Acid-base indicators are either weak organic acids or weak organic bases. Indicator change colour in dilute solution when the hydonium ion concentration reaches a particular calur For example. Phenolphthalein is a coloureless stbstance in any aqueous solution with a pH less than 8.3 In between the pH range 8.3 to 10, transition of colour (colourless to pink ) takes place and if pH of solution is greater than 10 solution is dark pink. Considering an acid indicator Hln, the equilibrium involving it and its conjgate base `In^(-)` can be represented as :
`" " underset("acidic from")(HIn)hArrH^(+)underset("basic from")(In^(-))`
pH of solution can be computed as :
`" " pH=pK_(In)+log.([IN^(-)])/([HIn])`
In general, transition of colour takes place in between the pH range `pK_(In+-1.`
Select the correct statement (s) :

Options

A. At midway in the transition of an acidic indicator, `pH=pK_("in")`
B. Methyl orange (3.1 to 4.4 ) is a suitable indicator for titration of weak acid and strong base
C. Bromothymol blue (6.0 to 7.6 ) is a good indicator for tatration of HCl and NaOH
D. Thymol blue (1.2 "to" 2.8) is a very good indicator for titration of 100 ML of 0.1 M `NH_(4) OH` (`pK_(b)` = 4.74) and 0.1 M HCl

Answer

To solve the question regarding acid-base indicators and their suitability for different titrations, we will analyze each statement provided and determine its correctness based on the principles of acid-base chemistry.

### Step-by-Step Solution:

1. **Understanding the Concept of pKa and Midway Point**:
- The first statement claims that at the midway point in the titration of an acidic indicator, the pH is equal to pKa. This is correct because at the halfway point of the titration, the concentration of the acid (HIn) equals the concentration of its conjugate base (In⁻), leading to pH = pKa.

**Hint**: Recall that at the halfway point of a titration, the concentrations of the acid and its conjugate base are equal, resulting in pH = pKa.

2. **Evaluating Methyl Orange as an Indicator**:
- The second statement suggests that methyl orange (pH range 3.1 to 4.4) is suitable for titration of weak acids with strong bases. This is incorrect because methyl orange is typically used for strong acid-weak base titrations, not weak acid-strong base titrations. For weak acid-strong base titrations, phenolphthalein is more appropriate.

**Hint**: Consider the pH range of the indicator and the nature of the titration (strong vs weak acids/bases) to determine suitability.

3. **Analyzing Bromothymol Blue**:
- The third statement states that bromothymol blue (pH range 6.0 to 7.6) is a good indicator for the titration of HCl and NH₄OH. This is correct because both HCl (a strong acid) and NH₄OH (a weak base) will result in a neutralization reaction that falls within the pH range of bromothymol blue.

**Hint**: Check if the pH at the equivalence point of the titration falls within the indicator's color change range.

4. **Assessing Thymol Blue**:
- The fourth statement claims that thymol blue (pH range 1.2 to 2.8) is a suitable indicator for titrating 100 mL of 0.1 M NH₄OH (pKa = 4.74) and 0.1 M HCl. This is incorrect because thymol blue is not suitable for titrations involving weak bases and strong acids, as the pH at the equivalence point will be above 2.8.

**Hint**: Consider the pKa of the weak base and the expected pH at the equivalence point to determine if the indicator is appropriate.

### Conclusion:
Based on the analysis:
- **Correct Statements**: Statement 1 and Statement 3 are correct.
- **Incorrect Statements**: Statement 2 and Statement 4 are incorrect.

### Final Answer:
The correct statements are **Statement 1 and Statement 3**.