Lecture: Mole Fraction

Introduction

• Mole Fraction: A way to describe the concentration of different components of a solution.
• Solution Components: Typically consists of a solute and a solvent.
  • Example: Chemical A (solute) and Chemical B (solvent).

Calculation of Mole Fraction

Mole Fraction Formula

• Symbol: ( x_A ), pronounced as "x sub A".
• Equation: [ x_A = \frac{\text{moles of A}}{\text{total moles in solution}} ]
  • Top: Moles of component A (e.g., 2.0 moles).
  • Bottom: Total moles of solution (e.g., moles of A + moles of B = 2.0 + 6.0 = 8.0 moles).

Example Calculation

1. Mole Fraction of A:
   • ( x_A = \frac{2.0}{8.0} = 0.25 )
   • Result: A dimensionless quantity (no units).
2. Mole Fraction of B:
   • ( x_B = \frac{6.0}{8.0} = 0.75 )

Key Points

• No Units: Mole fraction is a dimensionless quantity.
• Sum of Fractions: The sum of mole fractions of all components in a solution equals 1. (e.g., ( x_A + x_B = 1 ))

General Equation for Mole Fraction

• Equation: [ x_A = \frac{n_A}{n_{\text{total}}} ]
  • ( n_A ) = Number of moles of component A.
  • ( n_{\text{total}} ) = Total moles in the solution.
• Symbols: Sometimes the equation is abbreviated with symbols for simplicity.

Limitations of Certain Equations

• Two Component Limitation:
  • Simple equation: ( x_A = \frac{n_A}{n_A + n_B} )
  • Only suitable for solutions with exactly two components.
• Preference:
  • Use the total moles equation which is applicable for multiple components.

Conclusion

• Understanding different versions of the mole fraction equation is important.
• The preferred version uses total moles, accommodating solutions with more than two components.

Next Steps

• Application of these equations in practice problems in the next lecture.