Coaching Centre
Measuring concentration
Solutions, solutes and solvents, and every concentration unit used in HSC Chemistry: g/L, %(w/w), %(w/v), %(v/v), parts per million and per billion, and mol/L, with conversions between them and real Australian examples from drinking water, food and wine.
The same small number can be harmless or deadly depending on its unit. Australian tap water is fluoridated at about 1 ppm. Lead is allowed at no more than 0.01 ppm. A wine label says 13.5%, a vinegar bottle 4%, a saline drip 0.9%. Each of these numbers is a concentration, and each industry has its favourite way of writing it.
Solutions
A solution is a homogeneous mixture of a solute dissolved in a solvent. When water is the solvent, the solution is aqueous (aq). Concentration is the amount of solute in a given amount of solution. A concentrated solution has a lot of solute per unit volume and a dilute one has little; these words are comparisons, not numbers. A saturated solution holds the maximum amount of solute that will dissolve at that temperature, and that limit is the solubility.
Every concentration unit has the same shape:
concentration = amount of solute ÷ amount of solution
The units differ only in how each amount is measured: as a mass, a volume or a number of moles.
The units
| Unit | Meaning | Typical use |
|---|---|---|
| g L⁻¹ | grams of solute per litre of solution | salinity, sugar in soft drinks |
| %(w/w) | grams of solute per 100 g of solution (or mixture) | solids and creams, concentrated acids |
| %(w/v) | grams of solute per 100 mL of solution | medical solutions, vinegar, bleach |
| %(v/v) | mL of liquid solute per 100 mL of solution | alcoholic drinks, hand sanitiser |
| ppm | parts per million: mg per kg, or for dilute aqueous solutions mg per L | water quality, pollutants, trace elements |
| ppb | parts per billion: µg per kg, or µg per L | very toxic contaminants |
| mol L⁻¹ (molarity) | moles of solute per litre of solution | the chemist's unit for reactions (2F) |
The "w" in %(w/w) and %(w/v) means mass (it comes from "weight"). You may also see %(m/m) and %(m/v).
Percentage concentrations
(a) 10.0 g of sugar is dissolved in 90.0 g of water. The mass of solution is 100.0 g, so the concentration is 10.0 ÷ 100.0 × 100 = 10.0%(w/w). (Divide by the mass of solution, not the mass of water.)
(b) A saline drip is 0.90%(w/v) NaCl. A 500 mL bag contains 0.90 g per 100 mL × 5 = 4.5 g of NaCl.
(c) A 750 mL bottle of wine is 13.5%(v/v) ethanol. Volume of ethanol = 13.5 ÷ 100 × 750 = 101 mL.
Parts per million
For very small concentrations, percentages need too many zeros. One part per million means 1 g of solute in 10⁶ g of mixture, which is the same as 1 mg per kg. A litre of dilute aqueous solution has a mass of almost exactly 1 kg, so for water samples 1 ppm = 1 mg L⁻¹. One ppm is 10⁻⁴ %.
$$\text{ppm} = \frac{\text{mass of solute (mg)}}{\text{mass of solution (kg)}} \approx \frac{\text{mass of solute (mg)}}{\text{volume of solution (L)}}$$
A 250 mL sample of bore water contains 3.5 mg of lead. Calculate the concentration in ppm and compare it with the Australian Drinking Water Guidelines limit of 0.01 mg L⁻¹.
ppm = 3.5 mg ÷ 0.250 L = 14 mg L⁻¹ = 14 ppm.
That is 1400 times the guideline value: this water must not be drunk.
A 200 g fillet of shark contains 0.16 mg of mercury. The Food Standards Australia New Zealand maximum for shark is 1.0 mg kg⁻¹. Is it within the limit?
ppm = 0.16 mg ÷ 0.200 kg = 0.80 mg kg⁻¹ = 0.80 ppm. Yes, it is under 1.0 ppm. For solids, always divide by mass in kg, never by a volume.
Parts per billion work the same way, with µg instead of mg: 1 ppb = 1 µg L⁻¹ = 0.001 ppm. The guideline for arsenic in drinking water, 0.01 mg L⁻¹, is 10 ppb.
