Solved Examples on Mole Fraction

Example 1: If the molecular mass of CH₃OH is 39 and the molecular mass of H₂O is 27, what is the mole fraction of CH₃OH and H₂O in a solution made by dissolving 4.1 g of alcohol in 36 g of H₂O?

Answer:

Using the formula for moles,

Moles = wt(in gm) / molecular mass

Moles of H₂O = 36 / 27 
                      = 1.3 moles

Moles of CH₃OH = 4.1 / 39 
                           = 0.10 mole

Mole fraction of CH₃OH = 0.10 / (1.3 + 0.10)
                                      = 0.10 / 1.4

Mole fraction of CH₃OH = 0.0714

Now,

Mole fraction of H₂O = 1.3/(1.3+0.1)
                                 = 1.3/1.4

Mole fraction of  H₂O = 0.9286

Example 2: Calculate the mole fraction of each gas in a tank containing 2.5 × 10⁴ mol oxygen and 4.8 × 10⁴ mol helium.

Answer:

Number of moles of Helium = 4.8 × 10⁴

Number of moles of Oxygen = 2.5 × 10⁴

Since,

Mole Fraction of Helium = Number of moles of Helium / (Number of moles of Helium + Number of moles of Oxygen)

X_Helium = 4.8 × 10⁴ / (4.8 × 10⁴ + 2.5 × 10⁴)

            = 4.8 × 10⁴ / 7.3 × 10⁴

X_Helium = 0.6575

Mole Fraction of Oxygen = Number of moles of Oxygen / (Number of moles of Helium + Number of moles of Oxygen)

X_Oxygen = 2.5 × 10⁴ / (4.8 × 10⁴ + 2.5 × 10⁴)

            = 2.5 × 10⁴ / 7.3 × 10⁴

X_oxygen = 0.3424

Example 3: Calculate the acetone mole fraction in a solution of 6-mole benzene, 13 moles carbon tetrachloride, and 21 moles acetone.

Answer:

Moles of Benzene = 6

Moles of Carbon Tetrachloride = 13

Moles of Acetone = 21

Now,

Mole Fraction of Acetone = Moles of Acetone / (Moles of Benzene + Moles of Carbon Tetrachloride + Moles of Acetone)

X_acetone = 21 / (6+13+21)

X_acetone = 21 / 40

X_acetone = 0.525

Mole Fraction of Benzene = Moles of Benzene / (Moles of Benzene + Moles of Carbon Tetrachloride + Moles of Acetone)

X_benzene = 6 / (6+13+21)

X_benzene = 0.15

Mole Fraction of Carbon Tetrachloride = Moles of Carbon Tetrachloride / (Moles of Benzene + Moles of Carbon Tetrachloride + Moles of Acetone)

X_{carbon tetrachloride} = 6 / (6+13+21)

X_{carbon tetrachloride} = 0.15

Example 4: Calculate the mole fraction of solute, when the mole fraction of solvent is 0.23

Answer:

Since,

X_solute = 1 – X_solvent

X_solute = 1 – 0.23

X_solute = 0.77

Example 5: If the mole fraction of the solute is 0.64, determine the mole fraction of the solvent.

Answer:

Since,

X_solvent = 1 – X_solute

X_solvent = 1 – 0.64

X_solvent = 0.36

Mole fraction is one of the ways to represent the concentration of the solution. It is defined as the number of molecules of component A divided by the total number of molecules of all the components in the solution. Let’s learn about the mole fraction its formula and examples in this article.