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Chapter 24: Problem 82

How many structural isomers are there for a five-member straight carbon chain with one double bond? For a six-member straight carbon chain with two double bonds?

Short Answer

Expert verified
There are 4 structural isomers for a five-member straight carbon chain with one double bond, and 5 structural isomers for a six-member straight carbon chain with two double bonds.

Step by step solution

01

For a five-member carbon chain with one double bond, the molecular formula is C5H10. Now, let's identify the possible locations of the double bond in the carbon chain. #Step 2: Locate the double bond#

We have five carbon atoms in the chain, and the double bond will need two consecutive carbon atoms to form. We can form the double bond by placing it between: 1. The first and second carbon atoms. 2. The second and third carbon atoms. 3. The third and fourth carbon atoms. 4. The fourth and fifth carbon atoms. There are four possible locations for the double bond, so we have four structural isomers for this case. #Step 3: Six-member carbon chain with two double bonds#
02

For a six-member carbon chain with two double bonds, the molecular formula is C6H10. Now, let's identify the possible locations of the double bonds in the carbon chain. #Step 4: Locate the first double bond#

Similar to the previous case, we can form the first double bond by placing it between: 1. The first and second carbon atoms. 2. The second and third carbon atoms. 3. The third and fourth carbon atoms. 4. The fourth and fifth carbon atoms. 5. The fifth and sixth carbon atoms. #Step 5: Locate the second double bond for each case#
03

There are five possible locations for the first double bond. Now, let's find the number of possible second double bonds for each case: 1. If the first double bond is between carbon atoms 1 and 2, we can form the second double bond between carbon atoms 3 and 4, or between carbon atoms 4 and 5. 2. If the first double bond is between carbon atoms 2 and 3, we can form the second double bond between carbon atoms 4 and 5 or between carbon atoms 5 and 6. 3. If the first double bond is between carbon atoms 3 and 4, we can form the second double bond between carbon atoms 5 and 6. #Step 6: Count the total isomers for the six-member carbon chain#

Now, we just need to sum up the number of isomers for each case: - Case 1: 2 isomers. - Case 2: 2 isomers. - Case 3: 1 isomer. Total number of isomers for a six-member carbon chain with two double bonds is 2 + 2 + 1 = 5 isomers. So, there are 4 structural isomers for a five-member carbon chain with one double bond and 5 structural isomers for a six-member carbon chain with two double bonds.

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