Question

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

There are 3 structural isomers for the five-member straight carbon chain with one double bond (C5H10) and 2 structural isomers for the six-member straight carbon chain with two double bonds (C6H10).

Step-by-step solution

The first straight carbon chain has 5 carbon atoms and one double bond, represented as C5H10. The second straight carbon chain has 6 carbon atoms and two double bonds, represented as C6H10. #Step 2: Calculate the possible positions of the double bond in the five-carbon chain#

We have to find the number of possible positions for the one double bond within the five-carbon chain. There are a total of 5 carbon atoms, so we can have the double bond at any position between the first and the fifth carbon atom. However, we cannot place a double bond between the first and second carbon atoms, because that would result in ethene (C=C) being attached to a carbon chain, which is not a structural isomer for the given case. So, we can place the double bond between the 2nd and 3rd, 3rd and 4th, or between the 4th and 5th carbon atoms. Therefore, there are 3 possible positions for the double bond in the five-carbon chain. #Step 3: Calculate the possible positions of the double bonds in the six-carbon chain#

Now, we have to find the number of possible positions for the two double bonds within the six-carbon chain. There are a total of 6 carbon atoms, so we can have a double bond at any position between the first and the sixth carbon atom. Again, we cannot place a double bond between the first and second carbon atoms, because that would result in ethene (C=C) being attached to a carbon chain, which is not a structural isomer for the given case. Possible positions of the double bonds: (2nd and 3rd, 4th and 5th), (3rd and 4th, 5th and 6th), and (2nd and 3rd, 3rd and 4th). But, the third combination is not possible as it would result in two double bonds between the same two atoms, which violates the given condition. So, there are 2 possible positions for the two double bonds in the six-carbon chain. #Step 4: Report the number of structural isomers for each case#

There are 3 structural isomers for the five-member straight carbon chain with one double bond and 2 structural isomers for the six-member straight carbon chain with two double bonds.