Identify the titration type

The neutralization is: $\mathrm{CH_3COOH + NaOH \rightarrow CH_3COONa + H_2O}$

Here:

• $\mathrm{CH_3COOH}$ is a weak acid
• $\mathrm{NaOH}$ is a strong base

So this is a weak acid–strong base titration.

Locate the equivalence point pH

In a weak acid–strong base titration, the equivalence point lies in the basic range: $\text{pH at equivalence point} > 7$

Therefore, the suitable indicator must change colour in the basic pH range near the equivalence point.

Use the condition about the indicator

The question says compound $X$:

• is a weak acid
• shows colour change near the equivalence point
• exists in ionized form in basic medium

This matches the general behavior of acid-base indicators: $\mathrm{HIn \rightleftharpoons H^+ + In^-}$

In basic medium, equilibrium shifts right, so the indicator exists mainly as the ionized form $\mathrm{In^-}$.

Check the options

A. Methyl orange

• Transition range: about $3.1$ to $4.4$
• Suitable for strong acid–weak base titrations, not weak acid–strong base.
• Not correct.

B. Methyl red

• Transition range: about $4.4$ to $6.2$
• Also too low for the basic equivalence point of acetic acid vs NaOH.
• Not correct.

C. Phenolphthalein

• Transition range: about $8.2$ to $10.0$
• Ideal for weak acid–strong base titration.
• It is a weak acid indicator and in basic medium it exists in ionized form with a pink colour.
• Correct.

D. Eriochrome Black T

• Used mainly in complexometric titrations, not as the proper indicator here.
• Not correct.

Final conclusion

The compound $X$ is: $\boxed{\text{Phenolphthalein}}$

Comparison with stored answer

Stored correct answer: C

Our derived answer: C

Hence, the derived answer agrees with the stored answer.