A Solution At 25 Degrees Celsius Is $1.0 \times 10^{-5} , M , H_3O^+$. What Is The Concentration Of $OH^-$ In This Solution?A. $1.0 \times 10^{-5} , M , OH^-$ B. $1.0 \times 10^{-14} , M ,

Mar 12, 2025 by ADMIN 197 views

**A Solution at 25 Degrees Celsius: Calculating the Concentration of $OH^-$**

Understanding the Problem

In this problem, we are given a solution with a concentration of $1.0 \times 10^{-5} , M , H_3O^+$ at 25 degrees Celsius. We are asked to find the concentration of $OH^-$ in this solution. To solve this problem, we need to use the concept of the ion product constant of water ($K_w$) and the relationship between the concentrations of $H_3O^+$ and $OH^-$.

The Ion Product Constant of Water ($K_w$)

The ion product constant of water ($K_w$) is a measure of the concentration of $H_3O^+$ and $OH^-$ ions in water at a given temperature. At 25 degrees Celsius, the value of $K_w$ is $1.0 \times 10^{-14}$.

The Relationship Between $H_3O^+$ and $OH^-$ Concentrations

The concentration of $OH^-$ ions in a solution is related to the concentration of $H_3O^+$ ions by the following equation:

K_w = [H_3O^+][OH^-]

where $[H_3O^+]$ and $[OH^-]$ are the concentrations of $H_3O^+$ and $OH^-$ ions, respectively.

Solving for $[OH^-]$

We are given that $[H_3O^+] = 1.0 \times 10^{-5} , M$. We can substitute this value into the equation above and solve for $[OH^-]$:

1.0 \times 10^{-14} = (1.0 \times 10^{-5})[OH^-]

To solve for $[OH^-]$, we can divide both sides of the equation by $1.0 \times 10^{-5}$:

[OH^-] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-5}}

[OH^-] = 1.0 \times 10^{-9} \, M

Conclusion

Therefore, the concentration of $OH^-$ in the solution is $1.0 \times 10^{-9} , M$.

Answer

The correct answer is:

C. $1.0 \times 10^{-9} , M , OH^-$

Discussion

This problem illustrates the importance of understanding the relationship between the concentrations of $H_3O^+$ and $OH^-$ ions in a solution. By using the ion product constant of water ($K_w$) and the equation above, we can calculate the concentration of $OH^-$ ions in a solution given the concentration of $H_3O^+$ ions.

Real-World Applications

This concept is important in many real-world applications, such as:

Water Treatment: Understanding the relationship between $H_3O^+$ and $OH^-$ concentrations is crucial in water treatment processes, where the goal is to remove impurities and contaminants from water.
Environmental Science: The concentration of $OH^-$ ions in a solution can affect the pH of a solution, which is an important factor in environmental science, where the goal is to understand and mitigate the effects of pollution on ecosystems.
Biological Systems: The concentration of $OH^-$ ions in a solution can affect the activity of enzymes and other biomolecules, which is an important factor in biological systems, where the goal is to understand and regulate the activity of biomolecules.

Conclusion

In conclusion, the concentration of $OH^-$ ions in a solution can be calculated using the ion product constant of water ($K_w$) and the equation above. This concept is important in many real-world applications, such as water treatment, environmental science, and biological systems.

Understanding the Problem

In this article, we discussed how to calculate the concentration of $OH^-$ ions in a solution given the concentration of $H_3O^+$ ions. We used the ion product constant of water ($K_w$) and the equation $K_w = [H_3O^+][OH-]$ to solve for $[OH^-]$.

Q&A

Q: What is the ion product constant of water ($K_w$)?

A: The ion product constant of water ($K_w$) is a measure of the concentration of $H_3O^+$ and $OH^-$ ions in water at a given temperature. At 25 degrees Celsius, the value of $K_w$ is $1.0 \times 10^{-14}$.

Q: How is the concentration of $OH^-$ ions related to the concentration of $H_3O^+$ ions?

A: The concentration of $OH^-$ ions is related to the concentration of $H_3O^+$ ions by the equation $K_w = [H_3O^+][OH-]$.

Q: How do I calculate the concentration of $OH^-$ ions in a solution given the concentration of $H_3O^+$ ions?

A: To calculate the concentration of $OH^-$ ions in a solution given the concentration of $H_3O^+$ ions, you can use the equation $[OH^-] = \frac{K_w}{[H_3O^+]}$.

Q: What is the concentration of $OH^-$ ions in a solution with a concentration of $H_3O^+$ ions of $1.0 \times 10^{-5} , M$?

A: To calculate the concentration of $OH^-$ ions in a solution with a concentration of $H_3O^+$ ions of $1.0 \times 10^{-5} , M$, you can use the equation $[OH^-] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-5}}$, which gives a concentration of $OH^-$ ions of $1.0 \times 10^{-9} , M$.

Q: What are some real-world applications of understanding the relationship between $H_3O^+$ and $OH^-$ concentrations?

A: Understanding the relationship between $H_3O^+$ and $OH^-$ concentrations is important in many real-world applications, such as water treatment, environmental science, and biological systems.

Q: How can I use this concept to solve problems in chemistry?

A: You can use this concept to solve problems in chemistry by using the equation $K_w = [H_3O^+][OH-]$ to calculate the concentration of $OH^-$ ions in a solution given the concentration of $H_3O^+$ ions.

Conclusion

In conclusion, understanding the relationship between $H_3O^+$ and $OH^-$ concentrations is an important concept in chemistry. By using the ion product constant of water ($K_w$) and the equation $K_w = [H_3O^+][OH-]$, you can calculate the concentration of $OH^-$ ions in a solution given the concentration of $H_3O^+$ ions. This concept has many real-world applications, such as water treatment, environmental science, and biological systems.

Frequently Asked Questions

Q: What is the pH of a solution with a concentration of $H_3O^+$ ions of $1.0 \times 10^{-5} , M$?

A: The pH of a solution is related to the concentration of $H_3O^+$ ions by the equation $pH = -\log[H_3O^+]$. Therefore, the pH of a solution with a concentration of $H_3O^+$ ions of $1.0 \times 10^{-5} , M$ is $pH = -\log(1.0 \times 10^{-5}) = 5$.

Q: What is the concentration of $OH^-$ ions in a solution with a pH of 5?

A: To calculate the concentration of $OH^-$ ions in a solution with a pH of 5, you can use the equation $[OH^-] = \frac{K_w}{[H_3O^+]}$, where $[H_3O^+] = 10^{-pH} = 10^{-5} , M$. Therefore, the concentration of $OH^-$ ions in a solution with a pH of 5 is $[OH^-] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-5}} = 1.0 \times 10^{-9} , M$.