres, a t m for atmospheres, at five hundred kelvin, the capital K after the number, and P is one atmosphere. The shortcut gives root one point six four, about one point two eight. The sign pointing that way means greater than: more than one! But a fraction can never be more than one. Impossible! Right? Alpha is not small here, so use the exact formula. Alpha squared over one minus alpha squared equals one point six four; the double arrow means so. Alpha squared is one point six four over two point six four, and alpha is about zero point seven nine. So, use the shortcut only when alpha comes out small. Got it?

6:03Example 1: Kp for N2O4 that is 20% dissociated at 1 atm

Alright, example one, from the course. N two O four is twenty percent dissociated at one atmosphere. Find K p. Pause the video and try it first. Done? Okay, let's check. Twenty percent dissociated, so alpha equals twenty, right? Oh no, careful! Alpha is a fraction. Twenty percent, with the percent sign, is zero point two. And capital P is one atmosphere. With me? N two O four is type two. So, four times zero point two squared, times one, over one minus zero point zero four. That is zero point one six, over zero point nine six. Right? So K p is about zero point one six seven atmospheres. Keep this number; we need it next. Okay?

6:56Example 2: pressure for only 10% dissociation of N2O4

Now, the puzzle from the start. At what total pressure will the N two O four of example one be only ten percent dissociated, at the same temperature? Pause the video and try it. Done? Let's check. We changed the pressure. So, does K p change? No! K p is fixed at a fixed temperature, and capital T, the temperature, is the same. So K p is still zero point one six over zero point nine six: exactly one sixth of an atmosphere. Clear? Now alpha is ten percent, zero point one. So alpha squared is zero point zero one, and one minus alpha squared is zero point nine nine. Four times zero point zero one times P, over zero point nine nine, equals one sixth. With me? Solve for P: zero point nine nine, over six times zero point zero four. About four point one atmospheres. Right? So, was our guess of two atmospheres right? No! Half the alpha needed about four times the pressure, not two. Why? Because alpha comes in squared in K p. That was the trap in our puzzle. Got it?

8:12Quick revision: Kp in terms of alpha for the three types

So, quick revision. Start from one mole, find the total moles, and each partial pressure is the mole fraction times the total pressure. For P C l five, K p is alpha squared P, over one minus alpha squared; N two O four adds a four; and for hydrogen iodide, pressure has no effect. For small alpha in type one, alpha goes as one over root P: more pressure, less dissociation. Now go and try the practice problems on this page. You will find them easy. All the best!