Parts Per Million (ppm)
Parts per million (ppm) is a unit used to measure very small concentrations of a substance (solute) in a mixture or solution. It is defined as one part of the solute per one million parts of the total solution. For example, if you have one gram of salt dissolved in a million grams of water, the salt concentration would be 1 ppm.
This measurement makes ppm particularly suitable for expressing quantities that are too small to be represented in percentages or standard units like grams or liters. It is commonly used in environmental science, food safety, medicine, and various industrial processes. [1-4]
Formula
Mathematically, ppm is calculated using the following formula: [1-4]
ppm = (Mass of solute/ Mass of solution) x 106
This formula applies to both solid and liquid mixtures. In contexts such as gases, ppm is measured based on volume rather than mass. For instance, the concentration of carbon dioxide in the atmosphere is often expressed in ppm by volume. It is important to note that the mass of the solution includes both the solute and the solvent.
ppm is often converted to molarity for use in chemical calculations.
Parts Per Million to Molarity
Converting parts per million to molarity is useful when dealing with chemical solutions where concentrations are expressed in ppm, but calculations require molarity. Molarity is defined as the number of moles of solute per liter of solution. [1-4]
The relationship between ppm and molarity (M) can be expressed as:
M = ppm/(Msolute x 1000)
Where Msolute is the molar mass of the solute in g/mol. The factor 1000 converts ppm expressed in mg/L to g/L.
Beyond ppm: Parts Per Billion (ppb)
In some cases, measuring even smaller concentrations is necessary. For these scenarios, the unit parts per billion (ppb) is used, which is 1,000 times smaller than ppm. Ppb describes one part of a substance in one billion (1,000,000,000) parts of the total solution or mixture. [1-4]
The mathematical formula for ppb is similar to that of ppm, except the scaling factor is 109 instead of 106.
ppb = (Mass of solute)/(mass of solution) x 109
Applications [1-4]
- Environmental Monitoring: Tracks air pollutants (e.g., CO2, SO2), water contaminants (e.g., lead, mercury, arsenic), and pesticide residues in soil and water.
- Food Safety: Ensures safe levels of pesticides, additives, and preservatives in food products.
- Medicine: Monitors impurities in drugs and vaccines and analyzes electrolytes in intravenous fluids.
- Industrial Use: Verifies raw material purity and chemical additives in industrial processes.
- Forensic Science: Detects toxins or drugs in biological samples and analyzes trace elements in criminal investigations.
- Air Quality Control: Monitors urban air pollutants and oxygen levels in confined spaces, such as submarines.
Example Problems with Solutions
Problem 1: A sample of drinking water contains 0.005 grams of fluoride in 1 liter of water. Calculate the concentration of fluoride in ppm. Assume the density of water is 1 g/mL.
Solution
Given:
Mass of fluoride = 0.005 g
Mass of water = Volume of water x Density of water = 1 L x 1000 g/L = 1000 g.
Use the formula:
ppm = (Mass of fluoride)/(Mass of water) x 106
=> ppm = (0.005/1000) x 106 = 5 ppm
Problem 2: The concentration of carbon dioxide in a gas mixture is measured as 0.0004% by volume. Express this concentration in ppm.
Solution
1. Convert the percentage to a fraction:
0.0004% = 0.0004/100 = 0.000004
2. Multiply by 106 to convert to ppm:
ppm = 0.000004 x 106 = 4 ppm
Problem 3: A saline solution contains 0.02 grams of salt in 500 grams of water. What is the salt concentration in ppm?
Solution
Total mass of the saline solution = 0.02 g (salt) + 500 g (water) = 500.02 g.
Use the ppm formula:
ppm = (Mass of solute)/(Mass of solution) x 106
=> ppm = (0.02/500.02) x 106 ~ 40 ppm (rounded to two significant figures)
Problem 4: A laboratory test reveals that a fish sample contains 2 milligrams (mg) of mercury in a 1 kg sample of fish. Calculate the mercury concentration in ppm.
Solution
1. Convert the units for consistency:
2 mg = 0.002 g
1 kg = 1000 g
2. Use the ppm formula:
ppm = (Mass of solute)/(Mass of solution) x 106
=> ppm = (0.002/1000) x 106 = 2 ppm