A solution contains three components A, B and C, 0.2 mole each, then sum of their mole fractions is:

Concept:

• The total number of moles of a compound divided by the total number of moles of all constituents gives us mole fraction.
• Mathematically, it can be expressed as:

\({X_1} = \;\frac{{no.\;of\;moles\;of\;sustance\;1}}{{total\;number\;of\;moles\;in\;the\;solution}}\)

Calculate Mole Fractions
For each component (A, B, C), the mole fraction \(X\) is calculated as:
\( X_{\text{A}} = \frac{\text{moles of A}}{\text{total moles}} = \frac{0.2}{0.6} = \frac{1}{3} \)
\( X_{\text{B}} = \frac{\text{moles of B}}{\text{total moles}} = \frac{0.2}{0.6} = \frac{1}{3}\)
\( X_{\text{C}} = \frac{\text{moles of C}}{\text{total moles}} = \frac{0.2}{0.6} = \frac{1}{3} \)

Sum of all mole fraction of all = 1/3 +1/3 + 1/3 = 1

• The total mole fraction of a solution always adds up to 1.

\(\sum {X_i = 1} \)

Mole fraction unit is very useful in relating some physical properties of solutions, says vapour pressure with the concentration of the solution and quite useful in describing the calculations involving gas mixtures.

Formula -

Mole Fraction = Moles of one component / Total moles of all component 

X_A+X_B+X_C = (N_A/ N_A+N_B+N_C) + (N_B/ NA+NB+N_C) + (N_C/ NA+NB+N_C) = 1