What is an example of a specific mixture that could be separated with simple distillation and a specific mixture for which only fractional distillation would be used?

I think a methanol-water mixture could be done with simple distillation, since they have b.p which are further apart. But what about the other one?

Crude oil is separated by fractional distillation but that may not satisfy the requirement of being a "specific" mixture.

You are correct that a methanol-water mixture could be separated using simple distillation, as the boiling points of methanol (64.7°C) and water (100°C) are quite different.

For an example of a mixture that would require fractional distillation, we can consider a mixture of ethanol and water. The boiling points of ethanol (78.4°C) and water (100°C) are relatively close, which means that a simple distillation may not completely separate them.

To perform fractional distillation for this mixture, you would set up a fractionating column in the distillation apparatus. The fractionating column provides additional surface area for vapors to condense and re-evaporate, allowing for multiple distillation steps to occur within the column.

As the mixture is heated, the vapors rise through the fractionating column. The vapors with lower boiling points, in this case, ethanol, will condense and re-evaporate more easily in the column, while the higher boiling point component, water, will take longer to condense and re-evaporate. This process allows for more efficient separation of the components.

By implementing fractional distillation, the closeness of the boiling points of ethanol and water can be overcome, resulting in a more effective separation of the two components.