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 1.406. 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

Answer:

Mole fraction of hexane in your sample is 0,746

Explanation:

Based on the information you can write the following equations:

X + Y = 1 (1)

Where X is mole fraction of hecane and Y is mole fraction of toluene

Also, based on the assumption that the refractive index of the hexane + toluene mixture varies linearly with mole fraction you can write:

1,375X + 1497Y = 1406 (2)

Replacing (1) in (2):

1,375X + 1,497(1-X) = 1,406

1,375X - 1,497X + 1,497 = 1,406

-0,122X = -0,091

X = -0,091/-0,122

X = 0,746

Thus, the mole fraction of hexane in your sample is 0,746

Also you can know the mole fraction of toluene replacing this value in (1):

0,746 - Y = 1

Y = 1-0,746

Y = 0,254

I hope it helps!