CH16 Practice Set Part D: Problem 16.78 Enhanced With Expanded HintsHexamethylenetetramine { (C_6H_{12}N_4)$}$ Is A Weak Organic Base. A ${ 7.0 \times 10^{-3} \, \text{M}\$} Solution Of Hexamethylenetetramine Has A PH Of 8.37.Part

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Understanding the Problem

Hexamethylenetetramine, also known as urotropine, is a weak organic base with the chemical formula (C6H12N4)(C_6H_{12}N_4). In this problem, we are given a 7.0×10−3 M7.0 \times 10^{-3} \, \text{M} solution of hexamethylenetetramine and are asked to find its pH, which is already given as 8.37. However, we will work through the problem step by step to understand the concept of weak bases and their dissociation in water.

Weak Bases and Their Dissociation

A weak base is a base that does not completely dissociate in water. In other words, it only partially dissociates into its conjugate acid and hydroxide ions. The dissociation of a weak base can be represented by the following equation:

Base+H2O⇌Conjugate Acid+OH−\text{Base} + \text{H}_2\text{O} \rightleftharpoons \text{Conjugate Acid} + \text{OH}^-

For hexamethylenetetramine, the dissociation equation can be written as:

Hexamethylenetetramine+H2O⇌Conjugate Acid+OH−\text{Hexamethylenetetramine} + \text{H}_2\text{O} \rightleftharpoons \text{Conjugate Acid} + \text{OH}^-

Calculating the Dissociation Constant (Kb)

The dissociation constant (Kb) of a weak base is a measure of its strength. It is defined as the ratio of the concentration of the conjugate acid to the concentration of the base. The Kb value for hexamethylenetetramine is not given, but we can use the given pH value to calculate it.

Step 1: Calculate the pOH

The pOH of a solution can be calculated using the following equation:

pOH=−log⁡[OH−]\text{pOH} = -\log[\text{OH}^-]

We can rearrange this equation to solve for [OH^-]:

[OH−]=10−pOH[\text{OH}^-] = 10^{-\text{pOH}}

Given that the pH is 8.37, we can calculate the pOH as follows:

pH+pOH=14\text{pH} + \text{pOH} = 14

pOH=14−pH\text{pOH} = 14 - \text{pH}

pOH=14−8.37\text{pOH} = 14 - 8.37

pOH=5.63\text{pOH} = 5.63

Now, we can calculate [OH^-]:

[OH−]=10−5.63[\text{OH}^-] = 10^{-5.63}

[OH−]=2.81×10−6 M[\text{OH}^-] = 2.81 \times 10^{-6} \, \text{M}

Step 2: Calculate the Kb

The Kb value can be calculated using the following equation:

Kb=[Conjugate Acid][OH−][Base]\text{Kb} = \frac{[\text{Conjugate Acid}][\text{OH}^-]}{[\text{Base}]}

Since the dissociation of hexamethylenetetramine is a weak base, we can assume that the concentration of the conjugate acid is equal to the concentration of the hydroxide ions:

[Conjugate Acid]=[OH−][\text{Conjugate Acid}] = [\text{OH}^-]

Now, we can substitute the values into the Kb equation:

Kb=[OH−]2[Base]\text{Kb} = \frac{[\text{OH}^-]^2}{[\text{Base}]}

Kb=(2.81×10−6 M)27.0×10−3 M\text{Kb} = \frac{(2.81 \times 10^{-6} \, \text{M})^2}{7.0 \times 10^{-3} \, \text{M}}

Kb=1.23×10−9\text{Kb} = 1.23 \times 10^{-9}

Conclusion

In this problem, we have worked through the concept of weak bases and their dissociation in water. We have calculated the dissociation constant (Kb) of hexamethylenetetramine using the given pH value and the concentration of the base. The Kb value is an important parameter in understanding the strength of a weak base.

Key Takeaways

  • A weak base is a base that does not completely dissociate in water.
  • The dissociation constant (Kb) of a weak base is a measure of its strength.
  • The Kb value can be calculated using the concentration of the base, the concentration of the hydroxide ions, and the dissociation equation.

Practice Problems

  1. Calculate the Kb value for a 5.0×10−3 M5.0 \times 10^{-3} \, \text{M} solution of a weak base with a pH of 9.15.
  2. Calculate the pH of a 2.0×10−3 M2.0 \times 10^{-3} \, \text{M} solution of a weak base with a Kb value of 1.2 \times 10^{-8}.

References

  • Atkins, P. W., & De Paula, J. (2010). Physical Chemistry (9th ed.). Oxford University Press.
  • Chang, R. (2010). Chemistry: The Central Science (11th ed.). McGraw-Hill.

Q: What is the difference between a strong base and a weak base?

A: A strong base is a base that completely dissociates in water, producing a high concentration of hydroxide ions. A weak base, on the other hand, only partially dissociates in water, producing a low concentration of hydroxide ions.

Q: How is the dissociation constant (Kb) of a weak base calculated?

A: The dissociation constant (Kb) of a weak base is calculated using the following equation:

Kb=[Conjugate Acid][OH−][Base]\text{Kb} = \frac{[\text{Conjugate Acid}][\text{OH}^-]}{[\text{Base}]}

Q: What is the relationship between the pH and pOH of a solution?

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

pH+pOH=14\text{pH} + \text{pOH} = 14

Q: How is the pOH of a solution calculated?

A: The pOH of a solution is calculated using the following equation:

pOH=−log⁡[OH−]\text{pOH} = -\log[\text{OH}^-]

Q: What is the significance of the Kb value in understanding the strength of a weak base?

A: The Kb value is a measure of the strength of a weak base. A higher Kb value indicates a stronger base, while a lower Kb value indicates a weaker base.

Q: Can you give an example of a weak base and its Kb value?

A: Yes, an example of a weak base is hexamethylenetetramine (C6H12N4), which has a Kb value of 1.23 x 10^-9.

Q: How is the pH of a solution related to the concentration of the base?

A: The pH of a solution is related to the concentration of the base by the following equation:

pH=−log⁡[Base]+log⁡(1Kb)\text{pH} = -\log[\text{Base}] + \log\left(\frac{1}{\text{Kb}}\right)

Q: Can you explain the concept of the conjugate acid in the context of weak bases?

A: Yes, the conjugate acid is the species that is formed when a weak base dissociates in water. It is the acid that is formed when the base accepts a proton (H+ ion).

Q: How is the concentration of the conjugate acid related to the concentration of the base?

A: The concentration of the conjugate acid is equal to the concentration of the hydroxide ions (OH^-) in the solution.

Q: Can you give an example of a problem that involves calculating the Kb value of a weak base?

A: Yes, an example of a problem that involves calculating the Kb value of a weak base is:

Calculate the Kb value for a 5.0 x 10^-3 M solution of a weak base with a pH of 9.15.

Q: How is the Kb value used in real-world applications?

A: The Kb value is used in a variety of real-world applications, including:

  • Water treatment: The Kb value is used to determine the effectiveness of water treatment processes.
  • Environmental monitoring: The Kb value is used to monitor the pH of environmental samples.
  • Pharmaceutical applications: The Kb value is used to determine the pH of pharmaceutical solutions.

Conclusion

In this Q&A article, we have discussed various concepts related to weak bases, including the dissociation constant (Kb), the relationship between pH and pOH, and the significance of the Kb value in understanding the strength of a weak base. We have also provided examples of problems that involve calculating the Kb value of a weak base and discussed the real-world applications of the Kb value.