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

Step-by-step 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)) * 1.375 + x_(2) * 1.497`

1.456 =
`1.375 - 1.375x_(2) + 1.497x_(2)`

0.081 =
`0.122x_(2)`

`x_(2)` =
`(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.