Solubility in a Solution with a Given Sulfate Concentration

Oct 13, 2025 by pynkocean.com 2 views

Introduction

The solubility of a salt in a solution is a critical parameter in various chemical processes, including the formation of precipitates and the behavior of ions in aqueous solutions. In this article, we will calculate the solubility of barium sulfate (BaSO4) in pure water and in a solution with a given sulfate concentration. We will use the solubility product constant (Ksp) of BaSO4, which is a measure of the equilibrium between the dissolved ions and the solid salt.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is a measure of the equilibrium between the dissolved ions and the solid salt. It is defined as the product of the concentrations of the ions in a saturated solution. For BaSO4, the Ksp expression is:

K_{\text{sp}} = \left[ \text{Ba}^{2+} \right] \left[ \text{SO}_4^{2-} \right]

Given that the Ksp of BaSO4 is 1.1 × 10−10, we can use this value to calculate the solubility of BaSO4 in pure water and in a solution with a given sulfate concentration.

Solubility in Pure Water

To calculate the solubility of BaSO4 in pure water, we can use the Ksp expression and the fact that the concentration of Ba2+ ions is equal to the concentration of SO42− ions. Let's denote the concentration of Ba2+ ions as [Ba2+] and the concentration of SO42− ions as [SO42−]. Since the Ksp expression is a product of the concentrations of the ions, we can write:

K_{\text{sp}} = \left[ \text{Ba}^{2+} \right] \left[ \text{SO}_4^{2-} \right] = \left[ \text{Ba}^{2+} \right] \left[ \text{Ba}^{2+} \right] = \left[ \text{Ba}^{2+} \right]^2

Since the concentration of Ba2+ ions is equal to the concentration of SO42− ions, we can substitute [SO42−] with [Ba2+]. Therefore, the Ksp expression becomes:

K_{\text{sp}} = \left[ \text{Ba}^{2+} \right]^2

Now, we can solve for [Ba2+]. Taking the square root of both sides of the equation, we get:

\left[ \text{Ba}^{2+} \right] = \sqrt{K_{\text{sp}}} = \sqrt{1.1 \times 10^{-10}}

Using a calculator, we can find that:

\left[ \text{Ba}^{2+} \right] = 1.05 \times 10^{-5} \, M

Since the concentration of Ba2+ ions is equal to the concentration of SO42− ions, we can conclude that the solubility of BaSO4 in pure water is:

\text{Solubility} = \left[ \text{Ba}^{2+} \right] = 1.05 \times 10^{-5} \, M

Solubility in a Solution with a Given Sulfate Concentration

To calculate the solubility of BaSO4 in a solution with a given sulfate concentration, we can use the Ksp expression and the fact that the concentration of Ba2+ ions is equal to the concentration of SO42− ions. Let's denote the concentration of Ba2+ ions as [Ba2+] and the concentration of SO42− ions as [SO42−]. Since the Ksp expression is a product of the concentrations of the ions, we can write:

K_{\text{sp}} = \left[ \text{Ba}^{2+} \right] \left[ \text{SO}_4^{2-} \right]

Given that the concentration of SO42− ions is 0.221 M, we can substitute [SO42−] with 0.221 M. Therefore, the Ksp expression becomes:

K_{\text{sp}} = \left[ \text{Ba}^{2+} \right] \left( 0.221 \, M \right)

Now, we can solve for [Ba2+]. Dividing both sides of the equation by 0.221 M, we get:

\left[ \text{Ba}^{2+} \right] = \frac{K_{\text{sp}}}{0.221 \, M} = \frac{1.1 \times 10^{-10}}{0.221 \, M}

Using a calculator, we can find that:

\left[ \text{Ba}^{2+} \right] = 4.98 \times 10^{-10} \, M

Since the concentration of Ba2+ ions is equal to the concentration of SO42− ions, we can conclude that the solubility of BaSO4 in a solution with a given sulfate concentration is:

\text{Solubility} = \left[ \text{Ba}^{2+} \right] = 4.98 \times 10^{-10} \, M

Conclusion

In this article, we calculated the solubility of BaSO4 in pure water and in a solution with a given sulfate concentration. We used the solubility product constant (Ksp) of BaSO4, which is a measure of the equilibrium between the dissolved ions and the solid salt. We found that the solubility of BaSO4 in pure water is 1.05 × 10−5 M, and the solubility of BaSO4 in a solution with a given sulfate concentration is 4.98 × 10−10 M. These results demonstrate the importance of considering the concentration of ions in a solution when calculating the solubility of a salt.

