Concentration Calculations

Percent Concentration

  • Concentration can be expressed as mol/L (M) or as a percentage.

Percent by Mass (% m/m)

  • mass of solutemass of solution×100\frac{\text{mass of solute}}{\text{mass of solution}} \times 100
  • Units for mass must be the same on the top and bottom (e.g., mg, g, kg).
  • Mass of solution = mass of solute + mass of solvent.
  • Example:
    • 1.4 g of solid sodium chloride is dissolved in 5.0 g of water. Determine the % (m/m).

Percent by Volume (% v/v)

  • volume of solutevolume of solution×100\frac{\text{volume of solute}}{\text{volume of solution}} \times 100
  • Units for volume must be the same on the top and bottom (e.g., mL, L).
  • Example:
    • 80.0 mL of ethanol is diluted to a volume of 250 mL with water. Find the percent by volume.

Percent Mass by Volume (% m/v)

  • mass of solutevolume of solution×100\frac{\text{mass of solute}}{\text{volume of solution}} \times 100
  • A formula for antifungal shampoo contains 2% (m/v) ketoconazole. How many grams of ketoconazole would be needed to prepare a solution of 25 L?

Parts Per Million (ppm) and Parts Per Billion (ppb)

  • Used for very dilute solutions (less than 1% m/m).
  • Units: mass units must be the same on the top and bottom.
  • Parts Per Million (ppm): mass of solutemass of solution×106\frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6
  • Parts Per Billion (ppb): mass of solutemass of solution×109\frac{\text{mass of solute}}{\text{mass of solution}} \times 10^9
  • Example:
    • Researchers found 0.003 g of mercury in a 1000 kg sample of water. What is the concentration of mercury in parts per billion?