Concentrations in PPM
A focused revision guide to expressing and calculating concentrations in parts per million (ppm) for Edexcel International A Level Chemistry. This page covers the meaning of ppm, the formulae for solutions and for gases in air, and full worked examples for both contexts.
- 1.4iv
What these spec points say
- 1.4iv understand the terms: parts per million (ppm), including gases in the atmosphere
GCSE Recap: Percentages and Matching Units
Before you start, check that you can convert units and work out a percentage by mass, because parts per million uses the same method.
What Does Parts Per Million (ppm) Mean?
Concentrations of solutions can also be compared using the term parts per million, or ppm. This unit is often used for very low concentrations, such as pollutants in water or trace gases in the atmosphere.
The logic is simple. Think of the word “percent”; the “cent” part refers to 100, so 50% means 50 out of 100. Parts per million means out of a million. So 50 ppm means 50 parts out of 1 000 000 parts.
The “parts” usually refer to mass for solutions, or volume for gases. The parts can be measured in any unit of mass (or volume), but the unit must be the same on the top and the bottom of the fraction.
Definition: ppm tells you how many parts of solute are present in one million parts of the total sample. For very dilute concentrations, ppm is more convenient than mol dm−3.
Useful equivalents: a concentration of 1 ppm means 1 g of solute in 1 000 000 g of solution, or 1 mg in 1 000 000 mg. Grams and milligrams are the most commonly used units for solutions.
Quick Check: What a ppm Value Means
Answer five quick questions that link ppm to percentages and to everyday amounts.
Because the units cancel inside the fraction, ppm is dimensionless; the value itself carries the meaning regardless of whether the masses are in g or mg.
Calculations for Solutions in ppm
For a solute dissolved in a solvent, the ppm formula uses masses:
The mass of solution is the mass of solute plus the mass of solvent. In a very dilute solution the mass of solute is tiny, so the mass of solution is approximately equal to the mass of solvent.
If a question gives only the mass of solvent, usually water, use it as the mass of solution. The answer is the same to 3 significant figures.
The formula can be rearranged to find a mass: mass of solute = (concentration in ppm × mass of solution) ÷ 1 000 000.
The masses can be in any units, but they must be the same units on the top and the bottom. If they are given in different units, convert one of them before substituting.
Example A: Solute in solvent
A solution contains 0.176 g of solute dissolved in 750 g of solvent. What is the concentration in ppm?
The solution is very dilute, so the mass of solution is taken as the mass of solvent, 750 g. The two masses are already in the same unit (both in grams), so the values can be directly inserted into the expression.
Watch the units: if the question gives the solute in mg and the solvent in g, convert one of them so they match. Either change the solute to g (divide by 1000) or the solvent to mg (multiply by 1000) before substituting.
Quick Check: ppm of a Dissolved Solute
Calculate three concentrations in ppm, matching the mass units before you divide.
The multiplication by 1 000 000 is what shifts a tiny mass ratio into a value that can be quoted as a whole number, which is why ppm is the standard way to report trace pollutants.
Calculations for Gases in ppm
For gases in air, the ppm formula uses volumes rather than masses, because gas concentrations are most easily measured by volume.
The volumes can be in any unit (dm3, cm3, m3), but they must be the same on the top and the bottom of the fraction.
Example B: Finding the volume of a trace gas
5000 dm3 of air is found to contain ozone with a concentration of 87 ppm. What volume of ozone is in this sample of air?
Rearrange the expression to make the volume of gas the subject:
Volume of gas = (concentration in ppm × volume of air) ÷ 1 000 000
Learning tip: for ppm calculations with solutions, use the expression involving masses. For ppm calculations with gases, use the expression involving volumes. Mixing the two is a common error.
Quick Check: ppm of a Trace Gas
Choose the correct concentration for a gas in air when the two volumes are given in different units.
Atmospheric carbon dioxide is reported in ppm precisely because its concentration in air is far too small to make mol dm−3 a practical unit.
