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 1.401. 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?

Given:

refractive index of pure hexane, = 1.375

refractive index of pure hexane, = 1.497

refractive index of mixture, = 1.401

Formula used:

As refractive index here, behaves like a colligative prop. then using the following formula:

                        (1)

where,

= hexane  mole fraction

= toulene  mole fraction

+ = 1                                      (2)

Solution:

Now, using given formula from eqn (1)

             (3)

Multiply eqn (2) by 1.375, we get:

+ 1.375\times = 1.375         (4)

Now, solving eqn  (3) and (4):

= 0.213

Substituting the value of = 0.213 in eqn (1), we get:

= 1 - 0.213

= 0.787

Therefore, mole fraction of hexane in the sample is = 0.787