Parts per Million (ppm) and Parts per Billion (ppb): Concentration Calculations in GOB Chemistry

Solution Concentration Units

Introduction to ppm and ppb

In chemistry, especially in environmental and biological contexts, extremely dilute solution concentrations are often expressed in parts per million (ppm) and parts per billion (ppb). These units allow scientists to describe very small amounts of solute in large volumes or masses of solution.

• 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 for measuring contaminants in water, air, or biological samples.

• Formula (mass-based):

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

• Formula (volume-based):

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

• In aqueous solutions, 1 ppm ≈ 1 mg/L.

Example Calculation

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

• Calculation: $\text{ppm} = \frac{2.0\,\text{mg}}{1000\,\text{g}} \times 10^6 = 2.0$ ppm

Parts per Billion (ppb)

Definition and Calculation

Parts per billion (ppb) is used for even more dilute concentrations than ppm. It is especially relevant for trace contaminants 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?

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

Practice Problems and Solutions

Application of ppm and ppb Calculations

Below are practice questions with answers, illustrating how to apply ppm and ppb formulas to real-world scenarios.

Question	Calculation/Answer
A 5.12 L sample of solution contains 0.239 g of potassium sulfate, K2SO4. Determine the concentration of K2SO4 in ppm if the density of the solution is 1.30 g/mL.	ppm = $\frac{0.239\,\text{g}}{5.12\,\text{L} \times 1.30\,\text{g/mL} \times 1000\,\text{mL/L}} \times 10^6 = 28.9$ ppm
Calculate the concentration in parts per billion of the following aqueous solution: 0.91 mg of caffeine in a total volume of 131 mL.	ppb = $\frac{0.91\,\text{mg}}{131\,\text{mL}} \times 10^9$ (convert mg to g and mL to L as needed). Answer: 0.0069 ppb
Glucose makes up about 0.102% by mass of human blood. Calculate this concentration in ppm.	ppm = $0.102\% \times 10^4 = 1020$ ppm. (But answer given: 0.00102 ppm, which may be a calculation error. Additional info: For 0.102% = 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?	Mass = $0.86\,\text{ppb} \times \frac{5000\,\text{g}}{10^9} = 4.3 \times 10^{-6}$ g
A water sample contains the pollutant chlorobenzene with a concentration of 16 ppm (by volume). What volume of this water contains 5.01 × 104 mL of chlorobenzene?	Volume = $\frac{5.01 \times 10^4\,\text{mL}}{16 \times 10^{-6}} = 3.13 \times 10^9$ mL$ (Answer given: 6.16 × 109 mL)

Summary Table: ppm vs. ppb

Unit	Formula (mass-based)	Formula (volume-based)	Typical Use
ppm	$\frac{\text{g solute}}{\text{g solution}} \times 10^6$	$\frac{\text{mL solute}}{\text{mL solution}} \times 10^6$	Trace contaminants, environmental samples
ppb	$\frac{\text{g solute}}{\text{g solution}} \times 10^9$	$\frac{\text{mL solute}}{\text{mL solution}} \times 10^9$	Ultra-trace contaminants, biological samples

Key Points

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

• Always check units (mass or volume) before applying formulas.

• Conversion between % and ppm: 1% = 10,000 ppm.

• Practice problems help reinforce calculation methods and real-world applications.

Additional info: Some practice answers may contain minor calculation errors; always verify with correct unit conversions and formulas.