The concentration of a diluted solution (C2) can be precisely calculated using the fundamental formula C1 x V1 = C2 x V2, which accounts for the conservation of moles during dilution.
Dilution is a common laboratory procedure used to prepare solutions of lower concentrations from a more concentrated stock solution. Accurately determining the concentration of these newly prepared solutions is crucial for ensuring experimental validity, safety, and reproducibility.
Understanding the Dilution Formula: C1V1 = C2V2
This equation, often referred to as the dilution equation, is derived from the principle that the amount of solute remains constant before and after dilution. Only the volume of the solvent changes, thus altering the overall concentration.
The variables in this formula are defined as follows:
| Variable | Definition |
|---|---|
| C1 | Stock concentration (beginning concentration) |
| V1 | Volume of stock required to prepare the new solution. |
| C2 | Concentration of the new or working solution (the desired concentration, or the concentration to be calculated). |
| V2 | The final volume of the new or working solution after dilution. |
Note: The definitions for C1, V1, and C2, along with the C1V1=C2V2 formula, are foundational principles in chemistry and are consistent with widely referenced sources on stock solution dilutions.
Steps to Calculate the Concentration of a New Solution (C2)
To calculate the concentration of a solution diluted from a stock solution, you will typically know the stock concentration (C1), the volume of stock solution used (V1), and the final volume of the diluted solution (V2). Your goal is to solve for C2.
The formula C1 x V1 = C2 x V2 can be rearranged to solve for C2:
C2 = (C1 x V1) / V2
Follow these steps to perform the calculation:
- Identify C1 (Stock Concentration): Determine the concentration of your initial stock solution. This could be in units like Molarity (M), % (w/v), mg/mL, etc.
- Identify V1 (Volume of Stock Used): Measure the exact volume of the stock solution that you are taking for dilution.
- Identify V2 (Final Volume of New Solution): Determine the total final volume of your diluted solution after adding the solvent. This is often the volume of the volumetric flask or container used for dilution.
- Ensure Consistent Units: Before performing the calculation, ensure that the units for volume (V1 and V2) are consistent (e.g., both in mL or both in L). The units for concentration (C1 and C2) will also be consistent.
- Perform the Calculation: Plug the values into the rearranged formula:
C2 = (C1 x V1) / V2to find the concentration of your new solution.
Practical Example: Calculating C2
Let's say you have a 2.5 M (Molar) stock solution of sodium chloride (NaCl) and you take 20 mL of this stock solution to dilute it to a final volume of 500 mL. What is the concentration (C2) of your new diluted NaCl solution?
- C1 (Stock concentration) = 2.5 M
- V1 (Volume of stock used) = 20 mL
- V2 (Final volume of new solution) = 500 mL
Solution:
- Apply the formula:
C2 = (C1 x V1) / V2 - Substitute the values:
C2 = (2.5 M x 20 mL) / 500 mL - Calculate:
C2 = 50 M·mL / 500 mLC2 = 0.1 M
Therefore, the concentration of your new diluted NaCl solution (C2) is 0.1 M.
Important Considerations
- Accuracy of Measurements: The precision of your calculated C2 directly depends on the accuracy with which you measure C1, V1, and V2. Use appropriate laboratory equipment (e.g., volumetric flasks, pipettes) for accurate measurements.
- Units: Always pay close attention to units. If V1 is in mL and V2 is in L, convert one of them so they are consistent before calculation. The units of C2 will match those of C1.
