Rearranging the Formula to Solve for V1

Oct 13, 2025 by pynkocean.com 46 views

Understanding the Problem

To solve this problem, we need to understand the concept of dilution and how to calculate the amount of a solution required to achieve a specific concentration. Dilution is the process of adding a solvent to a solution to decrease its concentration. In this case, we are given a 10% solution and need to create a 2% solution by diluting it to 250 mL.

Calculating the Amount of the 10% Solution Needed

Let's start by identifying the given information:

The final volume of the solution is 250 mL.
The final concentration of the solution is 2%.
The initial concentration of the solution is 10%.

We can use the formula for dilution to solve this problem:

C1V1 = C2V2

where: C1 = initial concentration (10%) V1 = initial volume (unknown) C2 = final concentration (2%) V2 = final volume (250 mL)

Rearranging the Formula to Solve for V1

To solve for V1, we need to rearrange the formula:

V1 = (C2V2) / C1

Plugging in the values, we get:

V1 = (0.02 x 250) / 0.10

Performing the Calculation

Now, let's perform the calculation:

V1 = (0.02 x 250) / 0.10 V1 = 5 mL

Conclusion

Therefore, to create 250 mL of a 2% solution, we need to use 5 mL of the 10% solution. This means that we need to add 245 mL of the solvent to the 5 mL of the 10% solution to achieve the desired concentration.

Importance of Accurate Calculations in Chemistry

Accurate calculations are crucial in chemistry, as small errors can lead to significant differences in the final result. In this case, if we had used 4.5 mL of the 10% solution instead of 5 mL, the final concentration would have been 1.8% instead of 2%. This highlights the importance of precise calculations in chemistry.

Real-World Applications of Dilution Calculations

Dilution calculations have numerous real-world applications in various fields, including:

Pharmaceuticals: Dilution calculations are essential in the preparation of medications, where the concentration of the active ingredient needs to be accurately controlled.
Chemical Synthesis: Dilution calculations are used to prepare solutions for chemical reactions, where the concentration of the reactants needs to be precisely controlled.
Environmental Monitoring: Dilution calculations are used to analyze water and soil samples, where the concentration of pollutants needs to be accurately measured.

Conclusion

In conclusion, dilution calculations are essential in chemistry, and accurate calculations are crucial to achieve the desired concentration. By understanding the concept of dilution and using the correct formula, we can calculate the amount of a solution required to achieve a specific concentration. This knowledge has numerous real-world applications in various fields, including pharmaceuticals, chemical synthesis, and environmental monitoring.

Understanding the Problem

In our previous article, we discussed how to calculate the amount of a 10% solution needed to create 250 mL of a 2% solution. In this article, we will answer some frequently asked questions related to dilution calculations.

Q: What is dilution, and why is it important in chemistry?

A: Dilution is the process of adding a solvent to a solution to decrease its concentration. It is an essential concept in chemistry, as it allows us to prepare solutions with specific concentrations for various applications, such as pharmaceuticals, chemical synthesis, and environmental monitoring.

Q: How do I calculate the amount of a solution required to achieve a specific concentration?

A: To calculate the amount of a solution required to achieve a specific concentration, you can use the formula:

C1V1 = C2V2

where: C1 = initial concentration V1 = initial volume C2 = final concentration V2 = final volume

Q: What is the difference between a 10% solution and a 2% solution?

A: A 10% solution contains 10 grams of solute per 100 mL of solution, while a 2% solution contains 2 grams of solute per 100 mL of solution. In this case, we need to dilute a 10% solution to create a 2% solution.

Q: How do I calculate the amount of the 10% solution needed to create 250 mL of a 2% solution?

A: To calculate the amount of the 10% solution needed, we can use the formula:

V1 = (C2V2) / C1

Plugging in the values, we get:

V1 = (0.02 x 250) / 0.10 V1 = 5 mL

Q: What if I need to create a solution with a different concentration?

A: To create a solution with a different concentration, you can simply plug in the new values into the formula:

C1V1 = C2V2

Q: Can I use this formula to calculate the amount of a solution required to achieve a specific concentration for any type of solution?

A: Yes, this formula can be used to calculate the amount of a solution required to achieve a specific concentration for any type of solution, as long as you know the initial and final concentrations and volumes.

Q: What are some real-world applications of dilution calculations?

A: Dilution calculations have numerous real-world applications in various fields, including:

Pharmaceuticals: Dilution calculations are essential in the preparation of medications, where the concentration of the active ingredient needs to be accurately controlled.
Chemical Synthesis: Dilution calculations are used to prepare solutions for chemical reactions, where the concentration of the reactants needs to be precisely controlled.
Environmental Monitoring: Dilution calculations are used to analyze water and soil samples, where the concentration of pollutants needs to be accurately measured.

Q: Why is it important to accurately calculate the amount of a solution required to achieve a specific concentration?

A: Accurate calculations are crucial in chemistry, as small errors can lead to significant differences in the final result. In this case, if we had used 4.5 mL of the 10% solution instead of 5 mL, the final concentration would have been 1.8% instead of 2%.