How to Dilute a Concentrated Solution: From 0.25 M to 0.125 M

Understanding how to dilute a concentrated solution is a fundamental concept in chemistry. Let's explore the simple math and the dilution formula to achieve a 0.125 M solution from a 0.25 M solution. We'll also discuss the nuances of expressing the process in scientific terms.

The Mathematics Behind the Dilution

The relationship between the initial and final concentrations of a solution can be described using a simple mathematical principle. If you want to halve the concentration, you need to double the volume of the solution. In this case, you start with a 0.25 M (molar) solution and want to achieve a 0.125 M solution. Since 0.125 M is exactly half of 0.25 M, you need to double the volume of the solution.

Starting with 250 mL of a 0.25 M solution, you would need to double that volume to 500 mL. This means you need to add an additional 250 mL of water to the original 250 mL of solution. The scientific way to express this is to say, 'Add sufficient water to produce a final volume of 500 mL.'

Using the Dilution Formula

Vincent's explanation is correct, and we can use the dilution formula to corroborate this:

M1V1 M2V2

Here, M1 is the initial concentration (0.25 M), V1 is the initial volume (250 mL), M2 is the final concentration (0.125 M), and V2 is the final volume. Plugging in the values, we get:

0.25 M × 250 mL 0.125 M × V2

Calculating the right-hand side, we find:

0.25 M × 250 mL / 0.125 M V2

250 mL / 0.5 V2

500 mL V2

So, the final volume V2 must be 500 mL. Again, this is expressed as adding sufficient water to produce a final volume of 500 mL.

Understanding Molar Concentration

Molar concentration, or molarity, is defined as the number of moles of solute per liter of solution, represented by the formula:

[Molarity] (moles of solute) / (volume of SOLUTION in liters)

This has associated units of mol/L. In our example, the initial concentration is 0.25 M, and you want to halve it to 0.125 M. By doubling the volume of the solution from 250 mL to 500 mL, you achieve the desired concentration. This is a straightforward application of the dilution principle.

Conclusion

To summarize, to dilute a 0.25 M solution to 0.125 M, you need to double the volume of the solution. This translates to adding 250 mL of water to the original 250 mL of solution, resulting in a final volume of 500 mL. This ensures that the concentration is halved as required.

Understanding and applying the dilution formula can be a powerful tool in solving a wide range of chemistry problems, ensuring accurate and reliable results.