3.4 Other Units for Solution Concentrations

Solution concentration units are essential for describing the amount of solute in a solution. From mass percentage to molarity, these units help chemists quantify and communicate solution compositions accurately.

Understanding these units and how to convert between them is crucial for various applications. Whether working in a lab or analyzing environmental samples, mastering solution concentration units is key to success in chemistry.

Solution Concentration Units

Mass percentage, volume percentage, and mass-volume percentage as solution concentration units

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• Mass percentage (% w/w) represents the ratio of solute mass to total solution mass multiplied by 100%
  • Calculated using the formula: $\text{Mass percentage} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100\%$
  • Commonly used for solid-solid or solid-liquid solutions (salt in water)
• Volume percentage (% v/v) represents the ratio of solute volume to total solution volume multiplied by 100%
  • Calculated using the formula: \text{[Volume percentage](https://www.fiveableKeyTerm:Volume_Percentage)} = \frac{\text{Volume of solute}}{\text{Volume of solution}} \times 100\%
  • Commonly used for liquid-liquid solutions (ethanol in water)
• Mass-volume percentage (% w/v) represents the ratio of solute mass to total solution volume multiplied by 100%
  • Calculated using the formula: $\text{Mass-volume percentage} = \frac{\text{Mass of solute}}{\text{Volume of solution}} \times 100\%$
  • Commonly used for solid-liquid solutions (glucose in saline)
  • Frequently used in medical and pharmaceutical settings (antibiotics, intravenous fluids)

Parts-per-million and parts-per-billion

• Parts-per-million (ppm) represents the ratio of solute mass or volume to total solution mass or volume multiplied by 1,000,000
  • Calculated using the formula: $\text{ppm} = \frac{\text{Mass or volume of solute}}{\text{Mass or volume of solution}} \times 1,000,000$
  • 1 ppm is equivalent to 1 mg/L or 1 mg/kg
  • Used for very dilute solutions (contaminants in drinking water, pesticides in food)
• Parts-per-billion (ppb) represents the ratio of solute mass or volume to total solution mass or volume multiplied by 1,000,000,000
  • Calculated using the formula: $\text{ppb} = \frac{\text{Mass or volume of solute}}{\text{Mass or volume of solution}} \times 1,000,000,000$
  • 1 ppb is equivalent to 1 μg/L or 1 μg/kg
  • Used for extremely dilute solutions (trace contaminants in air, toxic substances in soil)

Mole-based concentration units

• Molarity (M) represents the number of moles of solute per liter of solution
  • Calculated using the formula: $\text{Molarity} = \frac{\text{Moles of solute}}{\text{Liters of solution}}$
  • Commonly used in laboratory settings and chemical reactions
• Molality (m) represents the number of moles of solute per kilogram of solvent
  • Calculated using the formula: $\text{Molality} = \frac{\text{Moles of solute}}{\text{Kilograms of solvent}}$
  • Used when temperature changes affect solution volume
• Mole fraction represents the ratio of moles of a component to the total moles of all components in a solution
  • Calculated using the formula: $\text{Mole fraction of A} = \frac{\text{Moles of A}}{\text{Total moles of all components}}$
  • Used in thermodynamic calculations and vapor pressure studies
• Normality (N) represents the number of equivalents of solute per liter of solution
  • Calculated using the formula: $\text{Normality} = \frac{\text{Equivalents of solute}}{\text{Liters of solution}}$
  • Used in acid-base titrations and redox reactions

Conversion of concentration units

• Converting molarity to mass percentage:
  1. Convert molar mass of solute to grams per liter (g/L)
  2. Divide solute mass by solution density to obtain mass fraction
  3. Multiply mass fraction by 100% to get mass percentage
• Converting mass percentage to molarity:
  1. Convert mass percentage to mass fraction by dividing by 100%
  2. Multiply mass fraction by solution density to obtain solute mass per liter (g/L)
  3. Divide solute mass per liter by molar mass of solute to get molarity
• Converting volume percentage to molarity:
  1. Convert volume percentage to volume fraction by dividing by 100%
  2. Multiply volume fraction by solute density to obtain solute mass per liter (g/L)
  3. Divide solute mass per liter by molar mass of solute to get molarity
• Converting molarity to parts-per-million (ppm) or parts-per-billion (ppb):
  1. Convert molarity to grams per liter (g/L) by multiplying by molar mass of solute
  2. Multiply grams per liter by 1,000 to obtain milligrams per liter (mg/L) for ppm, or by 1,000,000 to obtain micrograms per liter (μg/L) for ppb