Mole Fraction

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What is Mole Fraction?

The mole fraction is the number of moles of a specific component present in a solution divided by the total number of moles present in the given solution. Mole fraction is one of the several ways to indicate the concentration of the solution. A unit of concentration is considered as a mole fraction. The relative amount of solute and solvents present in a solution is measured by the mole fraction, and ‘x’ is used to represent the mole fraction. This is what is meant by the mole fraction. For example, the mole fraction of NaCl is 0.0176.


Formula Related to the Mole Fraction

Consider a solution that consists of two substances A and B, then the mole fraction of each substance is:

Mole fraction of solute =  (Moles of Solute) / (Total number of moles of the solutes and the solvent).

= XA = (mol A) / ( mol A + mol B)

And

= XB = (mol B) / ( mol A + mol B)


Note:

  1. In the given mixture, the sum of all the mole fractions present is equal to one 

XA +  XB = 1.

  1. When the mole fractions are multiplied by 100, they give the mole percentage.

  2. Mole fraction is a unitless and dimensionless expression.

(image will be uploaded soon)

The image shows some chemical solutions of which we can find the mole fraction of its components.


Advantages of Mole Fraction

The advantages of mole fraction are:

  • Mole fraction has never been dependent on the temperature.

  • To calculate the mole fraction, it is not necessary to find out the information about the density of the phase.

  • The mole fraction is represented by the ratio of partial pressure to the total pressure of the mixture, in the case of an ideal gas mixture.

Disadvantages of Mole Fraction

There is only one disadvantage of mole fraction, that is, mole fraction is not convenient for liquid solutions.


Properties of Mole Fraction

The properties of mole fraction are:

  • It is temperature independent which prevents it from variations when the temperature fluctuates. The knowledge of the densities of the phase involved is not necessary in the case of the mole fraction.

  • By weighing off the actual masses of the constituents, a mixture of a known mole fraction can be prepared.

  • The measure is symmetric, i.e., in the mole fraction x = 0.1 and x = 0.9, the roles of ‘solvent’ and ‘solute’ are reversed.

  • In a ternary mixture, a mole fraction of a component can be expressed as functions of other components’ mole fraction and binary mole ratios.

Solved  Examples

Example 1:

Calculate the mole fraction of NaCl and H₂O, if 0.010 moles of NaCl is dissolved in 100 grams of pure water.


Solution:

The molecular weight of water is considered to be 18.0153 grams per mole.

Number of moles of water = 100 grams / 18.0153 grams = 5.56 moles

Mole fraction of NaCl = 0.100 moles / ( 5.56 moles + 0.10 moles)

= 0.100 moles / 5.66 moles

Mole fraction of NaCl = 0.018

Mole fraction of H₂O = 5.56 moles / 5.66 moles

Mole fraction of H₂O = 0.982


Example 2:

Calculate the mole fraction of acetone that is present in a solution which consists of 2 moles of benzene, 3 moles of carbon tetrachloride, and 5 moles acetone.


Solution:

Number of moles of acetone = 5 moles

Number of moles of carbon tetrachloride = 3 moles

Number of moles of benzene = 2 moles

Total number of moles in the solution = number of moles present in acetone + number of moles present in carbon tetrachloride + number of moles present in benzene

= 5 moles + 3 moles + 2 moles

= 10 moles

Mole fraction of acetone = (Number of moles in acetone) / (Total number of moles in the solution)

= 5 moles / 10 moles

= 0.5

Mole fraction of carbon tetrachloride = (Number of moles in carbon tetrachloride) / (Total number of moles in the solution)

= 3 moles / 10 moles

= 0.3

Mole fraction of benzene = (Number of moles in benzene) / (Total number of moles in the solution)

= 2 moles / 10 moles

= 0.2  


Example 3:

A solution is prepared by mixing 30 grams of ethanol and 30 grams of water. Determine the mole fraction of each component.


Solution:

The molecular weight of ethanol is fixed at 46.07 g/mol.

The number of moles of ethanol present in the solution = 30 grams / 46.07 g/mol = 0.651 moles.

The molecular weight of water is fixed at 18g/mol.

The number of moles of water present in the solution =  30 grams / 18 g/mol = 1.67 moles

Total number moles = 0.651 + 1.67 =  2.321 moles

Mole fraction of ethanol = 0.651 moles / 2.321 moles = 0.28

Mole fraction of water = 1.67 moles / 2.321 moles = 0.72

FAQ (Frequently Asked Questions)

1. Discuss the Importance of the Mole Fraction.

Answer: Mole fraction can be calculated by dividing the number of molecules or moles in one component to the total number of molecules or moles present in the solution. Mole fractions are very useful in situations where two reactive components are mixed together as we can find out the ratio of the two components if we know the actual amount of moles present in both solutions. You can find out the mole percent by multiplying the mole fraction by 100, and it describes the same thing but in a different form. We can calculate the mole fraction from different factors such as molality, molarity, and mass percent compositions.

2. What is a Mole?

Answer: A mole is also spelled as mol. It is the term used in chemistry as a standard scientific unit for measuring large quantities of very small particles such as atoms, molecules, or other specified particles. The mole designates an extremely large number of units which is valued at 6.02214076 × 1023. This number is defined as the mole for the International System of Units by the General Conference Weights and Measures. The number of atoms or other particles in moles or molecules is the same in all the substances available.