Molarity and converting between units
Chemists prefer molarity (mol L⁻¹, sometimes written M) because reactions happen between numbers of particles, not masses. You'll use it constantly from 2F onwards. To convert between mass-based units and mol L⁻¹, go through g L⁻¹ and divide by the molar mass:
mol L⁻¹ = g L⁻¹ ÷ M g L⁻¹ = mol L⁻¹ × M
White vinegar is 4.0%(w/v) ethanoic acid, CH₃COOH (M = 60.05 g mol⁻¹). Express this in g L⁻¹ and mol L⁻¹.
4.0 g per 100 mL = 40 g per 1000 mL = 40 g L⁻¹.
40 ÷ 60.05 = 0.67 mol L⁻¹.
Fluoridated tap water contains 1.0 ppm fluoride ions. What is [F⁻] in mol L⁻¹?
1.0 ppm = 1.0 mg L⁻¹ = 1.0 × 10⁻³ g L⁻¹.
1.0 × 10⁻³ ÷ 19.00 = 5.3 × 10⁻⁵ mol L⁻¹.
- Dissolve 5.85 g of NaCl to make 500 mL. Check: 11.7 g L⁻¹, 1.17%(w/v), 0.200 mol L⁻¹ and 11 700 ppm.
- Keep the mass and double the volume to 1000 mL. Which numbers halve? Do any stay the same?
- Choose NaF (fluoridation): 2.21 mg in 1000 mL gives exactly 1.00 ppm of fluoride. Why is the ppm of NaF bigger than the ppm of F⁻?
- Choose ethanol: 60 mL in 500 mL is 12.0%(v/v), like a table wine. What is that in mol L⁻¹? (About 2.06.)
Test yourself
25.0 g of potassium nitrate is dissolved in water to make 200 mL of solution. What is the concentration in %(w/v)?
25.0 g per 200 mL = 12.5 g per 100 mL.
A 2.0 L water sample contains 0.30 mg of copper ions. What is the concentration of copper in ppm?
0.30 mg ÷ 2.0 L = 0.15 mg L⁻¹ = 0.15 ppm.
What is the molarity of a 5.85 g L⁻¹ solution of sodium chloride?
5.85 ÷ 58.44 = 0.100 mol L⁻¹.
Which concentration is the largest?
In mg L⁻¹: 50; 0.0030 g per 100 mL = 30; 100; 40. So 0.10 g L⁻¹ is the largest.
Hand sanitiser is 70%(v/v) ethanol. How much ethanol is in a 375 mL bottle?
0.70 × 375 = 262.5 mL.
Sort each unit by what it divides.
A solution is made of a dissolved in a solvent. %(w/v) is the mass in grams per of solution. For a dilute aqueous solution, 1 ppm equals 1 per litre. To convert g L⁻¹ to mol L⁻¹, divide by the .
The Australian Drinking Water Guidelines set a health limit of 50 mg L⁻¹ for nitrate ions (NO₃⁻), to protect babies from a blood disorder. A farm bore sample of 500.0 mL contains 0.0410 g of nitrate. (a) Calculate the nitrate concentration in ppm and decide whether the water is safe for infants. (b) Express the concentration in mol L⁻¹. (c) Explain why ppm and mg L⁻¹ can be treated as the same unit here.
(a) 0.0410 g = 41.0 mg; 41.0 mg ÷ 0.5000 L = 82.0 mg L⁻¹ = 82.0 ppm. This is above the 50 mg L⁻¹ guideline, so the water should not be used for babies' bottles.
(b) 82.0 mg L⁻¹ = 0.0820 g L⁻¹; M(NO₃⁻) = 14.01 + 3 × 16.00 = 62.01 g mol⁻¹; c = 0.0820 ÷ 62.01 = 1.32 × 10⁻³ mol L⁻¹.
(c) ppm is strictly mg of solute per kg of solution. The solution is very dilute, so its density is essentially that of water, 1.00 g mL⁻¹; 1 L therefore has a mass of 1.00 kg and mg L⁻¹ equals mg kg⁻¹.