Which of the following is correct?

Options

A. `pK_b = log(K_b)`
B. `pK_b = -log(K_b)`
C. `pK_b = ln(K_b)`
D. `pK_b = -ln(K_b)`

Answer

To determine which statement is correct regarding the relationship between the base dissociation constant (KB) and the base dissociation constant's negative logarithm (pKB), we can analyze the provided options step by step.

### Step 1: Understanding the Definitions
- **KB**: This is the base dissociation constant, which measures the strength of a base in solution.
- **pKB**: This is defined as the negative logarithm of the base dissociation constant, mathematically expressed as:
\[ pKB = -\log(KB) \]

### Step 2: Analyzing Each Statement
1. **Statement 1**: \( pKB = \log(KB) \)
- This is incorrect because it lacks the negative sign. The correct form is \( pKB = -\log(KB) \).

2. **Statement 2**: \( pKB = -\log(KB) \)
- This is correct as it accurately reflects the definition of pKB.

3. **Statement 3**: \( pKB = \ln(KB) \)
- This is incorrect. The natural logarithm (ln) is not the same as the common logarithm (log) used in the definition of pKB.

4. **Statement 4**: \( pKB = -\ln(KB) \)
- This is also incorrect because pKB is defined using the common logarithm, not the natural logarithm.

### Conclusion
Based on the analysis, the correct statement is:
\[ \text{Option 2: } pKB = -\log(KB) \]