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

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!

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).