How to Find Mass from Mole Fraction?

Mole fraction is simply the moles of a particular substance divided by the total number of moles present. Mole percent is mole fraction times 100. Similar to mole fraction, the mass fraction is nothing more than the mass of the substance divided by the total mass of all substances present. Although the mass fraction is what is intended to be expressed, ordinary usage employs the term mass fraction as well.

Mass (weight) fraction = mass (weight) of A / total mass (weight).

The term mass fraction and mole fraction are dimensionless. Mass percent is the amount of solute in grams present in 100g of the solution. Mole fraction is the ration of number of moles of a particular component to the total number of moles of the solution.

Let’s solve a problem based on mass and mole fraction.

Problem:

Consider 10mg of deprenyl is diluted in 10ml water. Water has the density of 1.0 g/ml. Calculate the mass fraction of the drug.

Solution:

To find the mass fraction first find the total mass of the solution, which is mass of water plus the mass of deprenyl.

m_{water} = (1.0g/mL) (10 mL) = 10g

Note that mass of the drug is negligible compared to the mass of water.

m_{total} = m_{water} + m_{drug} ~  m_{water}

The mass fraction of the drug is,

W_{drug} = m_{drug} / m_{water} = (10 mg/10g) (1g/1000mg) = 1.0 x 10^{-3}.