Concentration Calculations

Percent Concentration

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

Percent by Mass (% m/m)

• \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)

• \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)

• \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): \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6
• Parts Per Billion (ppb): \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?