Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (2024)

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (1)

The conversion between mole fraction and mass fraction is quite an easy task, but still, it gives valuable insight into the composition of mixtures and solutions.

So what are you waiting for? Dive into the article and learn all the tips and tricks for converting mole fraction to mass fraction.

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What is mole fraction?

The mole fraction refers to the relative amount of one component in a mixture of components.

Mole fraction (X) of component A in a mixture containing four components (A, B, C, and D) is expressed as:

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (2)

Where,

  • nA = Number of moles of component A
  • nB = Number of moles of component B
  • nC = Number of moles of component C
  • nD = Number of moles of component D

The mole fraction is a ratio and, thus, a unitless entity.

In a hom*ogenous solution containing a solute and a solvent;

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (3)

What is the mass fraction?

Quite similar to the mole fraction, the mass fraction refers to the amount or the proportion of one component in a mixture of components.

However, in this case, the mass (m) is taken as the point of reference instead of moles.

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (4)

Where,

  • wA = Mass of component A
  • wB = Mass of component B
  • wC = Mass of component C

The answer can be expressed as a decimal or a percentage (multiplying by 100).

Again, a ratio, therefore the mass fraction, is also a unitless entity.

What is the relation between mole fraction and mass fraction?

The mass of a substance is related to its number of moles via the molar mass.

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (5)

Molar mass is defined as the amount (mass) of substance present per unit moles.

It is calculated using the atomic weights of the different elements present in the substance. The atomic weights can be determined using the Periodic Table of Elements.

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (6)

The above equation can be rearranged as follows, making mass the subject of the formula:

∴ Mass = Moles (mol) x Molar mass (g/mol)

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (7)

How to convert mole fraction to mass fraction? – Examples

You can easily convert mole fraction to mass fraction, converting the number of moles of a given substance into its mass by applying the formula:

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (8)

Where,

∴ The total mass of the mixture = XA (molar mass of A) + XB (molar mass of B) + XC (molar mass of C)

Let’s see an example- The mole fractions of oxygen, nitrogen, and carbon dioxide in a gaseous mixture are 0.196, 0.744, and 0.060. Find the mass fraction of nitrogen (N2) in this mixture.

(Molar mass O2 = 16 g/mol)

(Molar mass N2 = 14 g/mol)

(Molar mass CO2 = 44 g/mol)

Solution:

As the mole fractions and molar masses of all three components are given, so we can find the mass of each component as follows:

∴ Mass = moles x molar mass

⇒ Mass of O2 = 0.196 x 16 = 3.136 g

⇒ Mass of N2 = 0.744 x 14 = 10.416 g

⇒ Mass of CO2 = 0.060 x 44 = 2.64 g

∴ Total mass of the mixture = 3.136 + 10.416 + 2.64 = 16.192 g

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (9)

Result: The mass fraction of nitrogen in the gaseous mixture is 64.3 %.

Another example is- In a solution of ethanol in water; the mole fraction of ethanol (C2H5OH) is 0.25, while its molar mass is 46.07 g/mol. Given also the molar mass of water (H2O) is 18.02 g/mol. Convert the mole fraction of ethanol to its mass fraction.

Solution:

In this example, ethanol is a solute, while water is used as a solvent.

Given that,

⇒ Mole fraction of ethanol = 0.25

⇒ Molar mass of ethanol = 46.07 g/mol

So we can easily find its mass:

⇒ Mass = moles x molar mass

∴ Mass of ethanol = 0.25 x 46.07 = 11.5175 g

For the binary solution, mole fraction of water = 1 – mole fraction of ethanol = 1-0.25 = 0.75

∴ Mass of water = 0.75 x 18.02 = 13.515 g

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (10)

Result: The mass fraction of ethanol in the given solution is 46 %.

FAQ

What is the difference between mole fraction and mass fraction?

Mole fraction and mass fraction are two different ways of expressing the concentration of a chemical solution or mixture.

Mole fraction is the ratio of the moles of a component to the total number of moles in the mixture.

In contrast, the mass fraction is the ratio of the mass of a component to the total mass of the mixture.

What is the direct formula for converting mole fraction to mass percent?

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (11)

Where,

  • XA = mole fraction of A
  • XB = mole fraction of B
  • XC = mole fraction of C

Why is the mole fraction equal to unity?

A mole fraction is never equal to unity; however, the sum of mole fractions of all the components in the mixture is always equal to 1, just as the sum of all mass percentages in the mixture equals 100%.

Mole fraction to Mass fraction, Converting, Formulas, Units, Examples (2024)

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