Mole Fraction Formula: Properties, Advantages, & Examples

Mole fraction is the number of molecules in a mixture of a certain component divided by the mixture's total moles. In chemistry, the mole fraction is basically a unit of concentration. 

• The mole fraction unit can be used to describe computations involving gas mixtures.
• It also relates some physical properties of solutions, such as the relationship between vapor pressure and concentration. 
• A mole fraction is a quantity that has no units. 
• The mole fraction is represented by the symbol "X."

Key Terms: Moles, Mole Fraction, Solvent, Solute, Molar Mass, Molecular Weight, Avogadro's Law

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Mole Fraction Formula

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The mole fraction formula can be simplified by using the formula. Let us suppose that there are two components 'A' and 'B' in a solution. The mole fraction which is written as 'X' can thus be written as =

X _solute = \(\frac{moles of solute}{total moles in solutions} = \frac{n}{n + N}\)

X _solvent = \(\frac{moles of solvent}{total moles in solutions} = \frac{n}{n + N}\)

X _solute + X _solvent = 1

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Properties of Mole Fraction

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The main properties of a mole fraction are as follows:

• The temperature has no impact on a mole fraction. Mole fraction does not need to know the densities of all the phases involved, unlike molar concentration.
• The measure is symmetrical, therefore the roles of "solvent" and "solute" are switched in the mole fractions where x = 0.1 and x = 0.9.
• Unlike with other measurement methods, a valid combination of mole fractions may be produced by taking into account the weight of the constituents.
• As a function of the binary mole ratios and mole fractions of the other components, one component's mole fraction in a ternary combination may be expressed.
• The mole fraction in ideal gases is defined as the ratio of the mixture's partial pressure to its total pressure.

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Advantages of Mole Fraction

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There are some advantages of mole fraction which are as follows:

• The temperature has never been a factor in mole fraction. 
• It is not necessary to ascertain the phase's density in order to compute the mole fraction. 
• The mole fraction of an ideal gas mixture is expressed by the ratio of the partial pressure to the mixture's total pressure.

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Solved Examples

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Example 1. In 100 grams of pure water, if 0.010 moles of NaCl is dissolved then calculate the mole fraction of NaCl and H₂O.

Solution. Molecular weight of water = 18.0153 gm/mole

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

Mole fraction of NaCl = 0.1 moles/ (5.56 moles + 0.10 moles)

= 0.100 moles /5.66 moles. = 0.018

Mole fraction of H₂O= 5.56 moles/ 5.66 moles

= 0.982

Example 2. When 5.5g of alcohol is dissolved in 40g of H₂O, then find the mole fraction of CH₃OH in this solution. (Molar mass of H₂O is 18 gm and that of CH₃OH is 32)

Solution. Moles of CH₃OH= 5.5/32 = 0.17 moles

Moles of H₂O= 40/18= 2.2 moles

Therefore, 

Mole Fraction of CH₃OH= 0.17/ (2.2 + 0.17) = 0.073

Example 3. Determine the mole fraction of HCl and H₂O in a solution of water and hydrochloric acid with a weight percentage of HCl of 30%.

Solution.  The molar mass of HCl= 36.5 gm/mole

Molar mass of H₂O = 18 gm/mole

Moles of HCl= 30/36.5 = .821 moles of HCl

Moles of H₂O= 70/18 = 3.88 moles of H₂O

Mole fraction of HCl = .821/(.821 + 3.88) = .174 Mole fraction of H₂O = 3.88/(.821 + 3.88) = .825

Example 4. Find the mole fraction of each component in the solution containing 1 mole of A, 2 mole of B, and 3 mole of C.

Solution. Mole fraction of each component 

χ_A = n_A / (n_A + n_B + n_C) = 1/(1+1+2) = .25

χ_B = n_B / (n_A + n_B + n_C ) = 1/(1+1+2) = .25

χ_C = n_C / (n_A + n_B + n_C ) = 2/(1+1+2)  = .5

Also χ_A + χ_B + χ_C =1

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Things to Remember

• The term "mole fraction" refers to the ratio of a component's molecular weight to the overall molecular weight of a combination. 
• A mole fraction is a quantity that has no units. 
• The mole fraction is represented by the symbol "X."
• The ratio of the partial pressure to the total pressure of an ideal gas mixture is used to express the mole fraction of the mixture.
• The sum of all the mole fractions in a given mixture is equal to one. X_A+X_B=1.
• There is only one drawback to mole fraction, and that is that it doesn't work well with liquid solutions. 
• Only certain molecules are represented by the mole fraction. 
• The individual fraction may differ from the mass fraction because different molecules can have varying masses.

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