Measures of Concentration¶
Syllabus mapping
CH-11-02 — Quantitative Chemistry. Covers: the uses of mol L⁻¹, g L⁻¹, mg L⁻¹, % (w/w), % (w/v), % (v/v), ppm and ppb; calculating molar concentration, moles and volume with \(C = \dfrac{n}{V}\); converting between concentration units; dilution problems with \(C_1V_1 = C_2V_2\); a laboratory experiment preparing a primary standard solution and performing a dilution; Aboriginal and Torres Strait Islander Peoples' methods of infusion, roasting, pounding and leaching to extract chemicals from plants and control their rate of delivery (explicit, examinable content integration point); real-world problems combining stoichiometry with reacting masses and solutions.
Wording above is paraphrased for teaching use — check the official syllabus before treating any line as verbatim NESA text.
You need to know: the different units for concentration and where each one is used, how to use \(C = \dfrac{n}{V}\) and \(C_1V_1 = C_2V_2\), how to convert between units, and how to prepare a standard solution.
Assumed knowledge check¶
Before this page makes sense, you should be comfortable with:
- Moles and \(n = \dfrac{m}{MM}\)
- Reacting-mass calculations (the four-step method)
- The words solute, solvent and solution
- Converting millilitres to litres: divide by 1000 (250 mL = 0.250 L)
Core¶
What is concentration?¶
Concentration is how much solute is dissolved in a certain amount of solution. Think of cordial: the same amount of cordial in a small glass of water tastes strong (concentrated); in a big jug it tastes weak (dilute).
There are lots of ways to measure it, because different jobs need different units.
The units and where they're used¶
| Unit | Means | Typically used for |
|---|---|---|
| mol L⁻¹ (also written M, "molar") | Moles of solute per litre of solution | Lab chemistry — anything involving reactions and equations |
| g L⁻¹ | Grams of solute per litre of solution | Making up solutions by weighing; industry |
| mg L⁻¹ | Milligrams of solute per litre | Water quality — e.g. fluoride in drinking water is around 1 mg L⁻¹ |
| % (w/w) | Grams of solute per 100 g of the whole mixture | Solids and creams — e.g. a 1% (w/w) hydrocortisone cream; 18-carat gold is 75% (w/w) gold |
| % (w/v) | Grams of solute per 100 mL of solution | Medicines and drips — e.g. saline is 0.9% (w/v): 0.9 g of salt per 100 mL |
| % (v/v) | mL of liquid solute per 100 mL of solution | Drinks — e.g. beer at 5% (v/v) alcohol has 5 mL of ethanol per 100 mL |
| ppm (parts per million) | Grams of solute per million grams of mixture — for water solutions, the same as mg L⁻¹ | Small amounts — pollutants, dissolved oxygen, chlorine in pools |
| ppb (parts per billion) | Grams of solute per billion grams — for water solutions, the same as µg L⁻¹ | Tiny amounts — e.g. lead in drinking water should be below 10 ppb |
The pattern: the smaller the amount of solute, the smaller the unit — so the numbers stay easy to read. Writing 10 ppb is a lot easier than 0.000 000 01 g mL⁻¹.
Molar concentration¶
where \(C\) = concentration (mol L⁻¹), \(n\) = moles of solute (mol), \(V\) = volume of solution in litres (L).
Concentration is written as a capital \(C\) — that's how the HSC formulae sheet writes it — to keep it separate from lowercase \(c\), which is specific heat capacity in \(q = mc\Delta T\) on the same sheet.
Rearranged: \(n = C \times V\) and \(V = \dfrac{n}{C}\).
The most common mistake: using millilitres. Always convert to litres first.
Worked example — finding concentration
\(0.250\ \text{mol}\) of sodium chloride is dissolved to make \(500\ \text{mL}\) of solution. What is its concentration?
Convert: \(500\ \text{mL} = 0.500\ \text{L}\)
Worked example — what mass do I need to weigh out?
What mass of sodium chloride is needed to make \(250.0\ \text{mL}\) of a \(0.200\ \text{mol L}^{-1}\) solution?
Step 1 — moles needed: \(n = C \times V = 0.200 \times 0.2500 = 0.0500\ \text{mol}\)
Step 2 — mass: \(m = n \times MM = 0.0500 \times 58.44 = 2.92\ \text{g}\)
Converting between units¶
Most conversions only need one or two steps:
| From | To | Do this |
|---|---|---|
| mol L⁻¹ | g L⁻¹ | × molar mass |
| g L⁻¹ | mol L⁻¹ | ÷ molar mass |
| g L⁻¹ | mg L⁻¹ | × 1000 |
| mg L⁻¹ | ppm (water solutions) | Same number |
| % (w/v) | g L⁻¹ | × 10 (because % (w/v) is per 100 mL, and 1 L is 10 × 100 mL) |
Worked example
Medical saline is 0.9% (w/v) sodium chloride. What is its concentration in mol L⁻¹?
