A dilution is a laboratory technique used to decrease the concentration of a solute within a solution, typically by adding more solvent, often referred to as a diluent. This process is fundamental across many scientific disciplines, including chemistry, biology, and medicine. Dilution allows practitioners to prepare solutions of exact, lower concentrations from a more concentrated stock. This procedure relies on specific mathematical principles to ensure the final product meets the required specifications.
Calculating the Required Concentration
Before measuring any liquid, calculations must determine the precise volumes required. The relationship between concentration and volume is governed by the Dilution Formula: $C_1V_1 = C_2V_2$. This equation states that the initial concentration ($C_1$) multiplied by the initial volume ($V_1$) of the stock solution must equal the final concentration ($C_2$) multiplied by the final volume ($V_2$) of the diluted solution. The core principle is that the total amount of solute remains constant.
The Dilution Factor (DF) is often expressed as the ratio of the final volume to the initial volume ($V_2/V_1$) or the ratio of the initial concentration to the final concentration ($C_1/C_2$). For instance, if a stock solution has a concentration of 10 M and an experiment requires 500 mL of a 2 M solution, the formula is used to find the required volume of the stock solution ($V_1$). Rearranging the equation to solve for $V_1$ yields $V_1 = (C_2V_2) / C_1$.
Inserting the values, the calculation becomes $V_1 = (2 \text{ M} \times 500 \text{ mL}) / 10 \text{ M}$, resulting in $V_1 = 100 \text{ mL}$. This means 100 mL of the 10 M stock solution is needed, which will then be brought up to a total volume of 500 mL with the diluent.
Performing a Simple Dilution
The physical process of performing a simple, single-step dilution requires careful attention to measurement and mixing techniques. Precision volumetric glassware, such as a volumetric pipette or a burette, should be used to accurately measure the calculated volume of the concentrated stock solution ($V_1$). A volumetric flask is the standard container for preparing the final solution, as it is designed to measure one specific, highly accurate volume denoted by a single calibration mark.
After the stock solution is measured, it is transferred into the volumetric flask, which is typically already partially filled with the solvent. It is important to rinse the measuring instrument with a small amount of solvent to ensure all the measured solute is transferred. The solvent is then added slowly until the liquid level approaches the calibration mark on the neck.
The final step involves carefully adding the last drops of solvent until the bottom of the meniscus aligns exactly with the volume mark. This technique is known as “making up to volume.” Once the volume is finalized, the flask must be sealed and inverted repeatedly, usually 10 to 15 times, to ensure the solute and solvent are thoroughly homogenized into a uniform solution.
Serial Dilutions: Iterative Preparation
While a simple dilution achieves a single target concentration in one step, a serial dilution involves a sequence of successive dilutions. In this process, the diluted solution from one step serves as the stock solution for the next. Serial dilutions are useful for creating extremely dilute solutions, such as those required in microbiology or toxicology studies.
This technique allows researchers to reach very high dilution factors, such as $10^{-6}$ or $10^{-8}$, which would be impractical to achieve accurately in a single step. A common format is a 1:10 serial dilution, where one part of the stock solution is combined with nine parts of the diluent in each successive tube. If three such steps are performed, the final dilution factor is the product of the individual factors: $1/10 \times 1/10 \times 1/10$, resulting in a final dilution of $1/1000$.
The benefit of this method is the creation of a logarithmic concentration scale, where each successive concentration decreases by the same factor. For example, a 1:2 serial dilution series would yield concentrations of $1/2, 1/4, 1/8, 1/16$, and so on. Calculating the final concentration requires multiplying the initial concentration by the reciprocal of the total dilution factor achieved across all steps.
Ensuring Accuracy and Avoiding Mistakes
Maintaining accuracy during the physical preparation of a dilution relies heavily on proper technique and the selection of appropriate measuring tools. The glassware chosen should be calibrated to the level of precision required for the application. Using the wrong type of equipment introduces systematic errors.
Equipment Selection
For preparing a precise solution, a volumetric flask is preferable to a simple beaker or Erlenmeyer flask.
Reading the Meniscus
One specific source of error involves reading the liquid level, or meniscus, in the measuring vessel. To ensure the volume is read accurately, the observer’s eye must be level with the surface of the liquid. This prevents parallax error, which results from viewing the meniscus at an angle. For aqueous solutions, the volume is read at the bottom curve of the meniscus.
Common Procedural Errors
Common mistakes include failing to mix the final solution adequately, which results in a concentration gradient rather than a uniform solution. Another frequent error is volumetric error, often caused by using non-calibrated tools or by not allowing the pipette to fully drain when transferring the stock solution.