Calculating the Volume of a Stock Solution for Dilution

When preparing solutions, it is often necessary to dilute a stock solution to obtain a solution of a different concentration. This process is known as dilution. In this article, we will explore how to calculate the volume of a stock solution needed to prepare a desired concentration of a solution. We will use a specific example to illustrate the process.

Example Problem: Preparing a 0.01M NaOH Solution from a 0.20M Stock Solution

Suppose you need to prepare 500 mL of a 0.01M NaOH solution from a 0.20M stock solution. The goal is to determine the volume of the 0.20M NaOH solution required for this dilution. We will use the dilution formula for this calculation:

Dilution Formula: CV CV

The dilution formula states that the initial concentration (C1) multiplied by the initial volume (V1) of the stock solution is equal to the final concentration (C2) multiplied by the final volume (V2) of the diluted solution. Mathematically, this can be expressed as:

C_1 V_1 C_2 V_2

Given and Unknown Values

Let's gather the known values:

C1 (initial concentration) 0.20 M NaOH (0.20 mol/L) V2 (final volume) 500 mL (0.500 L) C2 (final concentration) 0.01 M NaOH (0.01 mol/L)

Our unknown value is V1 (initial volume), which we need to calculate.

Calculation

Using the dilution formula, we can solve for V1:

V_1 frac{C_2 V_2}{C_1}

Substituting the known values:

V_1 frac{0.01 text{ mol/L} times 0.500 text{ L}}{0.20 text{ mol/L}} 0.025 text{ L}

Converting the volume from liters to milliliters:

V_1 0.025 text{ L} times 1000 text{ mL/L} 25 text{ mL}

Conclusion

To prepare 500 mL of a 0.01M NaOH solution, you would need 25 mL of a 0.20M stock solution. This is the amount of the stock solution required to achieve the desired concentration when diluted to the final volume.

Understanding this process is crucial in chemical and pharmaceutical applications where precise concentration control is essential. The dilution formula is a fundamental tool in these settings.

Keywords and Related Concepts

The key concepts discussed in this article include the dilution formula, concentration calculation, and stock solution volume. By mastering these concepts, you can effectively prepare solutions to achieve desired concentrations in various scientific and industrial applications.