Which of the following expression for `%` dissociation of a monoacidic base (BOH) in aqueous solution at appreciable concentration is not correct?
(a)`100xxsqrt((K_(b))/(c))`
(b)`(1)/(1+10^((pK_(b)-pOH))`
(c)`(K_(w)[H^(+)])/(K_(b)+K_(w))`
(d)`(K_(b))/(K_(b)+[OH^(-)])`

Options

A. `100xxsqrt((K_(b))/(c))`
B. `(1)/(1+10^((pK_(b)-pOH))`
C. `(K_(w)[H^(+)])/(K_(b)+K_(w))`
D. `(K_(b))/(K_(b)+[OH^(-)])`

Answer

To solve the question regarding the percentage dissociation of a monoacidic base (BOH) in aqueous solution, we need to analyze each of the provided expressions and determine which one is incorrect.

### Step-by-Step Solution:

1. **Understanding the Dissociation of BOH:**
- The dissociation of a monoacidic base (BOH) can be represented as:
\[ BOH \rightleftharpoons B^+ + OH^- \]
- Let the initial concentration of BOH be \( C \) and let \( \alpha \) be the degree of dissociation.

2. **Setting Up the Equilibrium Expression:**
- At equilibrium, the concentrations will be:
- \( [B^+] = C \alpha \)
- \( [OH^-] = C \alpha \)
- \( [BOH] = C(1 - \alpha) \)
- The expression for the base dissociation constant \( K_b \) is:
\[ K_b = \frac{[B^+][OH^-]}{[BOH]} = \frac{(C \alpha)(C \alpha)}{C(1 - \alpha)} = \frac{C \alpha^2}{1 - \alpha} \]

3. **Neglecting \( \alpha \):**
- For appreciable concentrations, we can assume \( \alpha \) is small compared to 1, hence \( 1 - \alpha \approx 1 \):
\[ K_b \approx C \alpha^2 \]
- Rearranging gives:
\[ \alpha \approx \sqrt{\frac{K_b}{C}} \]

4. **Calculating Percentage Dissociation:**
- The percentage dissociation \( \% \) can be calculated as:
\[ \% \text{ dissociation} = \alpha \times 100 = 100 \sqrt{\frac{K_b}{C}} \]
- This matches option (a).

5. **Analyzing Other Options:**
- **Option (b):**
\[ \frac{1}{1 + 10^{(pK_b - pOH)}} \]
- This expression is derived from the relationship between \( K_b \), \( pK_b \), and \( pOH \). It is correct.

- **Option (c):**
\[ \frac{K_w[H^+]}{K_b + K_w} \]
- This expression does not directly relate to the percentage dissociation derived from the equilibrium constant and is not a standard expression for \( \alpha \). Thus, it is likely incorrect.

- **Option (d):**
\[ \frac{K_b}{K_b + [OH^-]} \]
- This expression can be derived from the equilibrium expressions and is also correct.

6. **Conclusion:**
- After analyzing all options, we find that option (c) is the incorrect expression for the percentage dissociation of a monoacidic base in aqueous solution.

### Final Answer:
The expression for `%` dissociation of a monoacidic base (BOH) that is not correct is:
**(c) \(\frac{K_w[H^+]}{K_b + K_w}\)**