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 refactive index of 1.497. You collect a distillate sample which has a refractive index of 1.456. 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?

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OlaMacgregor OlaMacgregor · Answer 1 · 2019-10-02T12:01:15+02:00

Explanation:

The given data is as follows.

Refractive index of mixture = 1.456

Refractive index of hexane = 1.375

Refractive index of toulene = 1.497

Let mole fraction of hexane = [tex]x_{1}[/tex]

and, mole fraction of toulene = [tex]x_{2}[/tex]

Also, [tex]x_{1} + x_{2} = 1[/tex]

or, [tex]x_{1} = 1 - x_{2}[/tex]

Hence, calculate the mole fraction of hexane as follows.

refractive index mixture= mole fraction hexane × ref index hexane + mole fraction toluene × ref index toluene.

1.456 = [tex](1 - x_{2}) \times 1.375 + x_{2} \times 1.497[/tex]

1.456 = [tex]1.375 - 1.375x_{2} + 1.497x_{2}[/tex]

0.081 = [tex]0.122x_{2}[/tex]

[tex]x_{2}[/tex] = [tex]\frac{0.081}{0.122}[/tex]

= 0.66

Since, [tex]x_{1} = 1 - x_{2}[/tex]

= 1 - 0.66

= 0.34

Thus, we can conclude that mole fraction of hexane in your sample is 0.34.