Question

A solution contains A, B and C components. If the mole fraction of components A and B are 0.35 and 0.25 respectively. Then calculate the mole fraction of component C.

Answer 1

Hint: Mole fraction is defined as the amount (number of moles or molecules) of a constituent or component divided by the total amount of all the constituent or component present. It is an important concentration term. It is denoted by the symbol $x$ and the subscript describes the component present. Mole fractions are dimensionless.

Complete answer:
Mole fraction=Number of moles of component/Total number of moles of all the components
Suppose we have a mixture with 3 components A, B and C.
Mole fraction of A $ = {x_A} = \dfrac{{{n_A}}}{{{n_A} + {n_B} + {n_C}}}$
Mole fraction of B $ = {x_B} = \dfrac{{{n_B}}}{{{n_A} + {n_B} + {n_C}}}$
Mole fraction of C $ = {x_C} = \dfrac{{{n_C}}}{{{n_A} + {n_B} + {n_C}}}$
In a given solution the sum of all the mole fractions is equal unity.
Mathematically we can say, ${x_A} + {x_B} + {x_C} = 1 - - - - - (1)$
In the question we are given Mole fraction of component A is 0.35 and Mole fraction of component B is 0.25.
From Equation (1) we can find the mole fraction of C,
$
  0.35 + 0.25 + {x_C} = 1 \\
  0.60 + {x_C} = 1 \\
  {x_C} = 0.40 \\
$
Therefore the Mole fraction of component C is 0.40.

Additional Information:
In a mixture of Ideal gas, Mole fraction is calculated as the ratio of partial pressure of a gas to the total partial pressure of the mixture.

Note:
We can calculate Mole fraction using other concentration terms like Molality, Molarity etc. Mole fraction is useful when we have 2 or more reactive components mixed together. Mole fraction does not depend on temperature. The concept is of use in construction of the phase diagram.