Final answer:
The optically active compound with the molecular formula C8H14 can undergo catalytic hydrogenation to give an optically inactive product. Compound E, a 5 carbon ring with a double bond between carbons 1 and 2 and methyl substituents on carbons 1, 2, and 4, is the only structure consistent with the data provided.
Step-by-step explanation:
An optically active compound with molecular formula C8H14 can undergo catalytic hydrogenation to give an optically inactive product. This means that the compound is chiral before hydrogenation and achiral after hydrogenation. In order to determine which of the given structures are consistent with the data, we need to analyze each structure.
Compound A is a 6 carbon ring with a wedged bond to a methyl group on carbons 1 and 4, and a double bond between carbons 2 and 3. This structure is likely optically active and does not match the data.
Compound B is a 6 carbon ring with a wedged bond to a methyl group on carbon 1 and a dashed bond to a methyl group on carbon 4. It also has a double bond between carbons 2 and 3. This structure is likely optically active and does not match the data.
Compound C is a 6 carbon ring with a wedged bond to a methyl group on carbon 1 and a double bond between carbons 3 and 4. It has a methyl substituent on carbon 4. This structure is likely optically active and does not match the data.
Compound D is a 6 carbon ring with a wedged bond to a methyl group on carbon 1 and a dashed bond to a methyl group on carbon 5. It has a double bond between carbons 2 and 3. This structure is likely optically active and does not match the data.
Compound E is a 5 carbon ring with a double bond between carbons 1 and 2. It has a methyl substituent on carbons 1, 2, and 4. This structure is likely optically active and matches the data.
Based on the analysis, compound E is the only structure consistent with the data provided.