A Chemistry Teacher Adds 50.0 ML Of $1.50 \, \text{M} \, \text{H}_2\text{SO}_4$ Solution To 200 ML Of Water. What Is The Concentration Of The Final Solution? Use $M_1V_i = M_fV_f$.A. 0.300 M B. 0.375 M C. 6.00 M D. 7.50 M

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Introduction

In chemistry, dilution is a common process where a concentrated solution is mixed with a solvent to create a more diluted solution. This process is essential in various applications, including laboratory experiments, industrial processes, and even everyday life. In this article, we will explore a classic dilution problem involving a chemistry teacher who adds a concentrated sulfuric acid solution to water. We will use the formula $M_1V_i = M_fV_f$ to find the concentration of the final solution.

The Problem

A chemistry teacher adds 50.0 mL of $1.50 , \text{M} , \text{H}_2\text{SO}_4$ solution to 200 mL of water. What is the concentration of the final solution?

The Formula

To solve this problem, we will use the formula $M_1V_i = M_fV_f$, where:

  • M_1$ is the initial concentration of the solution (in this case, 1.50 M)

  • V_i$ is the initial volume of the solution (in this case, 50.0 mL)

  • M_f$ is the final concentration of the solution (which we want to find)

  • V_f$ is the final volume of the solution (in this case, 250 mL, which is the sum of the initial volume of the solution and the volume of water)

Solving the Problem

Now, let's plug in the values into the formula:

M1Vi=MfVfM_1V_i = M_fV_f

1.50 M×50.0 mL=Mf×250 mL1.50 \, \text{M} \times 50.0 \, \text{mL} = M_f \times 250 \, \text{mL}

To find $M_f$, we can rearrange the formula:

Mf=M1ViVfM_f = \frac{M_1V_i}{V_f}

Mf=1.50 M×50.0 mL250 mLM_f = \frac{1.50 \, \text{M} \times 50.0 \, \text{mL}}{250 \, \text{mL}}

Mf=75.0 M⋅mL250 mLM_f = \frac{75.0 \, \text{M} \cdot \text{mL}}{250 \, \text{mL}}

Mf=0.300 MM_f = 0.300 \, \text{M}

Conclusion

Therefore, the concentration of the final solution is 0.300 M.

Discussion

This problem is a classic example of a dilution problem, where a concentrated solution is mixed with a solvent to create a more diluted solution. The formula $M_1V_i = M_fV_f$ is a useful tool for solving such problems. By plugging in the values and rearranging the formula, we can find the final concentration of the solution.

Answer

The correct answer is:

A. 0.300 M

Additional Examples

Here are a few additional examples of dilution problems:

  • A chemist adds 100 mL of $2.00 , \text{M} , \text{NaOH}$ solution to 300 mL of water. What is the concentration of the final solution?
  • A laboratory technician adds 50.0 mL of $3.00 , \text{M} , \text{HCl}$ solution to 150 mL of water. What is the concentration of the final solution?

Solutions

  • A chemist adds 100 mL of $2.00 , \text{M} , \text{NaOH}$ solution to 300 mL of water. The concentration of the final solution is 0.667 M.
  • A laboratory technician adds 50.0 mL of $3.00 , \text{M} , \text{HCl}$ solution to 150 mL of water. The concentration of the final solution is 1.00 M.

Conclusion

Introduction

In our previous article, we explored a classic dilution problem involving a chemistry teacher who adds a concentrated sulfuric acid solution to water. We used the formula $M_1V_i = M_fV_f$ to find the concentration of the final solution. In this article, we will answer some frequently asked questions (FAQs) related to dilution problems.

Q&A

Q: What is dilution?

A: Dilution is the process of mixing a concentrated solution with a solvent to create a more diluted solution.

Q: Why is dilution important in chemistry?

A: Dilution is important in chemistry because it allows us to create solutions with specific concentrations, which is essential in various applications, including laboratory experiments, industrial processes, and even everyday life.

Q: What is the formula for dilution?

A: The formula for dilution is $M_1V_i = M_fV_f$, where:

  • M_1$ is the initial concentration of the solution

  • V_i$ 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 formula for dilution?

A: To use the formula for dilution, you need to plug in the values and rearrange the formula to find the final concentration of the solution.

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

A: Some common mistakes to avoid when solving dilution problems include:

  • Not converting the units of the initial and final volumes to the same unit (e.g., mL to L)
  • Not using the correct formula for dilution
  • Not plugging in the correct values into the formula
  • Not rearranging the formula correctly to find the final concentration of the solution

Q: Can I use the formula for dilution to find the initial concentration of the solution?

A: No, the formula for dilution is used to find the final concentration of the solution, not the initial concentration.

Q: Can I use the formula for dilution to find the final volume of the solution?

A: No, the formula for dilution is used to find the final concentration of the solution, not the final volume.

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

A: Some real-world applications of dilution include:

  • Creating solutions for laboratory experiments
  • Preparing medications for patients
  • Creating solutions for industrial processes
  • Creating solutions for everyday life, such as cleaning products and cosmetics

Conclusion

In conclusion, dilution is an essential process in chemistry, and the formula $M_1V_i = M_fV_f$ is a useful tool for solving dilution problems. By understanding the formula and avoiding common mistakes, you can solve dilution problems with confidence. Remember to always plug in the correct values and rearrange the formula correctly to find the final concentration of the solution.

Additional Resources

Practice Problems

  • A chemist adds 100 mL of $2.00 , \text{M} , \text{NaOH}$ solution to 300 mL of water. What is the concentration of the final solution?
  • A laboratory technician adds 50.0 mL of $3.00 , \text{M} , \text{HCl}$ solution to 150 mL of water. What is the concentration of the final solution?

Solutions

  • A chemist adds 100 mL of $2.00 , \text{M} , \text{NaOH}$ solution to 300 mL of water. The concentration of the final solution is 0.667 M.
  • A laboratory technician adds 50.0 mL of $3.00 , \text{M} , \text{HCl}$ solution to 150 mL of water. The concentration of the final solution is 1.00 M.