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5 Concentrations, Dilutions, and Reconstitution

Learn how to interpret concentration expressions, calculate ingredient amounts and volumes, prepare dilutions, and use product-specific instructions for reconstitution.

Reading expressions

A describes the amount of ingredient in a stated amount of preparation. Identify both the quantity and its units before calculating, such as mg/mL\mathrm{mg/mL} or g/100 mL\mathrm{g}/100\ \mathrm{mL}.

Common formats

Common expressions specify ingredient relative to a mass or volume of preparation:

  • Mass per volume: Examples include mg/mL\mathrm{mg/mL} and g/L\mathrm{g/L}.

  • : Grams of ingredient in each 100 mL100\ \mathrm{mL} of final solution. For example, 2% w/v2\%\ \mathrm{w/v} means 2 g2\ \mathrm{g} in each 100 mL100\ \mathrm{mL}.

  • Percent weight in weight (% w/w): Grams of ingredient in each 100 g100\ \mathrm{g} of final mixture. For example, 2% w/w2\%\ \mathrm{w/w} means 2 g2\ \mathrm{g} in each 100 g100\ \mathrm{g}.

  • Percent volume in volume (% v/v): Milliliters of ingredient in each 100 mL100\ \mathrm{mL} of final solution. For example, 5% v/v5\%\ \mathrm{v/v} means 5 mL5\ \mathrm{mL} in each 100 mL100\ \mathrm{mL}.

For percent weight in volume, converting grams to milligrams can make calculations easier:

1% w/v=1 g100 mL=1,000 mg100 mL=10 mg/mL1\%\ \mathrm{w/v}=\frac{1\ \mathrm{g}}{100\ \mathrm{mL}}=\frac{1{,}000\ \mathrm{mg}}{100\ \mathrm{mL}}=10\ \mathrm{mg/mL}

A such as 1:1,0001:1{,}000 means one part ingredient in 1,0001{,}000 parts of final preparation, but the mass or volume basis must be clear. For a 1:1,000 w/v1:1{,}000\ \mathrm{w/v} solution, 1 g1\ \mathrm{g} in 1,000 mL1{,}000\ \mathrm{mL} equals 1 mg/mL1\ \mathrm{mg/mL}. Because ratio notation can be misread, convert it to an explicit amount per volume before calculating a dose.

Calculating amounts and volumes

Use as a conversion factor to calculate the amount of ingredient:

Amount of ingredient=concentration×volume\text{Amount of ingredient}=\text{concentration}\times\text{volume}

For a 2% w/v2\%\ \mathrm{w/v} solution, the is 20 mg/mL20\ \mathrm{mg/mL}. Therefore, 15 mL15\ \mathrm{mL} contains:

20 mg/mL×15 mL=300 mg20\ \mathrm{mg/mL}\times15\ \mathrm{mL}=300\ \mathrm{mg}

To find the volume that contains a specified amount, divide the desired amount by the :

Volume=desired amountconcentration\text{Volume}=\frac{\text{desired amount}}{\text{concentration}}

At 20 mg/mL20\ \mathrm{mg/mL}, a 150 mg150\ \mathrm{mg} amount occupies:

150 mg20 mg/mL=7.5 mL\frac{150\ \mathrm{mg}}{20\ \mathrm{mg/mL}}=7.5\ \mathrm{mL}

Diluting a solution

lowers by increasing the amount of solvent or diluent while keeping the amount of ingredient constant. Use the relationship:

C1V1=C2V2C_1V_1=C_2V_2

Here, C1C_1 and V1V_1 are the starting and volume, while C2C_2 and V2V_2 are the desired final and final volume. units must match, and volume units must match.

Preparing a target

To prepare 100 mL100\ \mathrm{mL} at 10 mg/mL10\ \mathrm{mg/mL} from a 40 mg/mL40\ \mathrm{mg/mL} stock, calculate the required stock volume:

V1=C2×V2C1=10 mg/mL×100 mL40 mg/mL=25 mLV_1=\frac{C_2\times V_2}{C_1}=\frac{10\ \mathrm{mg/mL}\times100\ \mathrm{mL}}{40\ \mathrm{mg/mL}}=25\ \mathrm{mL}

Measure 25 mL25\ \mathrm{mL} of stock and add diluent to a final volume of 100 mL100\ \mathrm{mL}. This corresponds to approximately 75 mL75\ \mathrm{mL} of diluent only when volumes are additive. In practice, follow the preparation instructions and bring the mixture to its specified final volume.

Reconstituting a product

adds a specified diluent to a powder or other dry product to make a usable preparation. Product labeling or approved instructions determine the diluent, amount to add, mixing method, resulting , storage, and use period. Do not assume that the volume of diluent added equals the final solution volume; the powder may displace volume.

Calculating a withdrawal volume

When the final is stated, calculate the volume to withdraw by dividing the desired amount by the final :

Volume to withdraw=desired amountfinal concentration\text{Volume to withdraw}=\frac{\text{desired amount}}{\text{final concentration}}

For example, a vial contains 1,000 mg1{,}000\ \mathrm{mg} of drug, and the product instructions state that after the solution contains 250 mg/mL250\ \mathrm{mg/mL}. A 375 mg375\ \mathrm{mg} amount requires:

375 mg250 mg/mL=1.5 mL\frac{375\ \mathrm{mg}}{250\ \mathrm{mg/mL}}=1.5\ \mathrm{mL}

Withdraw 1.5 mL1.5\ \mathrm{mL}, following the product's preparation and handling instructions. Do not use this calculation to decide how much diluent to add; use the product-specific directions.

Checking calculations

Check the setup and result as well as the arithmetic:

  • Write units at every step and cancel them to verify that the answer has the intended units.

  • Distinguish the amount of diluent added from the final volume.

  • Keep and volume units consistent; convert units before substituting when necessary.

  • Check that decreases and that the final volume is at least as large as the stock volume.

  • Retain sufficient precision during the calculation, then round the final measurement as directed by the applicable instructions and equipment.

In short, express concentrations as ingredient per amount of preparation, and convert percentages or ratios into explicit units before calculating. For ordinary , use C1V1=C2V2C_1V_1=C_2V_2 to conserve the amount of ingredient. For reconstituted products, use the labeled final to calculate a withdrawal volume and follow product-specific preparation instructions.