An acidic indicator ionises as `I_(n) H hArr "In"^(-) + H^(+)` . The molecular and ions of the indicator show different colours. The indicator changed it colour if its acidic of basic form completely predominant.
An indicator with `P^(Kin)` = 5 is added to a solution with `p^(H)` = 5 . What is the percentage of acidic form of the indicator

Options

A. 0.25
B. 0.5
C. 0.75
D. 1

Answer

To solve the problem step by step, we need to determine the percentage of the acidic form of the indicator when the pKa of the indicator is equal to 5 and the pH of the solution is also 5.

### Step 1: Understand the relationship between pH, pKa, and the ratio of ionized and non-ionized forms.
The relationship is given by the Henderson-Hasselbalch equation:
\[ \text{pH} = \text{pKa} + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]
where:
- \([\text{A}^-]\) is the concentration of the ionized form (basic form),
- \([\text{HA}]\) is the concentration of the non-ionized form (acidic form).

### Step 2: Substitute the given values into the equation.
Given:
- pH = 5
- pKa = 5

Substituting these values into the equation:
\[ 5 = 5 + \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]

### Step 3: Simplify the equation.
Subtract 5 from both sides:
\[ 0 = \log\left(\frac{[\text{A}^-]}{[\text{HA}]}\right) \]

### Step 4: Solve for the ratio of ionized to non-ionized forms.
Since the logarithm of a number is zero when that number is 1:
\[ \frac{[\text{A}^-]}{[\text{HA}]} = 10^0 = 1 \]

This means that:
\[ [\text{A}^-] = [\text{HA}] \]

### Step 5: Determine the percentage of the acidic form.
If \([\text{A}^-] = [\text{HA}]\), then both forms are present in equal amounts. Therefore, the total amount can be considered as:
\[ [\text{Total}] = [\text{A}^-] + [\text{HA}] = x + x = 2x \]

The percentage of the acidic form \([\text{HA}]\) is given by:
\[ \text{Percentage of } [\text{HA}] = \left(\frac{[\text{HA}]}{[\text{Total}]}\right) \times 100 = \left(\frac{x}{2x}\right) \times 100 = \frac{1}{2} \times 100 = 50\% \]

### Final Answer:
The percentage of the acidic form of the indicator is **50%**.

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