Comparing Two ppm Concentrations
A common exam question asks you to compare two air samples and decide which has the higher concentration of a pollutant. The strategy is to calculate the ppm value for each sample using the same formula, then compare directly.
Example C: Comparing two air samples for SO2
Two samples of air containing sulfur dioxide were analysed.
- Sample 1: 500 dm3 of air contained 37 cm3 of sulfur dioxide.
- Sample 2: 4000 dm3 of air contained 1.4 dm3 of sulfur dioxide.
Show, by calculation, which sample has the higher concentration of SO2 in ppm.
Sample 1: the volume of gas is in cm3 and the volume of air is in dm3, so first convert 37 cm3 to 0.037 dm3 (or convert 500 dm3 to 500 000 cm3; either works).
Exam tip: always state the comparison conclusion in words after the calculation. If the question says “show, by calculation, which sample…”, you must do both the maths and the verbal statement to gain full marks.
Quick Check: Mixed ppm Calculations
Work through six calculations on paper, including rearrangements and comparisons, then flip each card to check your working.
Quick Check: Thinking in Ratios
In each round, pick the one statement about ppm that is accurate.
Common Exam Points
- ppm stands for parts per million; it is a way of expressing very dilute concentrations as a whole number.
- 1 ppm means 1 part of solute in 1 000 000 parts of sample (for example, 1 g in 1 000 000 g, or 1 mg in 1 000 000 mg).
- ppm is dimensionless: the units cancel inside the fraction, leaving a pure number.
- For solutions: ppm = (mass of solute × 1 000 000) ÷ mass of solution. Masses must be in the same unit.
- For gases in air: ppm = (volume of gas × 1 000 000) ÷ volume of air. Volumes must be in the same unit.
- When the units do not match, convert one of them before substituting (1 dm3 = 1000 cm3; 1 g = 1000 mg).
- The formula can be rearranged to find the volume (or mass) of solute when the ppm value is given.
- For “show by calculation” questions, write both the working and a written comparison or conclusion.
- Common real-world applications include atmospheric CO2, ozone, sulfur dioxide and trace metal pollutants in drinking water.
FAQs
These questions address the most common points of confusion students encounter when working with ppm.
What does ppm actually mean?
ppm stands for “parts per million”. It tells you how many parts of solute (or gas) are present in 1 000 000 parts of the total sample.
So 50 ppm means 50 parts in 1 000 000 parts. The word works in the same way as “percent”, which means out of 100.
When should I use ppm instead of mol dm−3?
ppm is used for very dilute concentrations, particularly trace pollutants in water and trace gases in air. For these, mol dm−3 values would be tiny decimals that are awkward to write, so ppm gives a more readable whole number.
Does it matter what units I use for the masses or volumes?
No, as long as the units are the same on the top and the bottom of the fraction. The units cancel inside the formula, leaving ppm as a dimensionless number. If the question gives different units, convert one of them first.
What is the difference between ppm for solutions and ppm for gases?
The structure of the formula is identical, but the quantities differ. For solutions, use masses (mass of solute over mass of solution). For gases in air, use volumes (volume of gas over volume of air). Choosing the wrong one is a common mistake.
Is 1 ppm the same as 1 mg dm−3 for dilute aqueous solutions?
Approximately, yes. A dilute aqueous solution has a density close to 1 g cm−3, so 1 dm3 has a mass of about 1 000 000 mg. This is a useful approximation, not part of the formula.
How do I rearrange the ppm formula to find the mass or volume of solute?
Multiply both sides of the formula by the mass (or volume) of the sample, then divide by 1 000 000. For gases this gives: volume of gas = (ppm × volume of air) ÷ 1 000 000.
Copyright notice: This OLS revision content, including the explanations, layout, diagrams, tables and embedded learning structure, is authored for Online Learning System by Dr. Mohammed Al-Fatah. It may not be copied, reproduced, redistributed or adapted without written permission.
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