Properties and Number of Geometrical Isomers

Transcript

0:00Introduction

Hello everyone! Here is a small puzzle. Maleic acid and fumaric acid have the same atoms and the same bonds. The only difference is that the two COOH groups are on the same side of the double bond in one, and on opposite sides in the other. Yet maleic acid melts at four hundred and three kelvin, and fumaric acid at five hundred and sixty kelvin. That is a gap of one hundred and fifty seven kelvin! How can just the shape do that? And one more for later: how many geometrical isomers can a chain with three double bonds have? Both kinds of question come up often in JEE, so let's begin.

0:42Dipole moment and boiling point

So, look at the figure. On the left is cis but two ene, with the two C H three groups on the same side of the double bond. The small three written low is a subscript. Next to it, trans but two ene, with them on opposite sides. The last two drawings show the E and Z names from the earlier lesson. Okay? Now, the bonds to these groups each carry a small dipole moment. Let me ask you this: in which of these two isomers do the bond moments cancel out? Yes, exactly, in the trans isomer! The matching groups point in opposite directions, so their moments cancel, while in cis they add up. This Greek letter is mu, the dipole moment, and this sign means greater than. So usually, the dipole moment of cis is greater than that of trans. Right? And when is it exactly zero for trans? When each carbon carries the same two groups, small a and small b, joined by the double bond, as in the formula on screen. Then the trans isomer has mu equal to zero. And but two ene is this type, with a C H three and an H on each carbon. In the figure, cis has mu not equal to zero, the slashed equals sign, and trans has mu equal to zero. Clear? Now the boiling point. The cis isomer is polar, and the trans isomer is not. So which one boils higher? That is right, it is cis, the more polar isomer. In the figure, b p means boiling point: cis but two ene boils at two hundred and seventy seven kelvin, the capital K, and trans at two hundred and seventy four kelvin. Got it?

2:22Melting point and stability

Now the melting point. Cis boils higher, so surely cis melts higher too, right? No, no, careful, it is the other way round! For melting point, trans is greater than cis. The trans molecule is more symmetrical, so it packs better in the solid. Okay? And that solves our puzzle. Fumaric acid is the trans acid, so it melts at five hundred and sixty kelvin, and maleic acid, the cis one, at only four hundred and three kelvin. With me? Next, stability, and again trans is greater than cis. Look at cis but two ene in the figure: the two bulky C H three groups are crowded together on one side. In trans they are far apart, so less crowding, and more stability. Right? Now, add hydrogen to either isomer of but two ene, and both give the same product, butane. So which one gives out more heat? The answer is cis, and here is why. The less stable isomer releases more heat, since the product is the same. So the cis isomer has the higher heat of hydrogenation, and also the higher heat of combustion. Clear? Last point: cis and trans isomers are diastereomers. They differ in physical properties, so they can be separated by physical methods. Okay?

3:47Counting geometrical isomers in a chain

Now the second half of the lesson: counting. Take a chain with n double bonds, where each one can show cis trans isomerism. That means each doubly bonded carbon carries two different groups. Got it? Each double bond can be cis or trans, two choices. With n double bonds, how many arrangements do we get? Two times two times two, n times, so two to the power n. The n written high is a superscript. When the two ends of the chain are different, that is the answer: two to the power n isomers. Okay? For example, hepta two four diene has two double bonds, and its two ends are different, C H three and C two H five. So n is two, and two squared gives four isomers. Clear?

4:35Trap: when both ends are the same

Now hexa two four diene, written on screen. The dashes are single bonds and the equals signs are double bonds. Two double bonds again, so two squared, four isomers, right? No, no, wait, look at the two ends: both are C H three! Take the cis, trans isomer and read it from the other end. It becomes trans, cis, the same molecule, counted twice! So when the ends are the same, two to the power n overcounts. With me? So for ends the same, we use this formula. Two raised to the power n minus one, where the whole of n minus one sits in the power, plus two raised to the power p minus one, again with p minus one in the power. Clear? And what is p? For even n, p is n over two. For odd n, p is n plus one, over two. Okay? For hexa two four diene, n is two, which is even, so p is one. Two to the power one, plus two to the power zero, is two plus one, which gives three. They are cis cis, trans trans, and cis trans. Got it?

5:41Example 1: dipole moment and bp of 1,2-difluoroethene

Now let us do Example one. Which isomer of one two difluoro ethene has the larger dipole moment, and which has the higher boiling point? Pause the video and try it first. Done? Okay, let's check. Each carbon carries one hydrogen and one fluorine. In the trans isomer, the two C F bond moments point in opposite directions and cancel, so mu equals zero. Right? In the cis isomer, the two moments add up, and mu is two point four debye. The capital D stands for debye, the unit of dipole moment. Okay? And the polar isomer boils higher. So the answer is the cis isomer in both cases. Same rule as but two ene, see?

6:29Example 2: geometrical isomers of octa-2,4,6-triene

Now a harder one, Example two, and it answers the second question from the start. How many geometrical isomers does octa two four six triene have? Here is a hint: check the ends first. Pause the video and try it first. Done? Okay, let's check. Octa means eight carbons, and triene means three double bonds, starting at carbons two, four and six. Every doubly bonded carbon carries a hydrogen and a different group, so all three double bonds qualify. Clear? So, three double bonds. Two to the power three gives eight isomers, right? No, no, careful, look at the ends again! Both ends are C H three, the same. So n is three, and we need the second formula. With me? Here n is odd, so p is n plus one, over two. Three plus one is four, and four over two gives two. Okay? Now put it in. Two to the power three minus one, plus two to the power two minus one. That is two squared plus two to the power one, so four plus two, which gives six. So the answer is six geometrical isomers, not eight!

7:45Quick revision: cis-trans properties and counting formulas

So, quick revision. Cis has the higher dipole moment and boiling point, while trans has the higher melting point and is more stable. The less stable cis isomer has the higher heat of hydrogenation and of combustion. And to count, two to the power n for different ends; for the same ends, two raised to n minus one, plus two raised to p minus one, with both minus ones in the powers. Now go and try the practice problems on this page. All the best!