Concentration of Solutions

Rucete ✏ Chemistry In a Nutshell

1. Molarity (M) vs. Molality (m)

Term	Definition	Formula	Unit
Molarity (M)	Moles of solute per liter of solution	$M = \frac{\text{moles of solute}}{\text{liters of solution}}$	mol/L
Molality (m)	Moles of solute per kilogram of solvent	$m = \frac{\text{moles of solute}}{\text{kg of solvent}}$	mol/kg

• Key Differences:
  • Molarity (M) depends on volume (affected by temperature changes).
  • Molality (m) depends on mass (independent of temperature).

2. Density & Percent Concentration

1. Density ($d$)

   • Measures the mass per unit volume of a solution.
   • Formula: $$d = \frac{\text{mass of solution}}{\text{volume of solution}}$$

2. Percent Concentrations:

   • Mass Percent (% w/w): $$\% w/w = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\%$$
   • Volume Percent (% v/v) (used for liquid mixtures): $$\% v/v = \frac{\text{volume of solute}}{\text{total volume of solution}} \times 100\%$$

3. Dilution Formula

• Dilution = Reducing concentration by adding solvent.
• Formula: $$M_1 V_1 = M_2 V_2$$
  • $M_1, V_1$ = Initial concentration & volume.
  • $M_2, V_2$ = Final concentration & volume.

4. Mole Fraction ($X_A$)

• The fraction of one component in a mixture.
• Formula: $$X_A = \frac{\text{moles of A}}{\text{total moles of all components}}$$
• Used in gas laws & colligative properties.

Concentration Units In a nutshell

• Molarity (M) = Volume-based (mol/L).
• Molality (m) = Mass-based (mol/kg), unaffected by temperature.