Suppose you have been given the task of distilling a mixture of hexane + toluene. Pure hexane has a refractive index of 1.375 and pure toluene has a refractive index of 1.497. You collect a distillate sample which has a refractive index of 1.441. Assuming that the refractive index of the hexane + toluene mixture varies linearly with mole fraction, what is the mole fraction of hexane in your sample?

0.4590

Explanation:

How the refractive index of the hexane + toluene mixture varies linearly with mole fraction, it means that the mole fraction is the fraction that each pure index contribute for the mixture index, so, calling xh the mole fraction of hexane and xt the mole fraction of toluene:

1.375xh + 1.497xt = 1.441

And, xh + xt = 1 (because there are only hexane and toluene in the mixture), so xt = 1 - xh

1.375xh + 1.497 (1-xh) = 1.441

1.375xh + 1.497 - 1.497xh = 1.441

-0.122xh = - 0.056

xh = - 0.056 / (-0.122)

xh = 0.4590