A chemical dilution is the process of reducing the concentration of a solute within a solution by adding more solvent. This increases the total volume of the liquid while keeping the original amount of the solute constant. Calculating dilutions is a foundational skill in many scientific fields, including laboratory work, medicine for preparing dosages, and mixing concentrated cleaning products. Accurate dilution ensures a substance is safe, effective, and at the correct strength. This article provides the methods and calculations needed to determine the exact volumes for preparing diluted solutions.
Understanding the Core Dilution Formula
Dilution calculations are governed by the principle of conservation of mass, meaning the amount of solute remains the same before and after the solvent is added. This mass-conservation principle is mathematically represented by the universal dilution formula: $C_1V_1 = C_2V_2$.
$C_1$ represents the initial concentration of the starting solution (stock solution), and $V_1$ is the volume of the stock solution required. $C_2$ is the desired final concentration of the diluted solution, and $V_2$ represents the total final volume after the solvent has been added. Because the amount of solute does not change, the initial concentration multiplied by the initial volume must equal the final concentration multiplied by the final volume. To use this formula effectively, the units for both concentration and volume must be consistent on both sides of the equation.
Calculating Simple Dilutions
The most common application of the core formula is solving for $V_1$, the specific volume of the stock solution needed to create a working solution of a lower concentration. For example, a scientist may need to determine how much of a 5 Molar (M) stock solution is necessary to prepare 250 milliliters (mL) of a 0.5 M working solution. The known variables are $C_1$ (5 M), $C_2$ (0.5 M), and $V_2$ (250 mL), leaving $V_1$ as the single unknown.
The formula is rearranged to isolate $V_1$: $V_1 = (C_2V_2) / C_1$. Substituting the numerical values from the example yields $V_1 = (0.5\text{ M} \times 250\text{ mL}) / 5\text{ M}$. Performing the calculation shows that $V_1$ equals 25 mL, meaning 25 mL of the 5 M stock solution is required.
The final step is to determine the volume of solvent, often water, that must be added to complete the dilution. The total final volume, $V_2$, is the sum of the volume of the stock solution ($V_1$) and the volume of the added solvent. To find the required solvent volume, the initial volume is subtracted from the final volume: $V_2 – V_1$. In this case, 250 mL minus 25 mL equals 225 mL of solvent needed to create the final 0.5 M solution.
Calculating Serial Dilutions
Serial dilutions are a distinct method involving a step-wise process where the product of one dilution step becomes the starting solution for the next. This technique achieves a very high dilution factor quickly and is commonly used when the initial concentration of a sample is too high to measure accurately, such as in microbiology. Each individual step in the series is a simple dilution, often using the same ratio repeatedly.
The individual dilution factor (DF) for each step is calculated as the total final volume divided by the volume of the sample transferred. For instance, adding 1 milliliter of solution to 9 milliliters of solvent creates a total volume of 10 milliliters, resulting in a 1:10 dilution factor for that step. The total or overall dilution factor for the entire series is found by multiplying the dilution factors of all the individual steps together.
A three-step serial dilution, where each step is a 1:10 dilution, would have an overall dilution factor of $10 \times 10 \times 10$, which equals 1,000. This overall factor, often expressed as 1:1000, indicates that the final solution has a concentration 1,000 times lower than the original stock. This cumulative process allows researchers to create a broad range of concentrations from a single stock, which is useful for generating standard curves for instrument calibration.