Calculate The Molar Concentration Of O H − OH^{-} O H − Ions In A 0.583 M Solution Of Hypobromite Ion ( B R O − ; K B = 4.0 × 10 − 6 (BrO^{-}; \, K_{b}=4.0 \times 10^{-6} ( B R O − ; K B ​ = 4.0 × 1 0 − 6 ].Express The Molarity To Two Significant Figures. [ O H − ] = □ M \left[ OH^{-} \right]= \square \, M [ O H − ] = □ M

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Introduction

In chemistry, understanding the molar concentration of ions in a solution is crucial for various applications, including chemical reactions and equilibrium calculations. In this article, we will calculate the molar concentration of $OH^{-}$ ions in a 0.583 M solution of hypobromite ion $(BrO^{-})$ with a given base dissociation constant ($K_{b}$) of $4.0 \times 10^{-6}$.

Understanding the Problem

The hypobromite ion $(BrO^{-})$ is a weak base that partially dissociates in water to produce $OH^{-}$ ions and $BrO_{2}^{-}$ ions. The base dissociation constant ($K_{b}$) is a measure of the strength of the base and is given by the equation:

$$K_{b} = \frac{[BrO_{2}^{-}][OH^{-}]}{[BrO^{-}]}$$

We are given the initial concentration of hypobromite ion $(BrO^{-})$ as 0.583 M and the base dissociation constant ($K_{b}$) as $4.0 \times 10^{-6}$. We need to calculate the molar concentration of $OH^{-}$ ions in the solution.

Calculating the Molar Concentration of $OH^{-}$ Ions

To calculate the molar concentration of $OH^{-}$ ions, we can use the base dissociation constant ($K_{b}$) equation. Since the hypobromite ion $(BrO^{-})$ is a weak base, we can assume that the concentration of $BrO_{2}^{-}$ ions is equal to the concentration of $OH^{-}$ ions. Let's denote the concentration of $OH^{-}$ ions as $x$.

We can rewrite the base dissociation constant ($K_{b}$) equation as:

$$4.0 \times 10^{-6} = \frac{x^{2}}{0.583}$$

Simplifying the equation, we get:

$$x^{2} = 2.32 \times 10^{-6}$$

Taking the square root of both sides, we get:

$$x = \sqrt{2.32 \times 10^{-6}}$$

Evaluating the square root, we get:

$$x = 1.53 \times 10^{-3}$$

Therefore, the molar concentration of $OH^{-}$ ions in the solution is $1.53 \times 10^{-3}$ M.

Expressing the Molarity to Two Significant Figures

To express the molarity to two significant figures, we can round the value to the nearest hundredth. Therefore, the molar concentration of $OH^{-}$ ions in the solution is approximately $1.5 \times 10^{-3}$ M.

Conclusion

In this article, we calculated the molar concentration of $OH^{-}$ ions in a 0.583 M solution of hypobromite ion $(BrO^{-})$ with a given base dissociation constant ($K_{b}$) of $4.0 \times 10^{-6}$. We used the base dissociation constant ($K_{b}$) equation to calculate the molar concentration of $OH^{-}$ ions and expressed the molarity to two significant figures. The molar concentration of $OH^{-}$ ions in the solution is approximately $1.5 \times 10^{-3}$ M.

References

• [1] Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
• [2] Brown, T. L., LeMay, H. E., Bursten, B. E., & Murphy, C. (2012). Chemistry: The Central Science (13th ed.). Pearson Education.

Additional Resources

• [1] Khan Academy. (n.d.). Chemistry. Retrieved from https://www.khanacademy.org/science/chemistry
• [2] Chemistry LibreTexts. (n.d.). Chemistry. Retrieved from https://chem.libretexts.org/

Table of Contents

1. Introduction
2. Understanding the Problem
3. Calculating the Molar Concentration of $OH^{-}$ Ions
4. Expressing the Molarity to Two Significant Figures
5. Conclusion
6. References
7. Additional Resources
8. Table of Contents
   Q&A: Calculating Molar Concentration of $OH^{-}$ Ions in a Hypobromite Solution ====================================================================================

Introduction

In our previous article, we calculated the molar concentration of $OH^{-}$ ions in a 0.583 M solution of hypobromite ion $(BrO^{-})$ with a given base dissociation constant ($K_{b}$) of $4.0 \times 10^{-6}$. In this article, we will answer some frequently asked questions related to the calculation of molar concentration of $OH^{-}$ ions in a hypobromite solution.

