Approximate relationship between dissociation constant of water (K) and ionic product of water `(K_(w))` is

Options

A. `K_(w) = K`
B. `K_(w) = 55.6 xx K`
C. `K_(w) = 18 xx K`
D. `K_(w) = 14 xx K`

Explanation

To find the approximate relationship between the dissociation constant of water (K) and the ionic product of water (K_w), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Dissociation of Water**:
Water (H₂O) dissociates into hydrogen ions (H⁺) and hydroxide ions (OH⁻). The dissociation can be represented as:
\[ H_2O \rightleftharpoons H^+ + OH^- \]

2. **Dissociation Constant (K)**:
The dissociation constant (K) for this reaction can be expressed as:
\[ K = \frac{[H^+][OH^-]}{[H_2O]} \]
Since water is a pure liquid, its concentration remains relatively constant and can be combined into the constant.

3. **Ionic Product of Water (K_w)**:
The ionic product of water (K_w) is defined as:
\[ K_w = [H^+][OH^-] \]
This product represents the equilibrium constant for the self-ionization of water.

4. **Relating K and K_w**:
From the expression for K, we can rearrange it as:
\[ K \cdot [H_2O] = [H^+][OH^-] \]
Thus, we can substitute the right side with K_w:
\[ K \cdot [H_2O] = K_w \]

5. **Concentration of Water**:
The concentration of water ([H₂O]) in pure water is approximately 55.55 mol/L (since the density of water is about 1 g/mL and the molar mass of water is about 18 g/mol).

6. **Final Relationship**:
Therefore, we can express the relationship between K and K_w as:
\[ K = \frac{K_w}{[H_2O]} \]
Substituting the value of [H₂O]:
\[ K \approx \frac{K_w}{55.55} \]

### Conclusion:
The approximate relationship between the dissociation constant of water (K) and the ionic product of water (K_w) is:
\[ K \approx \frac{K_w}{55.55} \]