Mole Fraction - Definition and Notation, Formula, Advantages and Disadvantages, Important Note, Practice Problems, FAQs

Properties of individual substances can be characterized in whole or fractional or mixed numbers, like an atomic mass of carbon is 12 and of chlorine is 37.45. The quantity could be 1 mole or 1.4 or any fractional. When it comes to the question of a mixture containing more than one pure substance, how to represent the individual characteristics, say amount? One way is to express the relative amounts as fractions of moles.

A most useful concentration term is mole fraction. We are going to explain this in a lot of detail in this article so let’s get started right away!

TABLE OF CONTENTS

Definition and Notation
Formula
Advantages and Disadvantages
Important Note
Practice Problems
Frequently Asked Questions

DEFINITION AND NOTATION

Mole fraction is defined as the ratio of the number of moles of a certain component in a mixture and the total number of moles in that given mixture. For instance, if we have a multicomponent system of “n” components, we can say that the mole fraction of i^th component is the number of moles of i divided by the total number of moles of all “n” substances.

It is frequently denoted by X_i or 𝛘_i when we want to talk about the mole fraction of the i^th component.

FORMULA

We calculate mole fraction as follows:

Where

𝛘_i = mole fraction of i

n_i= number of moles of i

n_j= number of moles of the j^th component

ADVANTAGES AND DISADVANTAGES

Advantages:

It is not a temperature dependent quantity.
It can directly be correlated to the partial pressures in the case of gas mixtures.
It eases theoretical calculations as we don’t need to know or use density data for calculations.

Disadvantages

It cannot be used in the case of a immiscible liquid mixture system.

IMPORTANT NOTE

It is critical to keep in mind that the sum of mole fractions of all individual components of a mixture adds up to 1. i=1ni = 1, for a multicomponent system having “n” components. This property helps in solving numericals which we will see later.
In the case of a solid solute in liquid solvent, we can say:i = nsolutensolute + nsolvent, for mole fraction of solute.
Mole fraction is a dimensionless quantity.

PRACTICE PROBLEMS

1. Calculate the mole fraction of sodium chloride if we have a solution with 0.3 moles in 180 mL of water.
Ans:

Density of water = 1 g mL-1Hence, mass of water = 180 mL x 1 gmL-1 = 180 g

No. of moles of water = 180 g18 gmol-1 =10 mol

Mole fraction of NaCl = nNaClnNaCl+ nwater= 0.30.3 + 10= 0.310.3 = 0.029

In a given gaseous mixture of 40 mol, if the mole fraction of nitrogen is 0.5 and oxygen is 0.2, what would be the volume of the third component at STP?

Ans:

Sum of all mole fractions = 1

So, mole fraction of nitrogen + mole fraction of oxygen + mole fraction of gas “k” = 1

0.5 + 0.2 + k = 1 k = 1 - 0.7 = 0.3

Number of moles of gas “k” = 0.3 x 40 = 12 mol

Thus, volume occupied at STP = 22.7 Lmol-1 x 12 mol = 272.4 L

If a sample of air contains 78% nitrogen by volume and 20% oxygen by volume, what will be their respective mole fractions?

0.78:0.2
0.2:0.78
0.5:.5
7:8

Ans: Option A

We know that the mole’s ratio is the same as the volume ratio. So if we can say that the volume ratio of nitrogen and oxygen is 0.78 and 0.2 respectively then we can also say that their mole fraction will be 0.78 and 0.2 respectively. Hence, the mole fraction of nitrogen is 0.78 and that of oxygen is 0.2 in the given air sample.

If 2 mol of ammonia and 5 mol of HCl gas are left in a closed container, what will be the mole fraction of ammonia in the mixture?

A) 2
B) 5
C) 3
D) 0

Ans: D

We cannot calculate mole fraction for a mixture of reacting gasses. Here, ammonia and HCl gas react to form ammonium chloride. Since ammonia here is the limiting reagent it is consumed fully and hence in the final mixture the mole fraction of ammonia is zero, assuming 100% reaction.

FREQUENTLY ASKED QUESTIONS

1. Is mole fraction an extensive property?
Ans: Mole fraction is an intensive property as there is no volume dependency in question. This makes it a very easy concentration term to work with. It is also important to know that mole fraction is temperature independent due to there being no dependency on volume.

2. Are mole fraction and gas fraction the same thing?
Ans: They are vastly different. Mole fraction is a concentration term commonly used in physical chemistry. Gas fraction is a term commonly encountered in astrophysics which is a ratio of the mass of gas (in a galaxy cluster) to that of the total mass in a galaxy i.e. the mass of gas + mass of stars.

3. What are examples of concentration terms?
Ans: Some common concentration terms we use are normality, molarity, molality, mole fraction and parts per million. Depending on the state of matter of solute and solvent, different terms can be used. It is also sometimes more convenient to express certain concentrations in one system over another, depending on the values.

4. What is Dalton’s Law?
Ans: Dalton’s Law states that for a mixture of non reacting gasses, the sum of partial pressures of each of the components will be equal to the total pressure of the system. This law is valid only for an ideal gas system.