Q: What is the base dissociation constant ($K_{b}$) and how is it related to the molar concentration of $OH^{-}$ ions?

A: The base dissociation constant ($K_{b}$) is a measure of the strength of a base and is related to the molar concentration of $OH^{-}$ ions. It is defined as the ratio of the concentrations of the conjugate base and the hydroxide ion to the concentration of the base.

Q: How do I calculate the molar concentration of $OH^{-}$ ions in a hypobromite solution?

A: To calculate the molar concentration of $OH^{-}$ ions in a hypobromite solution, you can use the base dissociation constant ($K_{b}$) equation. The equation is:

$$K_{b} = \frac{[BrO_{2}^{-}][OH^{-}]}{[BrO^{-}]}$$

You can rearrange the equation to solve for the molar concentration of $OH^{-}$ ions.

Q: What is the significance of expressing the molarity to two significant figures?

A: Expressing the molarity to two significant figures is important because it provides a more accurate representation of the molar concentration of $OH^{-}$ ions. It also helps to avoid rounding errors and ensures that the calculated value is consistent with the given data.

Q: Can I use the base dissociation constant ($K_{b}$) equation to calculate the molar concentration of $OH^{-}$ ions in any base?

A: Yes, you can use the base dissociation constant ($K_{b}$) equation to calculate the molar concentration of $OH^{-}$ ions in any base. However, you need to ensure that the base dissociation constant ($K_{b}$) is given and that the equation is applicable to the specific base.

Q: What are some common sources of error when calculating the molar concentration of $OH^{-}$ ions?

A: Some common sources of error when calculating the molar concentration of $OH^{-}$ ions include:

• Incorrect values for the base dissociation constant ($K_{b}$)
• Incorrect values for the initial concentration of the base
• Incorrect units for the concentrations
• Rounding errors

Q: How can I verify the accuracy of my calculated value for the molar concentration of $OH^{-}$ ions?

A: You can verify the accuracy of your calculated value for the molar concentration of $OH^{-}$ ions by:

• Checking the units of the concentrations
• Verifying that the base dissociation constant ($K_{b}$) is given and applicable to the specific base
• Using a calculator or computer program to perform the calculations
• Comparing your calculated value with the expected value

Conclusion

In this article, we answered some frequently asked questions related to the calculation of molar concentration of $OH^{-}$ ions in a hypobromite solution. We provided explanations and examples to help clarify the concepts and procedures involved in calculating the molar concentration of $OH^{-}$ ions.

References

• [1] Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
• [2] Brown, T. L., LeMay, H. E., Bursten, B. E., & Murphy, C. (2012). Chemistry: The Central Science (13th ed.). Pearson Education.

Additional Resources

• [1] Khan Academy. (n.d.). Chemistry. Retrieved from https://www.khanacademy.org/science/chemistry
• [2] Chemistry LibreTexts. (n.d.). Chemistry. Retrieved from https://chem.libretexts.org/

Table of Contents

1. Introduction
2. Q: What is the base dissociation constant ($K_{b}$) and how is it related to the molar concentration of $OH^{-}$ ions?
3. Q: How do I calculate the molar concentration of $OH^{-}$ ions in a hypobromite solution?
4. Q: What is the significance of expressing the molarity to two significant figures?
5. Q: Can I use the base dissociation constant ($K_{b}$) equation to calculate the molar concentration of $OH^{-}$ ions in any base?
6. Q: What are some common sources of error when calculating the molar concentration of $OH^{-}$ ions?
7. Q: How can I verify the accuracy of my calculated value for the molar concentration of $OH^{-}$ ions?
8. Conclusion
9. References
10. Additional Resources
11. Table of Contents