Final answer:
Systematic names in organic chemistry are corrected by finding the longest continuous chain and placing substituents in positions that provide the lowest numbering. 4-methylpentane is correctly named 2-methylpentane, and 3-butyl-7-methyloctane is named 3-ethyl-5-methylheptane.
Step-by-step explanation:
In the study of organic chemistry, the systematic naming of compounds follows specific rules outlined in IUPAC nomenclature to ensure each compound has a unique and descriptive name. For instance, when correcting the name for 4-methylpentane, we would first determine the longest continuous chain (LCC), which in this case is a five-carbon backbone, hence 'pentane' is correct. The position of the methyl group is actually on the second carbon when numbered to give the substituents the lowest possible numbers, which leads to the correct name, 2-methylpentane. Similarly, when naming 2-ethylbutane the correct approach would be to find the LCC and proper substituent positioning, resulting in the name 3-methylpentane
For the naming of 3-butyl-7-methyloctane, again we establish the LCC. However, the carbon chain cannot have more than eight carbons in a straight line, making the previous name incorrect. Instead, the longest chain has seven carbons (heptane) with the substituents at proper positions for the correct name 3-ethyl-5-methylheptane.