Common Registration Assessment, Part 1
Isotonicity by freezing point depression
Three original questions on adjusting solutions to isotonicity, with the working shown and the usual traps pointed out.
Published 4 October 2026. Independent revision material, not GPhC questions, not for patient care.
A solution is isotonic with body fluids when it freezes at minus 0.52 degrees Celsius. Each ingredient lowers the freezing point a little, and sodium chloride is added to make up the shortfall.
The questions here use fictional drugs and practise only the arithmetic. A 1% w/v sodium chloride solution lowers the freezing point by 0.576 degrees, which is the anchor for every question of this type.
The method
- Write the target depression, 0.52 degrees.
- Work out the freezing point contribution of every ingredient at its final concentration.
- Subtract the total contribution from 0.52 to find the shortfall.
- Divide the shortfall by 0.576 to get the sodium chloride needed in % w/v.
- Convert the percentage to a mass for the volume in the question.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
A 1% w/v solution of a fictional drug lowers the freezing point by 0.12 degrees. How much sodium chloride, in grams, makes 100 mL of a 1% solution isotonic?
Show the answer
Answer: 0.69 g
Working: Shortfall = 0.52 - 0.12 = 0.40. NaCl % = 0.40 / 0.576 = 0.694% w/v. For 100 mL that is 0.694 g, about 0.69 g.
Question 2
For the same fictional drug, a 2% w/v solution lowers the freezing point by 0.16 degrees. How much sodium chloride is needed for 50 mL?
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Answer: 0.31 g
Working: Shortfall = 0.52 - 0.16 = 0.36. NaCl % = 0.36 / 0.576 = 0.625% w/v. For 50 mL: 0.625 / 2 = 0.3125 g, about 0.31 g.
Question 3
A fictional eye drop contains drug X 1% (depression 0.1 degrees) and a preservative contributing 0.06 degrees. How much sodium chloride makes 200 mL isotonic?
Show the answer
Answer: 1.25 g
Working: Total contribution = 0.1 + 0.06 = 0.16. Shortfall = 0.52 - 0.16 = 0.36. NaCl % = 0.36 / 0.576 = 0.625% w/v. For 200 mL: 2 x 0.625 = 1.25 g.
Anchor on 0.576
Every freezing point question is one shortfall divided by 0.576. Write the anchor down first, then line up the contributions underneath it.
Where marks are lost
- Forgetting to scale a 1% contribution up to the actual concentration in the product.
- Adding contributions instead of subtracting the total from 0.52.
- Stopping at the percentage and not converting to a mass for the stated volume.
Frequently asked questions
Why 0.52 degrees?
Body fluids freeze at about minus 0.52 degrees Celsius, so an isotonic solution must show the same depression. The exam provides this figure.
Is the sodium chloride figure exact?
It is as exact as the data given. In practice you would weigh to the precision of your balance, and in the exam you round as the question directs.
Sources
- The Pharmaceutical Journal, preparing for the GPhC pharmaceutical calculations assessment
- GPhC, 2026 assessment specification and permitted items
The questions above are original and use fictional drugs. PreRegExamPrep is not affiliated with or endorsed by the General Pharmaceutical Council.
Practise until the method is automatic
Try 15 free questions with worked answers. No sign-up required.
More calculation topics
- Dose by weight calculations for the GPhC assessment
- Volume to give: liquid medicine calculations
- Percentage strength calculations: w/v, w/w and ratios
- Dilution calculations with C1V1 = C2V2
- Infusion rate calculations in mL per hour
- Drip rate calculations: drops per minute
- Body surface area calculations
- Creatinine clearance (Cockcroft-Gault) calculations
- Moles and millimoles calculations
- Displacement volume calculations for reconstitution
- Quantity to supply calculations
- Using a provided formula in calculations
- Dose information from packaging and labels
- Diluting a stock to a lower strength
- Medicine cost and switch calculations
- Rounding rules in calculations
- Enteral feed rate calculations
- Electrolyte content over time
- Infusion dose per kg per hour
- Rounding doses to measurable volumes
- Relative risk and relative risk reduction
- Absolute risk reduction and number needed to treat
- Odds ratio and confidence intervals
- Relative versus absolute risk reduction
- Loading dose and volume of distribution
- Top-up doses from measured drug levels
- Salt correction factors
- Mass and molar drug concentrations
- Half-life and falling drug levels
- Steady-state concentration and infusion rate
- Bioavailability and equivalent oral doses
- Oral maintenance dose and dosing interval
- Elimination rate constant and half-life
- Accumulation towards steady state
- Ratio strengths and one in X
- Serial dilution factors
- Mixing solutions of different strengths
- Tablet quantities for reducing regimens
- Equivalent doses from provided conversion tables
- Thresholds and dose-banding algorithms
- Unit conversions for mass and volume
- Units and units per mL
- Reconstituting powders and final concentration
- Millimoles and milliequivalents
- Infusion time and volume remaining
- Days supply from pack sizes
- Percentage w/v and w/w conversions
- Ideal and adjusted body weight from formulae
- Diluting creams and ointments by weight
- Scaling a formula to a batch size
- Age-band doses from a provided table
- Tablet fractions and split doses
- Stones, pounds, inches and metric conversions
- Micrograms per minute from mg per hour
- Percentage change and mark-up
- Molar solutions and mass per volume
- Osmolarity from component concentrations
- Direct proportion and cross-multiplication
- Scientific notation and very small quantities
- Stock use and reorder quantities
- Parts per million and very dilute solutions
- Sodium chloride equivalents and isotonic solutions
- Density and specific gravity conversions
- Doses per day and hours between doses
- Finding the volume of diluent to add
- Capping a dose at a stated maximum
- Whole vials and ampoules to draw up
- Reading values from a provided graph
- Micrograms per kg per minute infusions
- Percentage composition of a compound preparation
- Suppository displacement values
- Energy content of parenteral nutrition
- Syringe driver rate calculations
- Area under the curve calculations
- Renal dose adjustments using provided bands
- Insulin units and infusion calculations
- Working backwards from a stated dose
- Doses and days from multi-dose devices
- Combined additives in one infusion
See also the formula sheet, the eight sample questions and the approved calculator page.