Mole Fraction

The ratio of the number of moles of one component to the total number of moles of all the components (solute and solvent) present in the solution is known as the mole fraction. It is denoted by the Greek letter X (Chi), and the sum of all mole fractions in a solution always equals one.

• In general, the formula for Mole fraction (X) = Moles of solute ÷ Total number of moles.
• If you know the amount of moles of all of the solutes and the solvent, the mole fraction formula is very simple to grasp and apply. 
• When you just know the mass of one or more components in a solution, things get a little more difficult. All you have to do is convert the component’s mass to the number of moles, which is a simple arithmetic task if you know the chemical formula.

Mole Fraction Formula

Mole fraction calculations can be used to calculate any property that is proportional to the number of molecules (and so moles) present, such as partial pressure for gases. The number of moles of the nth component of a mixture divided by the total number of moles of all components is called the mole fraction (Xi).

Mole fraction of solute = Moles of solute ÷ Moles of solute + Moles of solvent

= nA/ nA + nB 

Mole fractions of solvent = Moles of solvent / Moles of solute + Moles of solvent

= nB / nA + nB

Check out some examples to solve mole fractions after applying this formula.

Examples of Mole Fraction

1. Find the mole fraction of both components in a 50 percent by mass mixture of water (H2O) and ethanol (C2H5OH)?

The density of ethanol is 789 gm per litre, so there are 789 gm (1mole÷46.07 g) =17.131 moles in 1 L

The density of water is 1000 g/L, so there are 1000 gm (1 mole÷18.0 gm)=55.55 moles in 1 L

Xethanol = 17.13÷17.13+55.55 = 0.236

XH2O = 55.55÷17.13+55.55 = 0.764

2. Determine the mole fraction of CH3OH and H2O in a solution prepared by dissolving 5.7 gm of alcohol in 50 gm of H2O. M CH3OH is 32, and M of H2O is 18?

Moles of CH3OH = 5.7 ÷ 32 = 0.178 mole

Moles of H2O = 50 ÷ 18 = 2.77 moles

Therefore, according to the equation

Mole fraction of CH3OH = 0.178 ÷ 2.77+0.178 = 0.060

Mole fraction of CH3OH = 0.060

3. Find the mole fraction of HCl in a solution of HCl containing 37.2% of HCl by mass?

Percentage by mass = 37.2 %

Mole fraction of HCl =?

Solution. Percentage by mass of HCl = 37.2%

Let us consider 100 gm of HCl solution.

Mass of solute (HCl) = 37.2 gram

Mass of solvent (H2O) = 100 – 37.2 = 62.8 gram

The molecular mass of HCl = 35.5 g ✕ 1+ 1 g ✕ 1 = 36.5 gm

Number of moles of solute (HCl) = given mass ÷molecular mass

Number of moles of solute (HCl) = nB = 37.2 ÷ 36.50 gm = 1.019 mol

The molecular mass of H2O = 1 gm ✕ 2 + 16 gm ✕ 1 = 18 gm

Number of moles of solvent (water) = nA = 62.8 gm ÷ 18 gm = 3.489 mol

Mole fraction of solute (HCl) = XB= nB ÷ (nA + nB) = 1.019 / 3.489 = 0.292

Mole fraction of HCl = 0.292

Mole percent 

The mole percentage, also known as amount/amount percent (abbreviated as n/n percent), is calculated by multiplying the mole fraction by 100. By dividing by 100, we can simply convert mole percent to mole fraction. As a result, a mole fraction of 0.60 equals a mole percent of 60.0.

Key points about mole fraction

• The number of moles of a component divided by the total number of moles in a solution yields a mole fraction, which is a concentration unit. Because it indicates a ratio, mole fraction is a unitless term. As mole fractions have no dimensions, hence the sum of all mole fractions in a combination is always 1.
• Please note that the mole fraction represents a fraction of molecules, and the mole fraction differs from the mass fraction since different molecules have different masses.
• We get mole percent by multiplying mole fraction by 100, which is the same as mole fraction but presented differently. Mole fractions can be created utilising various concentrations, including molality, molarity, and mass percent compositions.

Conclusion

A mole fraction is a concentration unit similar to molarity or molality. It is defined as the number of moles of a component divided by the total number of moles in a solution. Mole fraction is a unitless expression because it represents a ratio. Mole fraction does not depend upon temperature and can be extended to solutions having more than two components.