The PH Of A 1.00 X 10-3 M Solution Of Pyrrolidine Is 10.82. Calculate Kb.

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The pH of a 1.00 x 10^-3 M solution of pyrrolidine is 10.82. Calculate Kb

Understanding the Problem

In this problem, we are given the pH of a 1.00 x 10^-3 M solution of pyrrolidine and asked to calculate the base dissociation constant (Kb). To solve this problem, we need to understand the relationship between pH and pOH, as well as the definition of Kb.

pH and pOH Relationship

The pH and pOH of a solution are related by the equation:

pH + pOH = 14

At 25°C, the pOH of a solution can be calculated using the following equation:

pOH = -log[OH^-]

where [OH^-] is the concentration of hydroxide ions in the solution.

Calculating pOH

Given that the pH of the solution is 10.82, we can calculate the pOH using the equation:

pOH = 14 - pH = 14 - 10.82 = 3.18

Calculating [OH^-]

Now that we have the pOH, we can calculate the concentration of hydroxide ions in the solution using the equation:

[OH^-] = 10^(-pOH) = 10^(-3.18) = 1.95 x 10^-4 M

Understanding Kb

The base dissociation constant (Kb) is a measure of the strength of a base. It is defined as the ratio of the concentration of the conjugate acid to the concentration of the base, multiplied by the concentration of hydroxide ions:

Kb = [BH+][OH-] / [B]

where [BH^+] is the concentration of the conjugate acid, [OH^-] is the concentration of hydroxide ions, and [B] is the concentration of the base.

Calculating Kb

Given that the concentration of the base (pyrrolidine) is 1.00 x 10^-3 M, and the concentration of hydroxide ions is 1.95 x 10^-4 M, we can calculate the concentration of the conjugate acid using the equation:

[BH^+] = [B] - [OH^-] = 1.00 x 10^-3 M - 1.95 x 10^-4 M = 8.05 x 10^-4 M

Now that we have the concentrations of the conjugate acid and hydroxide ions, we can calculate the Kb using the equation:

Kb = [BH+][OH-] / [B] = (8.05 x 10^-4 M)(1.95 x 10^-4 M) / (1.00 x 10^-3 M) = 1.57 x 10^-8

Conclusion

In this problem, we were given the pH of a 1.00 x 10^-3 M solution of pyrrolidine and asked to calculate the base dissociation constant (Kb). We first calculated the pOH and [OH^-] using the pH and the relationship between pH and pOH. Then, we calculated the concentration of the conjugate acid using the equation [BH^+] = [B] - [OH^-]. Finally, we calculated the Kb using the equation Kb = [BH+][OH-] / [B]. The calculated Kb is 1.57 x 10^-8.

References

  • Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Brown, T. E., & LeMay, H. E. (2014). Chemistry: The Central Science. Pearson Education.

Key Takeaways

  • The pH and pOH of a solution are related by the equation pH + pOH = 14.
  • The pOH of a solution can be calculated using the equation pOH = -log[OH^-].
  • The base dissociation constant (Kb) is a measure of the strength of a base.
  • Kb can be calculated using the equation Kb = [BH+][OH-] / [B].
    The pH of a 1.00 x 10^-3 M solution of pyrrolidine is 10.82. Calculate Kb: Q&A

Q: What is the relationship between pH and pOH?

A: The pH and pOH of a solution are related by the equation:

pH + pOH = 14

At 25°C, the pOH of a solution can be calculated using the equation:

pOH = -log[OH^-]

where [OH^-] is the concentration of hydroxide ions in the solution.

Q: How do I calculate pOH from pH?

A: To calculate pOH from pH, you can use the equation:

pOH = 14 - pH

For example, if the pH of a solution is 10.82, you can calculate the pOH as follows:

pOH = 14 - 10.82 = 3.18

Q: What is the base dissociation constant (Kb)?

A: The base dissociation constant (Kb) is a measure of the strength of a base. It is defined as the ratio of the concentration of the conjugate acid to the concentration of the base, multiplied by the concentration of hydroxide ions:

Kb = [BH+][OH-] / [B]

where [BH^+] is the concentration of the conjugate acid, [OH^-] is the concentration of hydroxide ions, and [B] is the concentration of the base.

Q: How do I calculate Kb from the given values?

A: To calculate Kb, you need to know the concentrations of the conjugate acid, hydroxide ions, and the base. Given that the concentration of the base (pyrrolidine) is 1.00 x 10^-3 M, and the concentration of hydroxide ions is 1.95 x 10^-4 M, you can calculate the concentration of the conjugate acid using the equation:

[BH^+] = [B] - [OH^-] = 1.00 x 10^-3 M - 1.95 x 10^-4 M = 8.05 x 10^-4 M

Now that you have the concentrations of the conjugate acid and hydroxide ions, you can calculate the Kb using the equation:

Kb = [BH+][OH-] / [B] = (8.05 x 10^-4 M)(1.95 x 10^-4 M) / (1.00 x 10^-3 M) = 1.57 x 10^-8

Q: What is the significance of Kb in chemistry?

A: Kb is an important concept in chemistry as it helps us understand the strength of a base. A higher Kb value indicates a stronger base, while a lower Kb value indicates a weaker base.

Q: Can you provide examples of strong and weak bases?

A: Yes, here are some examples of strong and weak bases:

  • Strong bases:
  • Sodium hydroxide (NaOH)
  • Potassium hydroxide (KOH)
  • Calcium hydroxide (Ca(OH)2)
  • Weak bases:
  • Ammonia (NH3)
  • Pyrrolidine (C4H9N)
  • Triethylamine (C6H15N)

Q: How do I determine if a base is strong or weak?

A: To determine if a base is strong or weak, you can look at its Kb value. If the Kb value is high (greater than 1 x 10^-3), the base is considered strong. If the Kb value is low (less than 1 x 10^-3), the base is considered weak.

Q: What are some common applications of Kb in chemistry?

A: Kb is used in various applications in chemistry, including:

  • Determining the strength of a base
  • Calculating the pH of a solution
  • Understanding the behavior of acids and bases
  • Designing and optimizing chemical reactions

Q: Can you provide some tips for calculating Kb?

A: Yes, here are some tips for calculating Kb:

  • Make sure to use the correct units for the concentrations of the conjugate acid, hydroxide ions, and the base.
  • Use the correct equation for calculating Kb.
  • Check your calculations carefully to avoid errors.
  • Use a calculator or computer program to simplify the calculations.

Conclusion

In this Q&A article, we have discussed the relationship between pH and pOH, the definition of Kb, and how to calculate Kb from given values. We have also provided examples of strong and weak bases, and discussed the significance of Kb in chemistry. Additionally, we have provided some tips for calculating Kb and common applications of Kb in chemistry.