The `pH` of a solution of weak base at neutralisation with strong acid is `8. K_(b)` for the base is

Options

A. `1.0 xx 10^(-4)`
B. `1.0 xx 10^(-6)`
C. `1.0 xx 10^(-8)`
D. None of these

Explanation

To solve the problem, we need to determine the \( K_b \) (base dissociation constant) for a weak base when the pH of its solution at neutralization with a strong acid is given as 8. Here’s how we can approach this step by step:

### Step 1: Understand the Reaction
When a weak base (let's denote it as \( B \)) reacts with a strong acid (denote it as \( HA \)), it forms a salt (\( AB \)) and water. The reaction can be represented as:
\[ B + HA \rightarrow AB + H_2O \]

### Step 2: Identify the pH and Calculate pOH
Given that the pH of the solution at neutralization is 8, we can calculate the pOH using the relationship:
\[ \text{pH} + \text{pOH} = 14 \]
Thus,
\[ \text{pOH} = 14 - \text{pH} = 14 - 8 = 6 \]

### Step 3: Calculate the Concentration of Hydroxide Ions
The pOH can be used to find the concentration of hydroxide ions (\( [OH^-] \)):
\[ [OH^-] = 10^{-\text{pOH}} = 10^{-6} \, \text{M} \]

### Step 4: Relate Hydroxide Ion Concentration to \( K_b \)
At the equivalence point, the salt \( AB \) undergoes hydrolysis to produce hydroxide ions:
\[ AB + H_2O \rightleftharpoons A^- + OH^- \]
The equilibrium expression for this hydrolysis can be written as:
\[ K_b = \frac{[OH^-]^2}{[AB]} \]
Assuming that the concentration of the salt \( AB \) is \( C \) (which we will determine later), we can substitute \( [OH^-] \) into the equation:
\[ K_b = \frac{(10^{-6})^2}{C} = \frac{10^{-12}}{C} \]

### Step 5: Determine the Concentration \( C \)
We know that at neutralization, the pH is 8, which corresponds to the salt being in a solution that is slightly basic due to hydrolysis. However, we do not have the concentration \( C \) provided in the problem.

### Step 6: Conclusion
Since we cannot determine \( K_b \) without knowing the concentration \( C \), we conclude that the value of \( K_b \) cannot be calculated with the information provided.

### Final Answer
The answer is that we cannot determine \( K_b \) without additional information about the concentration of the salt formed.

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