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

Solution Concentration Units

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 solutes in large volumes or masses of solvent, such as pollutants in water or blood components.

• 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).

Parts per Million (ppm)

Definition and Calculation

Parts per million (ppm) is a unit used to express very dilute concentrations of substances. It is commonly used in environmental chemistry, medicine, and analytical chemistry.

• Formula (mass-based):

$\text{ppm} = \frac{\text{g of solute}}{\text{g of solution}} \times 10^6$

• Formula (volume-based):

$\text{ppm} = \frac{\text{ml of solute}}{\text{ml of solution}} \times 10^6$

• 1 ppm = 1 mg solute per 1 L solution (for aqueous solutions).

Example Calculation

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

• Given: 2.0 mg DDT, 1.0 kg tissue

• Convert units: 2.0 mg = 0.002 g, 1.0 kg = 1000 g

• Apply formula:

$\text{ppm} = \frac{0.002\,\text{g}}{1000\,\text{g}} \times 10^6 = 2\,\text{ppm}$

Practice Question

• A 5.12 L sample of solution contains 0.233 g of potassium sulfate, K2SO4. Determine the concentration of K2SO4 in ppm if the density of the solution is 1.30 g/mL.

• Answer: 34.6 ppm

Parts per Billion (ppb)

Definition and Calculation

Parts per billion (ppb) is used for even more dilute concentrations than ppm. It is commonly used for trace analysis in environmental and biological samples.

• Formula (mass-based):

$\text{ppb} = \frac{\text{g of solute}}{\text{g of solution}} \times 10^9$

• Formula (volume-based):

$\text{ppb} = \frac{\text{ml of solute}}{\text{ml of solution}} \times 10^9$

Example Calculation

Example: 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?

• Given: 0.012 mL NH3, 2.4 L = 2400 mL solution

• Apply formula:

$\text{ppb} = \frac{0.012\,\text{mL}}{2400\,\text{mL}} \times 10^9 = 5000\,\text{ppb}$

Practice Question

• Calculate the concentration in parts per billion of 0.91 mg of caffeine in a total volume of 131 mL.

• Answer: 0.0069 ppb

Applications and Practice Problems

Common Uses of ppm and ppb

• Environmental monitoring (e.g., pollutants in water or air)

• Medical and biological analysis (e.g., glucose in blood)

• Food safety and toxicology

Practice Problems and Solutions

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

• Answer: 1020 ppm

• The average human body contains about 5,000 grams of blood. What mass of arsenic is present in the body if the amount in blood is 0.86 ppb?

• Answer: $4.3 \times 10^3$ g

• A water sample contains the pollutant chlorobenzene with a concentration of 16 ppm (by volume). What volume of this water contains $5.01 \times 10^4$ mL of chlorobenzene?

• Answer: $1.6 \times 10^6$ mL

Comparison Table: ppm vs. ppb

Unit	Definition	Formula	Typical Use
ppm	Parts per million (1 part in $10^6$)	$\frac{\text{g solute}}{\text{g solution}} \times 10^6$	Trace pollutants, blood components
ppb	Parts per billion (1 part in $10^9$)	$\frac{\text{g solute}}{\text{g solution}} \times 10^9$	Ultra-trace analysis, environmental toxins

Summary

• ppm and ppb are essential units for expressing very low concentrations in chemistry.

• They are calculated using mass or volume ratios multiplied by $10^6$ (ppm) or $10^9$ (ppb).

• These units are widely used in environmental, medical, and analytical chemistry for monitoring trace substances.