References

[1] Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
[2] Brown, T. E., & LeMay, H. E. (2012). Chemistry: The Central Science (12th ed.). Pearson Education.
[3] Cengel, Y. A. (2013). Thermodynamics: An Interactive Introduction (2nd ed.). McGraw-Hill Education.

Note: The references provided are a selection of textbooks and resources that can be used to learn more about the topic of solubility and the solubility product constant (Ksp).

Introduction

In our previous article, we calculated the solubility of barium sulfate (BaSO4) in pure water and in a solution with a given sulfate concentration. We used the solubility product constant (Ksp) of BaSO4, which is a measure of the equilibrium between the dissolved ions and the solid salt. In this article, we will answer some frequently asked questions (FAQs) related to the solubility of BaSO4.

Q: What is the solubility product constant (Ksp) of BaSO4?

A: The solubility product constant (Ksp) of BaSO4 is 1.1 × 10−10.

Q: How do you calculate the solubility of BaSO4 in pure water?

A: To calculate the solubility of BaSO4 in pure water, we can use the Ksp expression and the fact that the concentration of Ba2+ ions is equal to the concentration of SO42− ions. We can write:

K_{\text{sp}} = \left[ \text{Ba}^{2+} \right] \left[ \text{SO}_4^{2-} \right] = \left[ \text{Ba}^{2+} \right] \left[ \text{Ba}^{2+} \right] = \left[ \text{Ba}^{2+} \right]^2

Q: What is the solubility of BaSO4 in pure water?

A: The solubility of BaSO4 in pure water is 1.05 × 10−5 M.

Q: How do you calculate the solubility of BaSO4 in a solution with a given sulfate concentration?

A: To calculate the solubility of BaSO4 in a solution with a given sulfate concentration, we can use the Ksp expression and the fact that the concentration of Ba2+ ions is equal to the concentration of SO42− ions. We can write:

K_{\text{sp}} = \left[ \text{Ba}^{2+} \right] \left[ \text{SO}_4^{2-} \right]

Q: What is the solubility of BaSO4 in a solution with a given sulfate concentration?

A: The solubility of BaSO4 in a solution with a given sulfate concentration is 4.98 × 10−10 M.

Q: Why is the solubility of BaSO4 in a solution with a given sulfate concentration lower than in pure water?

A: The solubility of BaSO4 in a solution with a given sulfate concentration is lower than in pure water because the sulfate ions in the solution can react with the barium ions to form a precipitate, reducing the concentration of barium ions in the solution.

Q: What are some common applications of BaSO4?

A: BaSO4 is commonly used as a pigment in paints and coatings, as a filler in plastics and rubber, and as a component in the manufacture of paper and textiles.

Q: Is BaSO4 toxic?

A: BaSO4 is generally considered to be non-toxic, but it can be harmful if ingested in large quantities.

Q: Can BaSO4 be used as a medication?

A: BaSO4 has been used as a medication to treat certain medical conditions, such as constipation and diarrhea. However, its use as a medication is limited due to its potential side effects.

Conclusion

In this article, we answered some frequently asked questions (FAQs) related to the solubility of BaSO4. We provided information on the solubility product constant (Ksp) of BaSO4, how to calculate the solubility of BaSO4 in pure water and in a solution with a given sulfate concentration, and some common applications of BaSO4. We also discussed the potential toxicity and medical uses of BaSO4.

References

[1] Atkins, P. W., & De Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
[2] Brown, T. E., & LeMay, H. E. (2012). Chemistry: The Central Science (12th ed.). Pearson Education.
[3] Cengel, Y. A. (2013). Thermodynamics: An Interactive Introduction (2nd ed.). McGraw-Hill Education.

Note: The references provided are a selection of textbooks and resources that can be used to learn more about the topic of solubility and the solubility product constant (Ksp).