How to Calculate Volume for a Hydrochloric Acid Dilution

Hydrochloric acid (HCl) is a commonly used chemical in laboratories and industries. Diluting a concentrated HCl solution requires careful mathematical calculations to obtain the desired concentration. In this guide, we will walk through the process of determining the volume of a 12.00 M hydrochloric acid solution needed to make 250 mL of a 1.00 M hydrochloric acid solution.

Understanding the Dilution Process

Dilution is a process in chemistry where a more concentrated solution is mixed with a solvent (usually water) to achieve a desired concentration. This is commonly done in laboratory settings to create solutions of varying concentrations. The key to understanding dilution lies in the dilution formula:

C1V1 C2V2

Where:

C1 is the initial concentration of the stock solution, V1 is the volume of the stock solution that is required, C2 is the final concentration of the diluted solution, V2 is the final volume of the diluted solution.

Applying the Dilution Formula

Let's apply the formula to find the required volume of a 12.00 M hydrochloric acid solution to create 250 mL of a 1.00 M solution.

Known Values:

Initial concentration (C1) 12.00 M Final concentration (C2) 1.00 M Final volume (V2) 250 mL (0.250 L)

Formula Application:

C1V1 C2V2

12.00 M × V1 1.00 M × 0.250 L

12.00 M × V1 0.250 mol

V1 0.250 mol ÷ 12.00 M

V1 0.02083 L

V1 0.02083 L × 1000 mL/L 20.83 mL

Therefore, to prepare 250 mL of a 1.00 M hydrochloric acid solution, you will need approximately 20.83 mL of a 12.00 M hydrochloric acid solution.

Explanation of the Units and Formulas

The units in the formula are crucial. Molarity (M) is a unit of concentration that represents the number of moles of solute per liter of solution. Volumes can be given in either milliliters or liters, but it's important to ensure consistency in the calculations. In this example, the final volume is given in milliliters, so the concentration (C2) is converted to a molar amount before solving for the volume.

Alternative Approach Using the V1S1 V2S2 Formula

Another method to solve this problem is by using the relation V1S1 V2S2, where V1 and V2 are the volumes and S1 and S2 are the strengths (molarities) of the two solutions.

In this case:

V1 is the volume of the 12 M HCl required, V2 is the final volume of 250 mL, S1 is the molarity of the 12 M HCl, S2 is the molarity of the 1.00 M dilute HCl.

The equation becomes:

V1 × 12 M 250 mL × 1 M

Solving for V1:

V1 250 mL × 1 M ÷ 12 M

V1 20.833 mL

Thus, the volume of 12 M HCl required is approximately 20.833 mL.

Diluting Hydrochloric Acid in a Volumetric Flask

To prepare the diluted solution in a volumetric flask, follow these steps:

Measure out 20.833 mL of the 12 M hydrochloric acid solution using a pipette or a calibrated burette. Transfer the 20.833 mL of HCl to a 250 mL volumetric flask. Rinse the pipette or burette into the volumetric flask to ensure all of the HCl is transferred. Add distilled water to the volumetric flask until the calibration mark (usually a horizontal line or a stopper) is reached. Mix the solution thoroughly.

Using a volumetric flask ensures that the final volume of the solution is accurate, which is crucial for many chemical applications.