pH Calculation of a Weak Base

Oct 13, 2025 by wbrum.org 17 views

In chemistry, pH is a measure of the concentration of hydrogen ions in a solution. It is an essential concept in understanding the properties and behavior of various substances. In this article, we will explore the calculation of pH in different solutions, including a weak base, a salt of a weak base, pure water, and a mixture.

pH Calculation of a Weak Base

A weak base is a substance that partially dissociates in water, releasing hydroxide ions (OH-). The dissociation of a weak base can be represented by the following equation:

\text{HONH}_2 + \text{H}_2\text{O} \rightleftharpoons \text{HONH}_3^+ + \text{OH}^-

The equilibrium constant for this reaction is given by the base dissociation constant (Kb):

K_b = \frac{[\text{HONH}_3^+][\text{OH}^-]}{[\text{HONH}_2]}

Given that the concentration of HONH2 is 0.100 M and Kb = 1.1 x 10^-8, we can calculate the concentration of OH- ions using the Kb expression:

[\text{OH}^-] = \sqrt{K_b \times [\text{HONH}_2]}

[\text{OH}^-] = \sqrt{(1.1 \times 10^{-8}) \times (0.100)}

[\text{OH}^-] = \sqrt{1.1 \times 10^{-9}}

[\text{OH}^-] = 1.048 \times 10^{-4.5}

Now that we have the concentration of OH- ions, we can calculate the pH of the solution using the pOH formula:

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

\text{pOH} = -\log(1.048 \times 10^{-4.5})

\text{pOH} = 4.98

Since pH + pOH = 14, we can calculate the pH of the solution:

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

\text{pH} = 14 - 4.98

\text{pH} = 9.02

pH Calculation of a Salt of a Weak Base

A salt of a weak base is a substance that is formed by the reaction of a weak base with a strong acid. The dissociation of a salt of a weak base can be represented by the following equation:

\text{HONH}_3^+ + \text{H}_2\text{O} \rightleftharpoons \text{HONH}_2 + \text{H}_3\text{O}^+

The equilibrium constant for this reaction is given by the acid dissociation constant (Ka):

K_a = \frac{[\text{HONH}_2][\text{H}_3\text{O}^+]}{[\text{HONH}_3^+]}

However, since the salt is formed from a weak base, we can assume that the concentration of HONH2 is negligible compared to the concentration of HONH3+. Therefore, we can simplify the Ka expression:

K_a = \frac{[\text{H}_3\text{O}^+]}{[\text{HONH}_3^+]}

Given that the concentration of HONH3Cl is 0.100 M, we can calculate the concentration of H3O+ ions using the Ka expression:

[\text{H}_3\text{O}^+] = K_a \times [\text{HONH}_3^+]

[\text{H}_3\text{O}^+] = (1.1 \times 10^{-8}) \times (0.100)

[\text{H}_3\text{O}^+] = 1.1 \times 10^{-9}

Now that we have the concentration of H3O+ ions, we can calculate the pH of the solution using the pH formula:

\text{pH} = -\log[\text{H}_3\text{O}^+]

\text{pH} = -\log(1.1 \times 10^{-9})

\text{pH} = 8.96

pH Calculation of Pure Water

Pure water is a neutral solution with a pH of 7. The pH of pure water can be calculated using the following equation:

\text{pH} = -\log[\text{H}_3\text{O}^+]

\text{pH} = -\log(1.0 \times 10^{-7})

\text{pH} = 7.00

pH Calculation of a Mixture

A mixture is a solution that contains multiple substances. The pH of a mixture can be calculated using the following equation:

\text{pH} = -\log\left(\frac{[\text{H}_3\text{O}^+]}{[\text{HONH}_2] + [\text{HONH}_3^+]} \right)

However, since the mixture contains multiple substances, we need to calculate the concentration of H3O+ ions and HONH2 and HONH3+ ions separately.

Assuming that the mixture contains 0.100 M HONH2 and 0.100 M HONH3Cl, we can calculate the concentration of H3O+ ions using the Ka expression:

K_a = \frac{[\text{H}_3\text{O}^+]}{[\text{HONH}_3^+]}

[\text{H}_3\text{O}^+] = K_a \times [\text{HONH}_3^+]

[\text{H}_3\text{O}^+] = (1.1 \times 10^{-8}) \times (0.100)

[\text{H}_3\text{O}^+] = 1.1 \times 10^{-9}

Now that we have the concentration of H3O+ ions, we can calculate the pH of the mixture using the pH formula:

\text{pH} = -\log\left(\frac{[\text{H}_3\text{O}^+]}{[\text{HONH}_2] + [\text{HONH}_3^+]} \right)

\text{pH} = -\log\left(\frac{1.1 \times 10^{-9}}{0.100 + 0.100} \right)

\text{pH} = -\log(5.5 \times 10^{-10})

\text{pH} = 9.26

In the previous article, we discussed the calculation of pH in various solutions, including a weak base, a salt of a weak base, pure water, and a mixture. However, we understand that there may be some questions and concerns that readers may have. In this article, we will address some of the frequently asked questions about pH calculation.

Q: What is pH, and why is it important?

A: pH is a measure of the concentration of hydrogen ions (H3O+) in a solution. It is an essential concept in understanding the properties and behavior of various substances. pH is important because it affects the reactivity of substances, the growth of microorganisms, and the stability of materials.

Q: How do I calculate the pH of a solution?

A: To calculate the pH of a solution, you need to know the concentration of hydrogen ions (H3O+) or hydroxide ions (OH-). You can use the pH formula:

pH = -log[H3O+]

pH = 14 - pOH

where pOH is the concentration of hydroxide ions.

Q: What is the difference between pH and pOH?

A: pH and pOH are two related but distinct concepts. pH is a measure of the concentration of hydrogen ions (H3O+), while pOH is a measure of the concentration of hydroxide ions (OH-). The relationship between pH and pOH is given by:

pH + pOH = 14

Q: How do I calculate the pH of a weak base?

A: To calculate the pH of a weak base, you need to know the concentration of the base and its base dissociation constant (Kb). You can use the following equation:

pH = -log[H3O+] = -log(Kb * [base])

where [base] is the concentration of the base.

Q: How do I calculate the pH of a salt of a weak base?

A: To calculate the pH of a salt of a weak base, you need to know the concentration of the salt and its acid dissociation constant (Ka). You can use the following equation:

pH = -log[H3O+] = -log(Ka * [salt])

where [salt] is the concentration of the salt.

Q: What is the pH of pure water?

A: The pH of pure water is 7. This is because pure water contains equal concentrations of hydrogen ions (H3O+) and hydroxide ions (OH-).

Q: How do I calculate the pH of a mixture?

A: To calculate the pH of a mixture, you need to know the concentrations of the individual substances and their acid dissociation constants (Ka) or base dissociation constants (Kb). You can use the following equation:

pH = -log\left(\frac{[H3O+]}{[base] + [salt]} \right)

where [base] and [salt] are the concentrations of the base and salt, respectively.

Q: What are some common mistakes to avoid when calculating pH?

A: Some common mistakes to avoid when calculating pH include:

Not knowing the concentration of hydrogen ions (H3O+) or hydroxide ions (OH-)
Not using the correct acid dissociation constant (Ka) or base dissociation constant (Kb)
Not considering the effects of temperature and pressure on pH
Not using the correct units for concentration (e.g., M, mol/L)

By avoiding these common mistakes, you can ensure that your pH calculations are accurate and reliable.