1. What determines electrical conductivity?

For aqueous solutions of acids, electrical conductivity depends mainly on the number of ions present in solution and their mobility.

For acids of the type $\text{HA}$:

$\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$

At the same concentration, the acid with greater ionization produces more ions, hence shows higher electrical conductivity.

2. Compare the acidic strengths of the given acids

The acids are:

• Acetic acid: $\text{CH}_3\text{COOH}$
• Chloroacetic acid: $\text{ClCH}_2\text{COOH}$
• Fluoroacetic acid: $\text{FCH}_2\text{COOH}$
• Difluoroacetic acid: $\text{CHF}_2\text{COOH}$

Their acidic strength depends on the electron-withdrawing inductive effect ($-I$ effect) of substituents attached near the $-\text{COOH}$ group.

• $\text{CH}_3$ has a weak electron-donating effect, so acetic acid is weakest.
• Halogens withdraw electrons by $-I$ effect, stabilizing the conjugate base and increasing acidity.
• Among halogens, $\text{F}$ has a stronger $-I$ effect than $\text{Cl}$.
• Two fluorine atoms withdraw more strongly than one fluorine atom.

Therefore, acidity order is:

$\text{CH}_3\text{COOH} < \text{ClCH}_2\text{COOH} < \text{FCH}_2\text{COOH} < \text{CHF}_2\text{COOH}$

3. Relate acidity to conductivity

Since all are $0.1\,\text{M}$ solutions, the strongest acid will ionize the most and hence conduct electricity the best.

Thus, the highest electrical conductivity will be for:

$\boxed{\text{CHF}_2\text{COOH}}$

which is difluoroacetic acid.

4. Check each option

• A: $0.1\,\text{M}$ acetic acid — weak acid, least ionization ❌
• B: $0.1\,\text{M}$ chloroacetic acid — stronger than acetic acid, but not the strongest ❌
• C: $0.1\,\text{M}$ fluoroacetic acid — stronger than chloroacetic acid, but weaker than difluoroacetic acid ❌
• D: $0.1\,\text{M}$ difluoroacetic acid — strongest acid, maximum ionization, highest conductivity ✅

5. Final answer

$\boxed{\text{D}}$