Solving for the Final Volume

Oct 13, 2025 by windailys.com 147 views

Introduction

In chemistry, dilution is a common process where a concentrated solution is mixed with a solvent to reduce its concentration. This process is essential in various applications, including laboratory experiments, industrial processes, and pharmaceutical manufacturing. In this article, we will discuss the concept of dilution and how to calculate the resulting volume of a solution after it has been diluted.

Understanding the Problem

A chemist has a 1.0 mL sample of 2.0 M KNO₃ (potassium nitrate) and wants to dilute it by adding water to it. The resulting solution has a concentration of 0.0080 M. We need to find the volume of the resulting solution.

The Dilution Formula

The formula for dilution is given by:

M_1 V_1 = M_f V_f

where:

$M_1$ is the initial concentration of the solution (2.0 M)
$V_1$ is the initial volume of the solution (1.0 mL)
$M_f$ is the final concentration of the solution (0.0080 M)
$V_f$ is the final volume of the solution (unknown)

Solving for the Final Volume

We can rearrange the formula to solve for the final volume ( $V_f$ ):

V_f = \frac{M_1 V_1}{M_f}

Substituting the given values, we get:

V_f = \frac{(2.0 \, \text{M})(1.0 \, \text{mL})}{0.0080 \, \text{M}}

Calculating the Final Volume

Now, we can calculate the final volume:

V_f = \frac{(2.0 \, \text{M})(1.0 \, \text{mL})}{0.0080 \, \text{M}} = \frac{2.0}{0.0080} \, \text{mL}

V_f = 250 \, \text{mL}

Conclusion

Therefore, the resulting volume of the solution after it has been diluted is 250 mL.

Discussion

In this problem, we used the dilution formula to calculate the resulting volume of a solution after it has been diluted. The formula is a simple and effective way to solve dilution problems. By understanding the concept of dilution and using the formula, chemists and scientists can accurately calculate the resulting volume of a solution.

Applications of Dilution

Dilution is a common process in various applications, including:

Laboratory experiments: Dilution is used to prepare solutions for experiments, such as titrations and chromatography.
Industrial processes: Dilution is used to prepare solutions for industrial processes, such as manufacturing and cleaning.
Pharmaceutical manufacturing: Dilution is used to prepare solutions for pharmaceutical manufacturing, such as preparing solutions for injection.

Importance of Accurate Calculations

Accurate calculations are essential in chemistry and other scientific fields. Inaccurate calculations can lead to incorrect results, which can have serious consequences. Therefore, it is crucial to use the correct formula and perform accurate calculations when working with dilution problems.

Conclusion

In conclusion, dilution is a common process in chemistry and other scientific fields. The dilution formula is a simple and effective way to calculate the resulting volume of a solution after it has been diluted. By understanding the concept of dilution and using the formula, chemists and scientists can accurately calculate the resulting volume of a solution. Accurate calculations are essential in chemistry and other scientific fields, and the dilution formula is a valuable tool for making accurate calculations.

Final Answer

The final answer is 250 mL.

Introduction

Understanding the Problem

The Dilution Formula

The formula for dilution is given by:

M_1 V_1 = M_f V_f

where:

$M_1$ is the initial concentration of the solution (2.0 M)
$V_1$ is the initial volume of the solution (1.0 mL)
$M_f$ is the final concentration of the solution (0.0080 M)
$V_f$ is the final volume of the solution (unknown)

Solving for the Final Volume

We can rearrange the formula to solve for the final volume ( $V_f$ ):

V_f = \frac{M_1 V_1}{M_f}

Substituting the given values, we get:

V_f = \frac{(2.0 \, \text{M})(1.0 \, \text{mL})}{0.0080 \, \text{M}}

Calculating the Final Volume

Now, we can calculate the final volume:

V_f = \frac{(2.0 \, \text{M})(1.0 \, \text{mL})}{0.0080 \, \text{M}} = \frac{2.0}{0.0080} \, \text{mL}

V_f = 250 \, \text{mL}

Conclusion

Therefore, the resulting volume of the solution after it has been diluted is 250 mL.

Discussion

Applications of Dilution

Dilution is a common process in various applications, including:

Laboratory experiments: Dilution is used to prepare solutions for experiments, such as titrations and chromatography.
Industrial processes: Dilution is used to prepare solutions for industrial processes, such as manufacturing and cleaning.
Pharmaceutical manufacturing: Dilution is used to prepare solutions for pharmaceutical manufacturing, such as preparing solutions for injection.

Importance of Accurate Calculations

Conclusion

Final Answer

The final answer is 250 mL.

Q&A: Dilution and the Dilution Formula

Q: What is dilution?

A: Dilution is the process of mixing a concentrated solution with a solvent to reduce its concentration.

Q: What is the dilution formula?

A: The dilution formula is given by:

M_1 V_1 = M_f V_f

where:

$M_1$ is the initial concentration of the solution
$V_1$ is the initial volume of the solution
$M_f$ is the final concentration of the solution
$V_f$ is the final volume of the solution

Q: How do I use the dilution formula to calculate the resulting volume of a solution?

A: To use the dilution formula, you need to rearrange it to solve for the final volume ( $V_f$ ):

V_f = \frac{M_1 V_1}{M_f}

Q: What are some common applications of dilution?

A: Dilution is used in various applications, including:

Laboratory experiments
Industrial processes
Pharmaceutical manufacturing

Q: Why is accurate calculation important in dilution problems?

A: Accurate calculations are essential in chemistry and other scientific fields. Inaccurate calculations can lead to incorrect results, which can have serious consequences.

Q: What is the final answer to the problem of diluting a 1.0 mL sample of 2.0 M KNO₃ to a concentration of 0.0080 M?

A: The final answer is 250 mL.

Q: Can I use the dilution formula to calculate the resulting concentration of a solution?

A: Yes, you can use the dilution formula to calculate the resulting concentration of a solution by rearranging it to solve for the final concentration ( $M_f$ ):

M_f = \frac{M_1 V_1}{V_f}

Q: What are some common mistakes to avoid when working with dilution problems?

A: Some common mistakes to avoid include:

Using the wrong formula
Making errors in calculation
Not considering the units of the variables

Q: How can I practice using the dilution formula to calculate the resulting volume of a solution?

A: You can practice using the dilution formula by working through example problems and checking your answers with a calculator or by using a dilution calculator.