Step 1 — to g L⁻¹: \(0.9\%\ (\text{w/v}) = 0.9\ \text{g per 100 mL} = 9\ \text{g L}^{-1}\)
Step 2 — to mol L⁻¹: \(\dfrac{9}{58.44} = 0.15\ \text{mol L}^{-1}\)
Worked example
A \(500\ \text{mL}\) water sample contains \(2.5\ \text{mg}\) of nitrate ions. What is the concentration in ppm?
Dilution¶
Diluting means adding more solvent (water). The amount of solute stays the same — it's just spread through a bigger volume. Since moles before = moles after, and \(n = CV\):
where \(C_1, V_1\) are the concentration and volume before diluting, and \(C_2, V_2\) are after. The volumes can be in mL here, as long as both are in the same unit.
Worked example — making a dilution
You need \(250\ \text{mL}\) of \(0.50\ \text{mol L}^{-1}\) hydrochloric acid. You have a stock solution of \(2.0\ \text{mol L}^{-1}\). What volume of stock do you need?
So: measure \(62.5\ \text{mL}\) of the stock acid and add water until the total volume is \(250\ \text{mL}\). (For acids, add the acid to the water, not the other way round.)
Solution stoichiometry: combining it all¶
Reacting-mass questions often involve solutions. Use the same four-step method as on the Mole Concept page — the only difference is that for a solution, you get moles from \(n = CV\) instead of \(n = \dfrac{m}{MM}\).
Worked example
What volume of \(0.100\ \text{mol L}^{-1}\) hydrochloric acid is needed to react completely with \(0.50\ \text{g}\) of calcium carbonate?
Step 1 — moles of CaCO₃: \(n = \dfrac{0.50}{100.09} = 0.00500\ \text{mol}\)
Step 2 — ratio: \(\ce{CaCO3} : \ce{HCl} = 1 : 2\), so \(n(\ce{HCl}) = 2 \times 0.00500 = 0.0100\ \text{mol}\)
Step 3 — volume of acid: \(V = \dfrac{n}{C} = \dfrac{0.0100}{0.100} = 0.100\ \text{L} = 100\ \text{mL}\)
Aboriginal and Torres Strait Islander content — placeholder, not yet written
NESA lists Aboriginal and Torres Strait Islander Peoples' methods of infusion, roasting, pounding and leaching to extract chemicals from plants and control the rate of chemical delivery as explicit, examinable syllabus content, not an optional cultural add-on. The chemistry links fit this page (extracting a substance into a solvent, and controlling how concentrated the result is and how quickly it's released), but the specific practices, plants and purposes, and whose Knowledge they are, need proper research — ideally with input from your school's Aboriginal Education team, local Community, or a community-verified source — rather than a generic paraphrase.
Deliberately left unwritten here rather than filled with unverified content.
Practical¶
Suggested prac: preparing a primary standard solution, then diluting it.
A primary standard is a substance pure and stable enough that you can weigh it out and know exactly how many moles you have. A good primary standard:
- is very pure and has a known formula
- is stable — doesn't react with air or absorb water from the air
- has a fairly high molar mass (so weighing errors matter less)
Anhydrous sodium carbonate (\(\ce{Na2CO3}\)) is a common choice.
Method:
- Calculate the mass needed (e.g. \(250.0\ \text{mL}\) of \(0.0500\ \text{mol L}^{-1}\) \(\ce{Na2CO3}\) needs \(0.01250 \times 105.99 = 1.325\ \text{g}\)).
- Weigh it accurately into a beaker and dissolve it in a little distilled water.
- Pour it into a \(250.0\ \text{mL}\) volumetric flask using a funnel. Rinse the beaker and funnel with distilled water into the flask several times, so no solute is left behind.
- Add distilled water until the bottom of the meniscus sits exactly on the line (use a dropper for the last few drops, with your eye level with the line).
- Stopper and invert the flask several times to mix.
- Dilution: use a pipette to transfer an exact volume (e.g. \(25.00\ \text{mL}\)) into a clean \(250.0\ \text{mL}\) volumetric flask and make it up to the line. Calculate the new concentration with \(C_1V_1 = C_2V_2\).
