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×14th Sep 2019 @ 11 min read

The mole is the fundamental SI unit for measuring the amount of substance. One mole comprises of approximately 6.022 × 10^{23} elementary units.

The mole is a frequently used unit in chemistry. Chemical reactions are always balanced using moles of the reactant and the product. The concentration of a solution involves the mole of a solute. Some examples are molar concentration or molarity, molality, mole fraction, molar density. The mole fraction is another way of expressing the concentration.

The mole fraction of a substance in the mixture is the ratio of the mole of the substance in the mixture to the total mole of the mixture. Since it is the ratio of moles to moles, it is a dimensionless quantity. The mole fraction is sometimes called the amount fraction.

For solutions and liquid mixtures, the symbol *x* is used to denote and for a gaseous component, the symbol *y* is used to denote it.

For a mixture of the *i*^{th} component,

Here, *x _{i}* is the molar fraction of the

From the above two equations,

Note: The sum of the mole fraction of each component is always equal to one.

Statement: A sample of air contains 39.05 mol of nitrogen, 10.47 mol of oxygen, 0.45 mol of argon, and 0.03 mol of argon.

Solution: Let *n*_{N2}, *n*_{O2}, *n*_{Ar}, and *n*_{CO2} be moles of nitrogen, oxygen, argon, and carbon dioxide.

The mole fraction of nitrogen, oxygen, argon, and carbon dioxide in the given of air be *y*_{N2}, *y*_{O2}, *y*_{Ar}, and *y*_{CO2}.

Thus, the sample of air consists of 0.781 0 of nitrogen, 0.209 4 of oxygen, 0.009 0 of argon, and 0.000 6 of carbon dioxide.

In a solution, the mole fraction of a solute is the ratio of the mole of the solute to the total mole of the solution.

Statement: Sucrose, aka table sugar or granulated sugar, is a disaccharide. It is made up of glucose and fructose and has a molecular formula of C_{12}H_{22}O_{11}. Sucrose has a high solubility in water. Consider a solution of two tablespoon (40 g) of sucrose in 100 g of water.

The molar mass of sucrose is 342 g mol^{−1} and of water, 18 g mol^{−1}.

Solution: The solution contains 40 g of sucrose and 100 g of water. The respective mole of sugar and water are as follows:

Let *x*_{C12H22O11} and *x*_{H2O} be the mole fraction of sucrose and water in the solution.

Thus, the solution has 0.021 of sugar and 0.979 of water.

Note: The mole fraction is an intensive property. So, it would not vary from sample to sample. It is also temperature and pressure independent.

The molar percentage or mole per cent is the same as mole fraction when expressed in the percentage.

Statement: Ferrous sulphate has the molecular formula FeSO_{4}. Its solution is typically greenish in colour. A solution of FeSO_{4} contains 20 g of FeSO_{4} and 100 g of H_{2}O. The molar mass of FeSO_{4} is 152 g mol^{−1} and of H_{2}O, 18 g mol^{−1}.

Solution: The gram of ferrous sulphate and water in the solution is 20 g and 100 g. The respective mole of ferrous sulphate and water is as follows:

The mole per cent of ferrous sulphate and water is as follows:

Thus, the solution is 2.3 % FeSO_{4} by the mole.

The mole fraction is a way to express the composition of a mixture. Other quantities are molarity, molality, mass fraction. The relationship between them can be established.

The molar concentration or molarity is the mole of a solute per unit volume of the solution. Typically volume is expressed in litre (L) or decimetre cube (dm^{−3}).

Converting the mole fraction to the molar concentration or molarity,

Here, is the total molar concentration.

The above equation relates the mole fraction, molar concentration, and total molar concentration.

Here, is the density of the solution and is the average molar mass of the solution. But we also know

The above equation relates the mole fraction, molar concentration, and density.

The mass concentration is the ratio the mass of a solute to the volume of the solution.

Converting the mole fraction into the mass concentration,

Here, *M _{i}* is the molar mass of the solute and

The mole fraction can also be expressed in terms of the density of a solution.

