Understanding the Initial Solution

Oct 13, 2025 by recoveryshake.com 43 views

Introduction

In chemistry, understanding the concentration of solutions is crucial in various applications, including industrial processes, medical treatments, and environmental monitoring. A chemist has 500 mL of a 30% acid solution and adds x milliliters of a 10% acid solution. The goal is to determine which statement is true about the graph of the function that represents the concentration of the final solution.

Understanding the Initial Solution

The chemist starts with 500 mL of a 30% acid solution. This means that 30% of the 500 mL solution is acid, while the remaining 70% is water. To calculate the amount of acid in the initial solution, we multiply the volume of the solution by the concentration of acid:

500 mL x 0.30 = 150 mL of acid

Understanding the Added Solution

The chemist adds x milliliters of a 10% acid solution. This means that 10% of the x milliliters solution is acid, while the remaining 90% is water. To calculate the amount of acid in the added solution, we multiply the volume of the added solution by the concentration of acid:

x mL x 0.10 = 0.10x mL of acid

Calculating the Final Concentration

After adding the x milliliters of the 10% acid solution to the initial 500 mL of the 30% acid solution, the total volume of the final solution is:

500 mL + x mL = (500 + x) mL

The total amount of acid in the final solution is the sum of the acid in the initial solution and the acid in the added solution:

150 mL + 0.10x mL = 150 + 0.10x mL

To calculate the concentration of the final solution, we divide the total amount of acid by the total volume of the final solution:

Concentration = (150 + 0.10x) / (500 + x)

Analyzing the Graph of the Function

The graph of the function that represents the concentration of the final solution is a rational function. To analyze the graph, we need to consider the following:

The concentration of the final solution increases as the amount of the 10% acid solution added increases.
The concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.
The concentration of the final solution approaches 10% as the amount of the 10% acid solution added approaches zero.

Conclusion

Based on the analysis of the graph of the function that represents the concentration of the final solution, we can conclude that the statement that is true is:

The concentration of the final solution increases as the amount of the 10% acid solution added increases.
The concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.
The concentration of the final solution approaches 10% as the amount of the 10% acid solution added approaches zero.

Final Answer

The final answer is that the concentration of the final solution increases as the amount of the 10% acid solution added increases, and the concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.

Discussion

The problem presented in this article is a classic example of a mixture problem in chemistry. The chemist starts with a 30% acid solution and adds a 10% acid solution to create a final solution with a concentration that depends on the amount of the 10% acid solution added. The graph of the function that represents the concentration of the final solution is a rational function that increases as the amount of the 10% acid solution added increases.

Key Takeaways

The concentration of the final solution increases as the amount of the 10% acid solution added increases.
The concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.
The concentration of the final solution approaches 10% as the amount of the 10% acid solution added approaches zero.

References

[1] Chemistry: An Atoms First Approach, by Steven S. Zumdahl
[2] General Chemistry: Principles and Modern Applications, by Linus Pauling

Additional Resources

[1] Khan Academy: Chemistry
[2] MIT OpenCourseWare: Chemistry

Introduction

In our previous article, we explored the problem of a chemist who has 500 mL of a 30% acid solution and adds x milliliters of a 10% acid solution. We analyzed the graph of the function that represents the concentration of the final solution and concluded that the concentration of the final solution increases as the amount of the 10% acid solution added increases, and the concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.

Q&A

Q: What is the initial concentration of the acid solution?

A: The initial concentration of the acid solution is 30%.

Q: What is the volume of the initial acid solution?

A: The volume of the initial acid solution is 500 mL.

Q: What is the concentration of the added acid solution?

A: The concentration of the added acid solution is 10%.

Q: What is the volume of the added acid solution?

A: The volume of the added acid solution is x milliliters.

Q: How do we calculate the concentration of the final solution?

A: To calculate the concentration of the final solution, we divide the total amount of acid by the total volume of the final solution.

Q: What is the total amount of acid in the final solution?

A: The total amount of acid in the final solution is the sum of the acid in the initial solution and the acid in the added solution.

Q: What is the total volume of the final solution?

A: The total volume of the final solution is the sum of the volume of the initial solution and the volume of the added solution.

Q: What is the formula for the concentration of the final solution?

A: The formula for the concentration of the final solution is:

Concentration = (150 + 0.10x) / (500 + x)

Q: What happens to the concentration of the final solution as the amount of the 10% acid solution added increases?

A: The concentration of the final solution increases as the amount of the 10% acid solution added increases.

Q: What happens to the concentration of the final solution as the amount of the 10% acid solution added increases without bound?

A: The concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.

Q: What happens to the concentration of the final solution as the amount of the 10% acid solution added approaches zero?

A: The concentration of the final solution approaches 10% as the amount of the 10% acid solution added approaches zero.

Conclusion

In this Q&A article, we have answered some of the most frequently asked questions about the problem of a chemist who has 500 mL of a 30% acid solution and adds x milliliters of a 10% acid solution. We have analyzed the graph of the function that represents the concentration of the final solution and concluded that the concentration of the final solution increases as the amount of the 10% acid solution added increases, and the concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.

Final Answer

Discussion

Key Takeaways

The concentration of the final solution increases as the amount of the 10% acid solution added increases.
The concentration of the final solution approaches 30% as the amount of the 10% acid solution added increases without bound.
The concentration of the final solution approaches 10% as the amount of the 10% acid solution added approaches zero.

References

[1] Chemistry: An Atoms First Approach, by Steven S. Zumdahl
[2] General Chemistry: Principles and Modern Applications, by Linus Pauling

Additional Resources

[1] Khan Academy: Chemistry
[2] MIT OpenCourseWare: Chemistry