Which of the following has no units?

Options

A. Molarity
B. Molality
C. Normality
D. Mole fraction

Explanation

To determine which of the following has no units, we will analyze the given concentration terms one by one:

1. **Molarity (M)**:
- Definition: Molarity is defined as the number of moles of solute per liter of solution.
- Units: Molarity = moles/liter (mol/L)
- Conclusion: Molarity has units.

2. **Molality (m)**:
- Definition: Molality is defined as the number of moles of solute per kilogram of solvent.
- Units: Molality = moles/kilogram (mol/kg)
- Conclusion: Molality has units.

3. **Normality (N)**:
- Definition: Normality is defined as the number of equivalents of solute per liter of solution.
- Units: Normality = equivalents/liter (eq/L)
- Conclusion: Normality has units.

4. **Mole Fraction (χ)**:
- Definition: Mole fraction is defined as the ratio of the number of moles of a component to the total number of moles of all components in the mixture.
- Calculation: Mole fraction of component A = (moles of A) / (moles of A + moles of B)
- Since both the numerator and denominator are in moles, the units cancel out.
- Conclusion: Mole fraction is unitless.

Based on the analysis, the correct answer is that the **Mole Fraction** has no units.

### Summary of Steps:
1. Define each concentration term (Molarity, Molality, Normality, Mole Fraction).
2. Identify the units associated with each term.
3. Determine which term has no units by checking if the units cancel out.