`pK_(a)`of a weak acid is defined as :

Options

A. `log K_(a)`
B. `1/logK_(a)`
C. `"log"1/K_(a)`
D. `"-log" 1/K_(a)`

Explanation

To define the \( pK_a \) of a weak acid, we need to understand the relationship between the acid dissociation constant (\( K_a \)) and \( pK_a \). Here’s a step-by-step explanation:

### Step 1: Understanding Acid Dissociation
A weak acid (HA) partially dissociates in water to form its conjugate base (A⁻) and hydronium ions (H₃O⁺). The dissociation can be represented as:
\[ HA \rightleftharpoons A^- + H_3O^+ \]

### Step 2: Defining the Acid Dissociation Constant (\( K_a \))
The acid dissociation constant (\( K_a \)) is a measure of the strength of the acid in solution. It is defined by the equilibrium expression:
\[ K_a = \frac{[A^-][H_3O^+]}{[HA]} \]
where:
- \([A^-]\) is the concentration of the conjugate base,
- \([H_3O^+]\) is the concentration of hydronium ions,
- \([HA]\) is the concentration of the undissociated acid.

### Step 3: Relating \( K_a \) to \( pK_a \)
The \( pK_a \) is defined as the negative logarithm of the acid dissociation constant:
\[ pK_a = -\log(K_a) \]

### Step 4: Alternative Expression for \( pK_a \)
Using properties of logarithms, we can also express \( pK_a \) as:
\[ pK_a = \log\left(\frac{1}{K_a}\right) \]

### Conclusion
Thus, the \( pK_a \) of a weak acid is defined as:
\[ pK_a = -\log(K_a) \quad \text{or} \quad pK_a = \log\left(\frac{1}{K_a}\right) \]

### Final Answer
The correct definition of \( pK_a \) of a weak acid is:
\[ pK_a = -\log(K_a) \quad \text{or} \quad pK_a = \log\left(\frac{1}{K_a}\right) \]