Expressing the Molarity to Two Significant Figures

Oct 13, 2025 by miodeya.com 6 views

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/

Introduction
Understanding the Problem
Calculating the Molar Concentration of $OH^{-}$ Ions
Expressing the Molarity to Two Significant Figures
Conclusion
References
Additional Resources
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/

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