🖼️ Diagram needed — the volumetric flask steps as a short strip: weigh → dissolve in beaker → transfer and rinse → fill to the line (with a close-up of the meniscus sitting on the line, eye level) → invert to mix. TODO — placeholder until sourced/drawn.
Advanced
Why sodium hydroxide isn't a primary standard. Solid \(\ce{NaOH}\) absorbs water from the air (so you're weighing some water too) and reacts with carbon dioxide in the air. You can't be sure how many moles of \(\ce{NaOH}\) you've actually weighed. Solutions like this are standardised against a primary standard instead — which is what titration (Year 12) is for.
Serial dilutions. Diluting by a factor of 10 several times in a row (\(1.0 \to 0.10 \to 0.010 \to 0.0010\ \text{mol L}^{-1}\)) is more accurate than one giant dilution, because you never have to measure a tiny volume.
ppm for solids. For solids (soil, food), ppm means mg per kg. A soil sample with \(0.045\ \text{g}\) of lead in \(1.5\ \text{kg}\) has \(\dfrac{45\ \text{mg}}{1.5\ \text{kg}} = 30\ \text{ppm}\) lead.
Multi-step real-world problems. A typical exam question chains several steps: e.g. find the mass of \(\ce{CO2}\) from a volume and concentration of acid reacting with excess carbonate, then compare it with a measured mass loss. Write each step on its own line with units — it's much easier to find (and get marks for) each step that way.
Extension
Beyond the syllabus for this course — won't appear in the HSC, included for interest / depth study inspiration.
Measuring concentration with colour. Coloured solutions absorb more light the more concentrated they are. Instruments called colorimeters (and the more precise spectrophotometers) shine light through a sample and measure how much gets through. By measuring a set of solutions of known concentration first (a calibration curve), you can read off the concentration of an unknown. This is how many water-quality and medical tests work.
📎 Depth study idea
Make a set of food-colouring solutions by serial dilution and photograph each one against a white screen with a phone camera. Use a free app to measure the colour intensity, build a calibration curve, and use it to find the concentration of an "unknown" sample — then evaluate how accurate the phone method is.
Video/visual resources¶
- 🎥 TODO: source a video demonstrating correct volumetric flask and pipette technique (meniscus reading, rinsing, inverting).
- 🎥 Khan Academy — TODO: source a molarity and dilution explainer.
- 🖥️ PhET Simulation — Molarity — change moles of solute and volume of solution and watch the concentration in mol L⁻¹
- 🖥️ PhET Simulation — Concentration — add solute, evaporate or dilute, and see when the solution becomes saturated
- 🖥️ PhET Simulation — Beer's Law Lab — measure how much light a coloured solution absorbs at different concentrations (goes with the Extension box)
Check yourself¶
-
\(0.200\ \text{mol}\) of potassium chloride is dissolved to make \(400\ \text{mL}\) of solution. Calculate its concentration in mol L⁻¹.
Answer
\(C = \dfrac{0.200}{0.400} = 0.500\ \text{mol L}^{-1}\)
-
What mass of potassium nitrate, \(\ce{KNO3}\) (\(MM = 101.11\)), is needed to make \(100.0\ \text{mL}\) of a \(0.150\ \text{mol L}^{-1}\) solution?
Answer
\(n = 0.150 \times 0.1000 = 0.0150\ \text{mol}\); \(m = 0.0150 \times 101.11 = 1.52\ \text{g}\)
-
\(50.0\ \text{mL}\) of \(1.00\ \text{mol L}^{-1}\) copper(II) sulfate is diluted to \(200\ \text{mL}\). What is the new concentration?
Answer
\(C_2 = \dfrac{C_1V_1}{V_2} = \dfrac{1.00 \times 50.0}{200} = 0.250\ \text{mol L}^{-1}\)
-
A bottle of wine is 13% (v/v) ethanol. How much ethanol is in a \(750\ \text{mL}\) bottle?
Answer
13 mL per 100 mL, so \(13 \times 7.5 = 97.5\ \text{mL}\) of ethanol.
-
Convert \(0.100\ \text{mol L}^{-1}\) sodium hydroxide (\(MM = 40.00\)) to g L⁻¹.
Answer
\(0.100 \times 40.00 = 4.00\ \text{g L}^{-1}\)
-
Which unit would be most sensible for reporting (a) the amount of mercury in a fish, (b) the alcohol content of a drink, (c) the concentration of an acid for a lab reaction?
Answer
(a) ppm (or ppb) — a very small amount in a solid, so mg per kg. (b) % (v/v) — a liquid dissolved in a liquid. (c) mol L⁻¹ — used whenever you need to do calculations with a balanced equation.