If an acidic indicator `HIn` ionies as `HInhArrH^(+)+In^(-)`. To which maximum `pH` value its solution has distinct colour characterstic of `HIn`

Options

A. `pK_("in")-1`
B. `pK_("in") pm1 `
C. `pK_("in")`
D. 7

Explanation

To solve the problem, we need to determine the maximum pH value at which the acidic indicator \( HIn \) retains its distinct color characteristic. The ionization of the indicator is given by:

\[ HIn \rightleftharpoons H^+ + In^- \]

### Step-by-Step Solution:

1. **Understanding the Indicator Ionization**:
- The indicator \( HIn \) is a weak acid that dissociates into \( H^+ \) ions and its conjugate base \( In^- \).
- The color change of the indicator occurs due to the equilibrium between \( HIn \) and \( In^- \).

2. **Using the Henderson-Hasselbalch Equation**:
- For an acidic indicator, the pH can be related to the concentrations of the acid and its conjugate base using the Henderson-Hasselbalch equation:
\[ pH = pK_{In} + \log\left(\frac{[In^-]}{[HIn]}\right) \]

3. **Finding the Range for Distinct Color Change**:
- The distinct color characteristic of the indicator is observed when the pH is within a certain range. This range is typically \( pK_{In} \pm 1 \).
- This means that the indicator will show a distinct color when:
\[ pH = pK_{In} - 1 \quad \text{to} \quad pH = pK_{In} + 1 \]

4. **Determining the Maximum pH Value**:
- The maximum pH value for the distinct color characteristic of \( HIn \) occurs at:
\[ pH = pK_{In} + 1 \]

5. **Conclusion**:
- Therefore, the maximum pH value at which the solution has a distinct color characteristic of \( HIn \) is:
\[ \text{Maximum } pH = pK_{In} + 1 \]

### Final Answer:
The maximum pH value at which the solution has distinct color characteristic of \( HIn \) is \( pK_{In} + 1 \).

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