A weak base has a base hydrolysis constant, K₁, of 3.1 × 106. What is the pH of a 0.11 M solution of the weak base? pH =

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**Problem Statement:**

A weak base has a base hydrolysis constant, \( K_b \), of \( 3.1 \times 10^{-6} \). What is the pH of a 0.11 M solution of the weak base?

**Solution:**

To find the pH of the solution, we first need to determine the concentration of hydroxide ions, \([OH^-]\), in the solution. We can use the expression for the base hydrolysis constant:

\[ K_b = \frac{[BH^+][OH^-]}{[B]} \]

Assuming the initial concentration of the base, [B], is 0.11 M, and \([BH^+]\) and \([OH^-]\) are both \( x \) at equilibrium, we have:

\[ K_b = \frac{x \cdot x}{0.11 - x} \]

Given the small value of \( K_b \), we can approximate \( 0.11 - x \approx 0.11 \), thus:

\[ 3.1 \times 10^{-6} = \frac{x^2}{0.11} \]

Solving for \( x \):

\[ x^2 = 3.1 \times 10^{-6} \cdot 0.11 \]

\[ x^2 = 3.41 \times 10^{-7} \]

\[ x = \sqrt{3.41 \times 10^{-7}} \]

\[ x \approx 5.84 \times 10^{-4} \]

This \( x \) is the concentration of \( OH^- \) ions. To find the pOH:

\[ \text{pOH} = -\log(5.84 \times 10^{-4}) \]

\[ \text{pOH} \approx 3.23 \]

Finally, to find the pH:

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

\[ \text{pH} \approx 14 - 3.23 \]

\[ \text{pH} \approx 10.77 \]

Thus, the pH of the 0.11 M solution of the weak base is approximately 10.77.
Transcribed Image Text:**Problem Statement:** A weak base has a base hydrolysis constant, \( K_b \), of \( 3.1 \times 10^{-6} \). What is the pH of a 0.11 M solution of the weak base? **Solution:** To find the pH of the solution, we first need to determine the concentration of hydroxide ions, \([OH^-]\), in the solution. We can use the expression for the base hydrolysis constant: \[ K_b = \frac{[BH^+][OH^-]}{[B]} \] Assuming the initial concentration of the base, [B], is 0.11 M, and \([BH^+]\) and \([OH^-]\) are both \( x \) at equilibrium, we have: \[ K_b = \frac{x \cdot x}{0.11 - x} \] Given the small value of \( K_b \), we can approximate \( 0.11 - x \approx 0.11 \), thus: \[ 3.1 \times 10^{-6} = \frac{x^2}{0.11} \] Solving for \( x \): \[ x^2 = 3.1 \times 10^{-6} \cdot 0.11 \] \[ x^2 = 3.41 \times 10^{-7} \] \[ x = \sqrt{3.41 \times 10^{-7}} \] \[ x \approx 5.84 \times 10^{-4} \] This \( x \) is the concentration of \( OH^- \) ions. To find the pOH: \[ \text{pOH} = -\log(5.84 \times 10^{-4}) \] \[ \text{pOH} \approx 3.23 \] Finally, to find the pH: \[ \text{pH} = 14 - \text{pOH} \] \[ \text{pH} \approx 14 - 3.23 \] \[ \text{pH} \approx 10.77 \] Thus, the pH of the 0.11 M solution of the weak base is approximately 10.77.
Expert Solution
Step 1: Determine the pH of the solution using given data:

Given,

Molarity of a weak base = 0.11 M

Kb of base = 3.1 x 10-6 

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