How to convert mole fraction to mass fraction? – (Mole fraction to mass fraction)

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.

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:

Where,

• n_A = Number of moles of component A
• n_B = Number of moles of component B
• n_C = Number of moles of component C
• n_D = Number of moles of component D

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

In a homogenous solution containing a solute and a solvent;

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.  

Where,

• w_A = Mass of component A
• w_B = Mass of component B
• w_C = 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.

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.

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

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

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:

Where,

∴ The total mass of the mixture = X_A (molar mass of A) + X_B (molar mass of B) + X_C (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

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

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

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