Module 3 of 14 · 14 min
Dilution & concentration
Making a weaker solution from a stock — a mouthwash, a soak, a paediatric oral dilution, an IV admixture — is daily pharmacy work, and the exam tests whether you know the difference between the volume of DILUENT to add and the FINAL volume.
🧠 Drug in = drug out. V2 is the bottle you end with, not the water you pour.
Diluting adds solvent, never drug. The amount of drug, $Q = C\times V$, is the same before and after, which gives $C_1V_1 = C_2V_2$. Any matching units work (% with mL, mg/mL with mL, % w/w with g) as long as both sides use the same ones.
$V_2$ is the FINAL volume, not the volume of water you add. Diluent to add $= V_2 - V_1$ (assuming volumes are additive; for alcohol–water mixtures make up 'qs to volume' because they shrink on mixing).
'Dilute 1 in 20' means 1 part of stock in 20 parts TOTAL (1 + 19 diluent), so the concentration falls by a factor of 20. In a serial dilution, the factors multiply: a 1-in-10 followed by a 1-in-10 is a 1-in-100 overall.
A trituration is a dilution of a potent powder with an inert one (usually lactose) so a tiny dose can be weighed accurately. A 1:20 trituration contains 1 g of drug in every 20 g of mixture — so you weigh 20× the drug amount you need.
🧭 The method
- 1Put both strengths in the same units (convert ratio strength to %, mg/mL to %, etc.).
- 2Write C1V1 = C2V2 and label which side is the stock and which is the product.
- 3Solve for the unknown (usually the stock volume V1).
- 4If asked how much diluent, subtract: V2 − V1.
- 5Check: the product must be weaker than the stock and its volume larger.
Before each reveal, predict the next step — then check.
Prepare 250 mL of a 0.1% w/v solution from a 5% w/v stock. How much stock and how much water?
- 1
Find the amount of drug the final product must contain.
$$250\,\text{mL}\times\frac{0.1\,\text{g}}{100\,\text{mL}} = 0.25\,\text{g}$$ Find the volume of stock that holds 0.25 g.
$$0.25\,\cancel{\text{g}}\times\frac{100\,\text{mL}}{5\,\cancel{\text{g}}} = 5\,\text{mL of stock}$$Same result straight from C1V1 = C2V2.
$$V_1 = \frac{C_2V_2}{C_1} = \frac{0.1\%\times 250\,\text{mL}}{5\%} = 5\,\text{mL}$$Diluent = final volume − stock volume.
$$250\,\text{mL} - 5\,\text{mL} = 245\,\text{mL water}$$
Same method — the last steps are yours. Work on paper, then reveal.
A 10 mg/mL stock is diluted 1 in 20. Then 3 mL of that dilution is made up to 30 mL. What is the final concentration?
- 1
'1 in 20' divides the concentration by 20.
$$\frac{10\,\text{mg/mL}}{20} = 0.5\,\text{mg/mL}$$ - 2
Your turn
Now you: the second step takes 3 mL to 30 mL — what is that dilution factor?
Work it out on paper, then reveal.
$$\frac{30\,\text{mL}}{3\,\text{mL}} = 10\quad(\text{a 1 in 10 dilution})$$ - 3
Your turn
Now you: apply it to 0.5 mg/mL.
Work it out on paper, then reveal.
$$C_2 = \frac{0.5\,\text{mg/mL}\times 3\,\text{mL}}{30\,\text{mL}} = 0.05\,\text{mg/mL}$$
Type your number. Your first try decides when this module comes back for review.
How many mL of 95% v/v ethanol are needed to make 500 mL of 70% v/v ethanol?
C1V1 = C2V2 with V2 = 500 mL. (In practice: measure it and make up to 500 mL — alcohol and water shrink on mixing.)
= 368.4 mL
You have 100 mL of a 15% w/v solution. How much water must you ADD to make it 6% w/v?
