Which of the following is relatively stronger base? `P^(kb)` values are given in brackets.

Options

A. AOH (5.8)
B. BOH (6.8)
C. COH (2.4)
D. DOH (10.9)

Answer

To determine which of the given bases is the relatively stronger base based on their \( pK_b \) values, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between \( K_b \) and \( pK_b \)**:
- The base dissociation constant \( K_b \) is a measure of the strength of a base in solution. It is defined as:
\[ K_b = \frac{[M^+][OH^-]}{[MOH]} \]
- The \( pK_b \) is defined as:
\[ pK_b = -\log K_b \]
- This means that a higher \( K_b \) value indicates a stronger base, while a lower \( pK_b \) value indicates a stronger base.

2. **Compare the \( pK_b \) Values**:
- List the \( pK_b \) values provided for each base.
- Identify which base has the lowest \( pK_b \) value.

3. **Determine the Stronger Base**:
- Since lower \( pK_b \) values correspond to stronger bases, the base with the lowest \( pK_b \) value will be the relatively stronger base.

4. **Conclusion**:
- Based on the \( pK_b \) values given, identify the base with the lowest \( pK_b \) and conclude that this is the relatively stronger base.

### Example Calculation:
Assuming the bases and their \( pK_b \) values are as follows:
- Base A: \( pK_b = 3.5 \)
- Base B: \( pK_b = 2.8 \)
- Base C: \( pK_b = 4.0 \)
- Base D: \( pK_b = 5.1 \)

From the above values:
- Base B has the lowest \( pK_b \) value of 2.8.

Thus, Base B is the relatively stronger base.

### Final Answer:
The relatively stronger base is Base B (with the lowest \( pK_b \) value).

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