Mole Fraction Formula

What is Mole fraction?

Mole fraction represents the number of molecules of a particular component in a mixture divided by the total number of moles in the given mixture. It’s a way of expressing the concentration of a solution.

Mole Fraction formula

The molar fraction can be represented by X. If the solution consists of components A and B, then the mole fraction is,

                           =

                             =

Therefore, the sum of mole fraction of all the components is always equal to one.

Please note that mole fraction represents a fraction of molecules, and since different molecules have different masses, the mole fraction is different from the mass fraction.

Example 1  

A tank is charged with a mixture of 1.0 x 10³ mol of oxygen and 4.5 x 10³ mol of helium. Calculate the mole fraction of each gas in the mixture.

Solution

The given parameters are

N_He = 4.5 x 10³ mol and N_O2 = 1.0 x 10³ mol

Mole fraction can be calculated as

X_He = 4.5 x 10³ mol / (4.5 x 10³ mol + 1.0 x 10³ mol)

X_He =  4.5 mol / 5.5 mol

X_He = 0.82

X_O2 = (2.0 x 10³ mol / (4.5 x 103 mol + 1.0 x 10³ mol)

X_O2  = 1.0 x 10³ / 5.5 x 10³

 X_O2 = 0.18

Example 2

Determine the mole fraction of CH₃OH and H₂O in a solution prepared by dissolving 5.5 g of alcohol in 40 g of H₂O. M of H₂O is 18 and M of CH₃OH is 32.

Solution

Moles of CH₃OH = 5.5 / 32 = 0.17 mole

Moles of H₂O = 40 / 18 = 2.2 moles

Therefore, according to the equation

mole fraction of CH₃OH = 0.17 / 2.2 + 0.17

mole fraction of CH₃OH = 0.073

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