C1V1=C2V2 - Mathcentre

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AT A GLANCE/ PHARMACY CALCULATIONS C1V1 = C2V2 Using proportional sets to calculate equivalent amounts, strengths and substitutes.

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Proportional sets

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C1V1=C2V2 is used to calculate an unknown quantity where two solutions/mixtures are proportional …

Acknowledgments All materials checked by Dr Scott Wildman, Dr Cleopatra Branch, Jerome Durodie and Andrew Lea, Medway School of Pharmacy, Anson Building, Central Avenue, Chatham Maritime, Chatham, Kent. ME4 4TB. This leaflet has been produced in conjunction with sigma Network for Excellence in Mathematics and Statistics Support

C1V1 = Concentration/amount (start) and Volume (start) C2V2 = Concentration/amount (final) and Volume (final) 1. Amounts Calculating how much ingredient is contained in a different volume of the same concentration. Example 1 If a 300mL bottle of a product contains 15g of ingredient A, how much will contained in a 5mL spoonful? Method

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Step 1: Use c1/v1= c2/v2 15 𝑥(𝑔) = 300 5

Step 2: Transpose for x and solve

Step 2: Transpose for x and solve 𝑥=

Example 2

15 × 5 = 𝟎. 𝟐𝟐𝟐 300



𝑥=

100 = 400 = 1 part in 400 0.25



3. Substitute Quantities

If a 15mL dose of a product contains 300mg of ingredient B, how much will be contained in 500mL ? Method

Calculate the quantity of a concentration needed to produce a different final desired concentration and volume (a serial dilution). Example 1

Step 1: Use c1/v1= c2/v2

How much 10% solution is needed to make up 500mL of a 2% solution?

300 𝑥 (𝑚𝑚) = 15 500

Method NB: In this case we use C1 x V1 = C2 x V2

Step 2: Transpose for x and solve 𝑥=

300 × 500 = 10,000𝑚𝑚 = 𝟏𝟏𝟏 15



Step 1: Use c1 x v1= c2 x v2 2 × 500 = 10 × 𝑥 (mL)

2. Equivalent Strengths

Converting from one measure of strength to another.

Step 2: Transpose for x and solve

Example 1 What is 1 part in 20 expressed as a percentage? Method

Example 2

Step 1: Use c1/v1= c2/v2

Example 2

Step 1: Use c1 x v1= c2 x v2



What is 0.25% expressed as a ratio strength? Method Step 1: Use c1/v1= c2/v2 0.25 1 = 100 𝑥



Method

Step 2: Transpose for x and solve 100 = 𝟓𝟓 20

2 × 500 = 𝟏𝟏𝟏𝟏𝟏 10

How much 5% solution is needed to make up 80ml of a 0.4% solution?

1 𝑥 = 20 100 𝑥=

𝑥=

0.4 × 80 = 5 × 𝑥 (mL) Step 2: Transpose for x and solve 𝑥=

0.4 × 80 = 𝟔. 𝟒𝟒𝟒 5