Here, *ρ* is the density of the solution, *M* is the average molar mass of the solution.

The molality is the mole of a solute per unit mass of the solvent. The molality is denoted by *b* and has the unit mol kg^{−1}.

Consider a single-solute solution, where *b* is the molality, *x* is the mole fraction of the solute.

Here, *M*_{0} is the molar mass of the solvent.

For a single-solvent solution having *j* solutes,

The mass fraction is a very similar quantity. It is the ratio of the mass of a solute to the total mass of the solution.

Here, *M _{i}* is the molar mass of the

The mixing ratio of two pure substances is the ratio of the mole of a substance to the other.

Expressing *r* in terms of *x*_{1},

Expressing *r* in terms of *x*_{2},

Statement: A ferric chloride solution contain 40 g of ferric chloride and 60 g of water. The molar mass of ferric chloride is 162.2 g mol^{−1} and of water, 18.0 g mol^{−1}.

Solution: Converting the gram to the mole,

The mole fraction of the ferric chloride solution and water are as follows:

Thus, the solution contains 6.9 % of ferric chloride.

Statement: A sample of flue gas from a factory comprise of 20 g of carbon dioxide, 10 g of water vapour, 31 g of oxygen, and 48 g of nitrogen. The molar mass of carbon dioxide, water vapour, oxygen, and nitrogen is 44 g mol^{−1}, 18 g mol^{−1}, 32 g mol^{−1}, and 28 g mol^{−1}.

Solution: Converting the gram to the mole,

The mole fraction of these gases are as follows:

Statement: When two methyl groups are attached to a benzene ring at an ortho position, o-xylene is formed. o-Xylene is an aromatic compound having the formula C_{6}H_{4}(CH_{3})_{2}. It is soluble in dimethyl ether, one of the most common solvents in chemical industries. If 2.3 mol of o-xylene is dissolved in 12.1 mol of dimethyl ether, estimate the mole percent of each.

Solution: Let *n*_{xy} and *n*_{dme} be the mole of o-xylene and dimethyl ether.

Let *x*_{xy} and *x*_{dme} be the mole fraction of o-xylene and dimethyl ether.

Thus, the mixture has 16 % o-xylene and 84 % dimethyl ether.

Find the mole fraction in the following problems.

Sodium chloride is a common salt having formula NaCl. It is highly soluble in water. A beaker contains 100 g of water, and 23.4 g of sodium chloride is dissolved in it. The molar mass of sodium chloride is 58.44 g mol^{−1} and of water, 18.02 g mol^{−1}.

Indigo dye is a naturally occurring dye having a dense blue colour. It is widely used for dyeing of textiles. The molar mass of indigo dye is 262.27 g mol^{−1} and of water, 18.02 g mol^{−1}. A industrial vessel has 0.1 g of indigo per 100 g of water.

The water-gas shift reaction is a famous industrial reaction. Carbon monoxide reacts with steam to form carbon dioxide and hydrogen.

An industrial pipe has a flow rate of 40 mol s^{−1} of carbon monoxide, 40 mol s^{−1} of steam, 17 mol s^{−1} of carbon dioxide, and 23 mol s^{−1} of hydrogen.

- 067 3 of sodium chloride and 0.933 7 of water
- 007 % of indigo dye and 99.993 % of water
- 33 of carbon monoxide, 0.33 of steam, 0.15 of carbon dioxide, and 0.19

- The mole fraction of a component in the mixture is the ratio of the mole of the component to the total mole of the mixture. It is denoted by
*x*for liquids and solids or*y*for gases. - For solution,
- The mole fraction is an intensive property. So, it would not vary from sample to sample for a given uniform mixture. It is also independent of temperature and pressure.
- The sum of each mole fraction in a mixture is always equal to one.

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Thanks for your response!

John

24th Sep 2020

24th Sep 2020

Great article on molar fractions, helps a lot in understanding various concepts about molar fraction.

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