Question

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?

Answer 1

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 = $x_{1}$

and, mole fraction of toulene = $x_{2}$

Also,        $x_{1} + x_{2} = 1$

or,            $x_{1} = 1 - x_{2}$

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 = $(1 - x_{2}) \times 1.375 + x_{2} \times 1.497$

               1.456 = $1.375 - 1.375x_{2} + 1.497x_{2}$

               0.081 = $0.122x_{2}$

                   $x_{2}$ = $\frac{0.081}{0.122}$

                                = 0.66

Since,     $x_{1} = 1 - x_{2}$

                          = 1 - 0.66

                          = 0.34

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