Dilution is a fundamental process across various scientific disciplines, including chemistry, biology, and medicine. It involves reducing the concentration of a solute in a solution, typically by adding more solvent. This process is not limited to laboratories; it is also encountered in everyday life, such as when preparing concentrated juice or diluting household cleaning products.
Understanding Dilution Concepts
To grasp dilution calculations, it is helpful to define several core terms. Concentration refers to the amount of a specific substance, known as the solute, dissolved within a given volume of a liquid, or solvent. Common ways to express concentration include molarity (moles per liter), percentage (e.g., mass/volume or volume/volume), and parts per million (ppm). Volume quantifies the amount of space a substance occupies.
A stock solution is a highly concentrated solution that serves as the starting material for preparing less concentrated solutions. From this stock, a working solution is prepared by adding more solvent, effectively lowering the solute concentration to a desired level. The dilution factor describes the ratio by which the concentration of the stock solution has been reduced. It can be expressed as a ratio (e.g., 1:10) or as a fold dilution (e.g., 10x).
The Universal Dilution Formula
The most widely used formula for calculating dilutions is C1V1 = C2V2. This equation applies when the amount of solute remains constant during the dilution process. C1 represents the initial concentration of the stock solution, and V1 is its initial volume. Similarly, C2 denotes the final concentration of the diluted solution, and V2 is its final volume.
The formula’s principle is that the total amount of solute remains constant; only the solvent volume increases, lowering concentration. When using this formula, ensure that the units for concentration (C1 and C2) are consistent, and likewise for the volume units (V1 and V2). The formula can be rearranged to solve for any unknown variable, such as initial volumes or final concentrations.
Practical Dilution Calculations
Consider an example where you add 400 mL of water to 200 mL of a 3 mol/L hydrogen peroxide solution. The initial concentration (C1) is 3 mol/L, and the initial volume (V1) is 200 mL. The final volume (V2) becomes the sum of the initial solution volume and the added water, which is 200 mL + 400 mL = 600 mL. Using C1V1 = C2V2, we have (3 mol/L)(200 mL) = C2(600 mL). Solving for C2 gives (600 mol·mL) / 600 mL = 1 mol/L, resulting in a concentration of 1 mol/L.
Alternatively, you might need to calculate the initial volume of a concentrated stock solution required to prepare a specific volume of a working solution at a lower concentration. For example, to prepare 1.0 L of a 1.0 mol/L hydrochloric acid (HCl) solution from a 12 mol/L HCl stock, you would solve for V1. Here, C1 is 12 mol/L, C2 is 1.0 mol/L, and V2 is 1.0 L. Using the formula (12 mol/L)(V1) = (1.0 mol/L)(1.0 L), V1 equals (1.0 mol·L) / 12 mol/L, which calculates to approximately 0.0833 L, or 83.3 mL. This means 83.3 mL of the concentrated acid is needed to prepare the 1.0 L solution.
Serial Dilutions
Serial dilution is a technique used to progressively reduce the concentration of a solution through a sequence of successive dilutions. This method is useful for achieving very high dilution factors or when working with samples that have an extremely high initial concentration, such as microbial cultures. By performing multiple smaller, manageable dilution steps, researchers can achieve a large overall dilution factor that would be difficult to accomplish in a single step.
In a serial dilution, each subsequent dilution is prepared from the previously diluted solution, typically using a constant dilution factor at each step. For example, if a 1:10 dilution is performed three times in a series, the total dilution factor is the product of the individual dilution factors (1/10 1/10 1/10), resulting in an overall dilution of 1:1000. This technique enables accurate measurements and observations in fields like microbiology for counting bacterial colonies.