Difference Between Mole Fraction and Mass Fraction

Key Difference – Mole Fraction vs Mass Fraction
 

Mole fraction and mass fraction are terms used to express the ratios between different components in compounds. The key difference between mole fraction and mass fraction is that mole fraction deals with the moles of different components of a compound whereas mass fraction deals with the masses of different components in a compound. Mole fraction can be converted into the mass fraction of the same compound and vice versa.

CONTENTS

1. Overview and Key Difference
2. What is Mole Fraction 
3. What is Mass Fraction
4. Similarities Between Mole Fraction and Mass Fraction
5. Side by Side Comparison – Mole Fraction vs Mass Fraction in Tabular Form
6. Summary

What is Mole Fraction?

Mole fraction is the ratio between amounts of components in a mixture expressed by their number of moles. It is the ratio between the moles of a constituent and the sum of moles of all constituents in a mixture. It can be given as below.

Mole fraction = moles of a constituent/sum of moles of all constituents (mass of the mixture)

Or

X_i = n_i / n_total

The mole fractions of all components equals 1 since the mole fraction is a ratio. The mole fraction can be used to express the mole percentage by multiplying the mole fraction from 100. The mole fraction can also be called the amount fraction because moles give the amount of a constituent. Mole fraction is unit-less since it is a ratio between moles (units cancel out).

Figure 01: Density of NaCl as a Function of the Mole Fraction

Calculation of Mole Fraction

Let us consider a sample problem to understand what mole fraction is.

Question:

Find the mole fraction of NaCl when 0.1 mol of NaCl is dissolved in 100 grams of pure water.

Answer:

Number of moles of water              = 100 g / 18 gmol^-1

= 5.56 mol

Sum of moles of all constituents  = 0.1 (NaCl) + 5.56 (H₂O)

= 5.66 mol

The mole fraction of NaCl            = 0.1 mol/ 5.66 mol

= 0.018

What is Mass Fraction?

Mass fraction is the ratio between the mass of a constituent and the total mass of a mixture. Since it is a ratio between masses, the mass fraction is unit-less (units cancel out). It can be given as an equation (given below).

Mass fraction = mass of a constituent/sum of masses of all constituents (mass of the mixture)

Or

W_i = m_i / m_total

The mass fractions of all components is equal to 1 since the mass fraction is a ratio. The mass fractions of individual components are always lower values than 1. Mass fraction can be given as mass percentage as well. Here, the mass fraction is multiplied by 100. In elemental analysis calculations, mass fraction refers to the ratio between the mass of a chemical element and the compound. The mass fraction is independent of temperature because mass does not change when the temperature is changed.

Calculation involving Mass Fraction

Question:

Find the mass of sucrose in a solution of sucrose (500 g) in which water is having mass fraction of 0.65.

Answer:

Total mass of the mixture                = 500 g

Mass fraction of water                      = 0.65

Then the mass fraction of sucrose = 1-0.65 = 0.35

The mass of sucrose                          = 0.35 x 500g

= 175 g

What are the Similarities Between Mole Fraction and Mass Fraction?

• Both terms express ratios.
• Both mole fraction and mass fraction are unit-less terms.
• Both gives values that are either equal or less than 1.
• Both are independent of temperature changes.

What is the Difference Between Mole Fraction and Mass Fraction?

Summary – Mole Fraction vs Mass Fraction

Mole fraction and mass fraction are used to express the relative fractions of different constituents in a mixture. Both are unit-less terms since the ratios have the same unit, and thus the units cancel out. The key difference between mole fraction and mass fraction is that mole fraction deals with the moles of different components of a compound whereas mass fraction deals with the masses of different components in a compound.

Reference:

1. “Mole Fraction.” Wikipedia, Wikimedia Foundation, 12 Mar. 2018, Available here.
2. “Mole Fraction”, Chemsteam, Available here.
3. “Mass Fraction (Chemistry).” Wikipedia, Wikimedia Foundation, 3 Mar. 2018, Available here.

Image Courtesy:

1. “Salt mole fraction” By Jzana – Own work (CC BY-SA 3.0) via Commons Wikimedia

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