Mole Fraction: Definition, Calculation, and Formula

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What is Mole Fraction?

The mole fraction is defined as the ratio of number of moles of a given component present in a solution to total number of moles present in the given solution.

Mole fraction is one of the ways to find the concentration of the given solution.

A unit of concentration is termed as a mole fraction.

The mole fraction thus calculates the relative amount of solute and solvents present in each solution.

Mole fraction are unitless quantity, have no dimensions, and the sum of all fraction in a mixture is always equal to 1.

Mole fraction is represented by a symbol X.

Mole Fraction Formula

if a mixture is composed of two substance that are A and B, then the mole fraction is calculated as given below:

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

Mole Fraction of Solute = Moles of solute / (Mole of Solute + Mole of Solvent)

For instance, if a mixture contains 0.80 mol A and 1.0 mol B

mole fraction of A =0.8/1.5 =0.44

mole fraction of B = 1.0/1.8 = 0.55

The Mole fraction can also be converted into mole percentage by multiplying it by 100.

Properties of the Mole Fraction

The mole fraction is used broadly in the construction of phase diagrams. It has a lot of advantages which are mentioned below:

Mole fraction does not generally depend on temperature as compared to molar concentration, and it does not need knowledge of the densities of the involved phases.

It is very easy to make a mixture of known mole fractions by weighing the appropriate masses of the constituents used to form a mixture.

A mole fraction of a substance is referred to as the function of other component present in a tertiary mixture.

Disadvantages of Mole Fraction

The one disadvantage of mole fraction is that mole fraction is not suitable for liquid solutions.

How to Find Mole Fraction in Mixtures?

A mixture of gases is made by combining 6.8 moles of O2 and 4.6 moles of N2, find the mole fraction of nitrogen in this mixture?

Total number of moles = 6.8 +4.6 = 11.4

moles of N2 = 5.6 /11.9

= 0.403

So, mole fraction of N2 = 0.403

How to Find Mole Fraction in Solution?

Find the mole fraction of NaCl if 0.200 moles of sodium chloride are dissolved in water.

Primarily, convert volume of water into mass and then to moles

Density is defined as mass divided by its volume.

Density = Mass / Volume

M = D*V = 1g/ml * 100 ml =100 g

So, Moles of water = Mass / total molar mass

= 100 / 18 = 5.55 moles

Total number of moles = 5.55 + 0.200 = 5.75 moles

Thus, Mole fraction of NaCl = 0.200 / 5.75 = 0.0347

How to Find Mole Fraction Multi-Component Mixtures?

To find the mole fraction of Hexane in the mixture of 10.0 g of pentane(C5H12), 10.0 f of hexane (C6H14) and 10.0 g of benzene (C6H6).

Primarily, find the number of moles in 10.0 g of each component by the formula:

Number of moles = Given mass /Molar Mass

Number of moles of Pentane is equal to 0.138 moles

Moles of hexane is equal to 0.116 moles

Moles of benzene is equal to 0.128 moles

Hence, Total number of moles present = 0.138 + 0.116 + 0.128 = 0.382

Lastly, The mole fraction of hexane is = 0.116 / 0.382 = 0.303.

How to Find Mole Fraction from Molality?

If 1.82 m solution of table sugar (C6H12O6) is formed in water, find the mole fraction of the table sugar?

As the molality of a solution is given thus, we can convert it to the equivalent mole fraction, which is a mass ratio as given below;

Molality = moles solute / kg of solvent.

As per the definition of molality, we have 1.82 moles of sugar solution and 1.00 kg (1000 g) of water. We know the number of moles of sugar, thus we need to find the moles of water using its molecular weight as given below;

Moles of water = 1000 / 18 = 5.55 moles

Total number of moles is equal to 5.55 + 1.82 = 7.37 moles

Mole fraction of sugar = 1.82 / 7.37 = 0.246

How to Find Mole Fraction from Mass Percent?

Find the mole fraction of cinnamic acid with a mole percent of 60.00% urea in cinnamic acid. The molecular weight of urea is 60.16 g/mol and the molecular weight of cinnamic acid is 148.16 g/mol.

By assuming a total mass of 100.0 g which means that we have 60.0 g of urea and 40.0 g of cinnamic acid.

Thus, we can then find the moles present of Urea and Cinnamic acid by dividing each by its molecular weight as shown below;

Numbers of moles of Urea = 60.0 / 60.16 g/mol = 0.997 moles

Numbers of moles of cinnamic acid = 40.0/148.16g/mol = 0.269 moles

Total number of moles is equal to 1.266 moles

Mole fraction of cinnamic acid = 0.269/1.266 = 0.2124



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