Dilution and Alligation Methods for the PTCB Exam

The Dilution Formula

The dilution formula C1V1 = C2V2 is used when you need to dilute a concentrated solution to a weaker concentration. C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.

Example: How much of a 10% stock solution is needed to make 500 mL of a 2% solution? Using C1V1 = C2V2: (10%)(V1) = (2%)(500 mL), so V1 = 100 mL. Add enough diluent to reach 500 mL total.

Alligation Method

Alligation is used to determine the ratio of two different concentrations needed to create a desired intermediate concentration. Draw a tic-tac-toe grid with the higher concentration and lower concentration on the left, the desired concentration in the middle, and calculate the parts needed by finding the differences diagonally.

This method is especially useful in compounding when mixing two strengths of a cream or solution.

Exam Practice

Dilution and alligation problems require repetition to master. Practice extensively with our calculation flashcards and PTCB mini exams.