Parts per Million (ppm) and Parts per Billion (ppb): Calculations and Applications in Solution Chemistry

Concentration Units: Parts per Million (ppm) and Parts per Billion (ppb)

Introduction to ppm and ppb

In chemistry, extremely dilute solution concentrations are often expressed in parts per million (ppm) or parts per billion (ppb). These units are useful for describing trace amounts of solute in a large quantity of solvent, especially in environmental and biological contexts.

• ppm stands for parts per million, representing 1 part solute per 1,000,000 parts solution.

• ppb stands for parts per billion, representing 1 part solute per 1,000,000,000 parts solution.

• Units can be mass-based (grams) or volume-based (milliliters).

Calculating ppm and ppb

There are two main ways to express ppm and ppb: by mass or by volume. The formulas are as follows:

• Parts per Million (ppm):

Type	Formula
Mass	$\text{ppm} = \frac{\text{g solute}}{\text{g solution}} \times 10^6$
Volume	$\text{ppm} = \frac{\text{ml solute}}{\text{ml solution}} \times 10^6$

• Parts per Billion (ppb):

Type	Formula
Mass	$\text{ppb} = \frac{\text{g solute}}{\text{g solution}} \times 10^9$
Volume	$\text{ppb} = \frac{\text{ml solute}}{\text{ml solution}} \times 10^9$

Examples and Applications

• Example 1 (ppm): What is the concentration in parts per million of DDT (nonbiodegradable pesticide) in 2.0 mg in 1.0 kg needlefish tissue?

  • Convert mg to g: 2.0 mg = 0.002 g

  • 1.0 kg = 1000 g

  • Apply formula: $\text{ppm} = \frac{0.002}{1000} \times 10^6 = 2.0$ ppm

• Example 2 (ppb): A 2.4 L sample of an aqueous solution contains 0.012 mL of NH3. What is the concentration of NH3 in the solution, expressed as parts per billion?

  • Convert L to mL: 2.4 L = 2400 mL

  • Apply formula: $\text{ppb} = \frac{0.012}{2400} \times 10^9 = 5000$ ppb

Practice Problems

• 1. Calculate the concentration in ppm: A 5.12 L sample of solution contains 0.239 g of potassium sulfate, K2SO4. The density of the solution is 1.30 g/mL.

  • Convert volume to mass: $5.12 \text{ L} = 5120 \text{ mL}$; $5120 \text{ mL} \times 1.30 \text{ g/mL} = 6656 \text{ g}$

  • Apply formula: $\text{ppm} = \frac{0.239}{6656} \times 10^6 \approx 35.9$ ppm

  • Answer marked: 26.8 ppm (original calculation)

• 2. Calculate the concentration in ppb: 0.91 mg of caffeine in 131 mL solution.

  • Convert mg to g: 0.91 mg = 0.00091 g

  • Apply formula: $\text{ppb} = \frac{0.00091}{131} \times 10^9 \approx 6,946$ ppb

  • Answer marked: 0.00069 ppb (original calculation)

• 3. Calculate glucose concentration in ppm: Glucose makes up about 0.102% by mass of human blood.

  • Convert percent to ppm: $0.102\% = 0.102 \times 10^4 = 1020$ ppm

  • Answer marked: 0.102 ppm (original calculation)

• 4. Calculate mass of arsenic in blood: Average human body contains 5,000 g of blood; arsenic concentration is 0.86 ppb.

  • Apply formula: $\text{mass} = \text{ppb} \times \frac{\text{g solution}}{10^9}$

  • $0.86 \times \frac{5000}{10^9} = 4.3 \times 10^{-6}$ g

  • Answer marked: 4.3 x 10-6 g

• 5. Calculate volume of water containing chlorobenzene: Water sample contains 16 ppm chlorobenzene; total volume is 5.01 x 102 mL.

  • Apply formula: $\text{volume} = \frac{\text{ppm} \times \text{total volume}}{10^6}$

  • $16 \times 5.01 \times 10^2 / 10^6 = 8.016 \times 10^{-3}$ mL

  • Answer marked: 8.016 x 10-3 mL

Summary Table: ppm and ppb Calculations

Unit	Formula (mass)	Formula (volume)	Typical Application
ppm	$\frac{\text{g solute}}{\text{g solution}} \times 10^6$	$\frac{\text{ml solute}}{\text{ml solution}} \times 10^6$	Environmental analysis, blood chemistry
ppb	$\frac{\text{g solute}}{\text{g solution}} \times 10^9$	$\frac{\text{ml solute}}{\text{ml solution}} \times 10^9$	Trace contaminants, toxicology

Key Points

• ppm and ppb are used for very dilute concentrations.

• Always match units (mass/mass or volume/volume) when applying formulas.

• These units are common in environmental, biological, and analytical chemistry.

Additional info: Calculations above are based on standard formulas for ppm and ppb. Some answer choices in the original file may reflect rounding or alternative calculation methods.