You are performing a simple distillation of roughly 50:50 liquid solution containing two components, hexane and nonane You place 15 ml of the mixture in a round bottom flask, and then collect the distillate sequentially as four three ml samples labeled S1, S2, S3, and S4. Pure hexane has a refractive index of 1.375 and pure nonane has a refractive index of 1.407. You measure a refractive index of 1.385 for one of the four samples. Assuming the refractive index varies linearly with mole fraction, estimate the mole fraction of hexane in this sample.

Refractive index is a undimensional measurement that describes how fast light travels through the material. It is used to see the liquid purity of compounds.

In this problem you have in the beginning a 50:50 solution oh hexane:nonane and realize distillation.

In distillation the collect is enriched with the most volatille substance (hexane). So you will have in the final sample more hexane than nonane.

Assuming the refractive index varies linearly with mole fraction, you will have:

1,375 → 100% hexane

1,407 → 100% nonane

1,385 → ???

molar fraction of hexane:

100 - (1,385 - 1,375) / (1,407 - 1,375) × 100 = 69 %

molar fraction of nonane:

100 - (1,407 - 1,385) / (1,407 - 1,375) × 100 = 31 %

The relation of the distillating fraction is (69:31) of (hexane:nonane)

You can see that distillation is a technique that allows the separation of a liquid mixture, for example.

I hope it helps!