A solution is a homogeneous mixture where one substance, the solute, is uniformly dispersed throughout a second substance, the solvent. Creating a more dilute solution is a fundamental and frequently performed process in chemistry, biology, and medicine. Dilution decreases the concentration of a solution by adding a precise amount of pure solvent to a known volume of a more concentrated stock solution. This controlled process allows researchers to prepare reagents at the exact concentration required for an experiment or procedure.
Understanding the Solute-Solvent Relationship
The core principle governing dilution is that the total amount of the dissolved substance, the solute, remains unchanged throughout the process. When a concentrated solution is diluted, solvent is added, increasing the total volume of the mixture. This increase in volume causes the solute particles to spread out over a larger space, which directly results in a lower overall concentration.
The concentration and volume are inversely proportional; as one increases, the other decreases by a corresponding factor. If the volume of a solution is precisely doubled by adding solvent, the concentration of the solute will be exactly halved. This constancy of the solute amount allows for accurate prediction and calculation of the final concentration of any diluted solution.
Mathematical Tools for Precision Dilution
Accurately creating a dilute solution requires a specific calculation to determine the exact volumes needed to achieve a target concentration. The mathematical tool used for this purpose is the dilution equation, \(M_1V_1 = M_2V_2\), which expresses the conservation of the solute amount. The product of concentration and volume on both sides of the equation represents the identical amount of solute.
In this formula, \(M_1\) is the initial concentration of the stock solution, and \(V_1\) is the volume of stock solution used for the dilution. \(M_2\) is the desired final concentration, and \(V_2\) is the total final volume of the solution. This equation works regardless of the specific units used for concentration (such as molarity or percent concentration) and volume, as long as the units are consistent on both sides.
A typical application involves calculating the volume of the stock solution (\(V_1\)) needed to prepare a specific final volume (\(V_2\)) at a desired concentration (\(M_2\)). For example, to prepare 500 milliliters of a 0.5 M solution from a stock of 2.0 M, the formula is rearranged to \(V_1 = (M_2V_2) / M_1\). Plugging in the values calculates the required initial volume (\(V_1\)) as 125 milliliters. The volume of solvent to be added is then found by subtracting \(V_1\) from the total final volume \(V_2\) (500 mL – 125 mL = 375 mL).
Step-by-Step Procedure for Accurate Dilution
The practical execution of a dilution begins with the calculated volumes. Precision measuring tools are necessary, and volumetric flasks are the preferred glassware because they are calibrated to contain a very accurate total volume. After calculating the required volume of the concentrated stock solution (\(V_1\)), it is carefully measured using a calibrated pipette or graduated cylinder.
The measured stock solution is introduced into the volumetric flask. A predetermined amount of solvent is then added, but the flask should not be filled immediately to the final volume mark. For highly concentrated solutions, especially acids or bases, it is a standard safety practice to first add a significant portion of the solvent before adding the concentrated stock solution. This technique helps manage the heat generated when the stock and solvent mix.
The solution is mixed thoroughly to ensure the solute is homogeneously dispersed. Finally, the remaining solvent is added until the total volume reaches the calibration mark on the neck of the volumetric flask, which indicates the exact final volume (\(V_2\)). The container must then be labeled clearly with the solute name, final concentration (\(M_2\)), date of preparation, and preparer’s initials.