C1V1 = C2V2 gives the FINAL volume. The question asks what to add.
= 150 mL
How many grams of 2.5% w/w hydrocortisone ointment are needed to make 60 g of 1% w/w ointment (the rest is plain base)?
C1W1 = C2W2 works with weights too.
= 24 g
How many mL of a 17% w/v benzalkonium chloride concentrate are needed to make 1 L of a 1:5000 solution?
Convert 1:5000 to a percentage first: % = 100/5000.
= 1.18 mL
A 50 mg/mL stock: 2 mL is diluted to 100 mL, then 5 mL of that is diluted to 50 mL. What is the final concentration in mcg/mL?
Multiply the two dilution factors (1 in 50, then 1 in 10), and remember the unit asked for.
= 100 mcg/mL
You need 12 capsules each containing 0.25 mg of a potent drug. You prepare a 1:20 trituration (1 g drug + lactose to 20 g). How many mg of trituration are needed for all 12 capsules?
Total drug first, then each 1 mg of drug comes with the trituration's 20 mg of mixture.
= 60 mg
⚠️ Tricky
How many mL of water must be ADDED to 30 mL of a 1:500 solution to make it 1:2000?
A 1:2000 solution is WEAKER than 1:500. Convert both to % (or use fractions) before C1V1 = C2V2.
= 90 mL
⚠️ The trap: Plugging the ratio numbers straight into C1V1 = C2V2 (500 × 30 = 2000 × V2) gives a final volume of 7.5 mL — smaller than what you started with.
⚠️ Tricky
2 mL of a 25 mg/mL stock is added to 8 mL of water. Then 1 mL of this mixture is added to 24 mL of water. What is the final concentration in mcg/mL?
'Added to' 8 mL of water makes a 10 mL total. Each step's factor is total ÷ aliquot.
= 200 mcg/mL
⚠️ The trap: Dividing by the water volumes (8 mL and 24 mL) instead of the total volumes gives about 260 mcg/mL.
⚠️ Tricky
A '100 mL' bag of 0.9% sodium chloride actually contains 110 mL because of manufacturer overfill. You add 2 g of a drug reconstituted to 10 mL. What is the true concentration in the bag, in mg/mL?
Use the real volume in the bag, plus the volume you add.
= 16.67 mg/mL
⚠️ The trap: Using the nominal 100 mL (100 + 10 = 110 mL) gives 18.18 mg/mL.
⚠️ Tricky
A stock solution contains 4 mg/mL. How many mL of stock are needed to make 250 mL of a 0.02% w/v solution?
Put both strengths in the same units first: 1% = 10 mg/mL.
= 12.5 mL
⚠️ The trap: Treating 0.02% as 0.02 mg/mL gives 1.25 mL — a ten-fold under-strength solution.
⚠️ Tricky
How many grams of potassium permanganate are needed to make 120 mL of a stock solution such that 10 mL of the stock, diluted to 500 mL with water, gives a 1:4000 solution?
Start from the diluted solution: how much drug is in 500 mL of 1:4000? All of it came from 10 mL of stock.
= 1.5 g
⚠️ The trap: Making the 120 mL itself 1:4000 gives only 0.03 g — the strength of the diluted solution, not of the stock.
🕵️ Spot the mistake
How much water must be added to 40 mL of a 25% w/v solution to make a 10% w/v solution?
A student wrote
⚠️ Traps examiners set
- Reporting V2 (final volume) when the question asks for diluent to ADD.
- Using a ratio strength (1:5000) directly in C1V1 without converting it to %.
- Reading 'dilute 1 in 20' as 1 part + 20 parts (= 1 in 21).
- Adding serial dilution factors instead of multiplying them.
- Forgetting the unit asked for (mg/mL vs mcg/mL).
💬 Explain it in your own words
Why does C1V1 = C2V2 hold for diluting a solution but not for evaporating one that also loses drug? What exactly is being kept constant?