Nature of the titration

We are titrating benzoic acid with sodium hydroxide.

• Benzoic acid is a weak acid.
• NaOH is a strong base.

Reaction: $\mathrm{C_6H_5COOH + OH^- \rightarrow C_6H_5COO^- + H_2O}$

Conductance at the start

Since benzoic acid is a weak acid, it is only slightly ionized: $\mathrm{C_6H_5COOH \rightleftharpoons C_6H_5COO^- + H^+}$

Therefore, the initial conductance is low.

What happens as NaOH is added before equivalence?

Added $\mathrm{OH^-}$ neutralizes the acid and forms sodium benzoate, which is a strong electrolyte: $\mathrm{C_6H_5COOH + NaOH \rightarrow C_6H_5COONa + H_2O}$

As sodium benzoate forms, the number of ions in solution increases, so conductance increases gradually.

At equivalence point

All benzoic acid has been converted into sodium benzoate. Conductance has increased up to this point.

After equivalence point

Further addition of NaOH introduces excess $\mathrm{OH^-}$ ions, which have high mobility. Hence conductance now increases more sharply.

Shape of the conductometric titration curve

So the graph must show:

• Low initial conductance
• Gradual rise before equivalence
• Sharper rise after equivalence

This is the standard curve for weak acid vs strong base conductometric titration.

Matching with options

The correct figure is therefore the one showing an increasing line with a change to steeper slope after the equivalence point.

Hence, the correct option is: $\boxed{\text{C}}$

Comparison with stored answer

Stored correct answer = C.

Our derived answer = C.

Therefore, the answers agree.