Identify the substance to be prepared

We need to obtain peroxodisulphuric acid, $\mathrm{H_2S_2O_8}$, by electrolysis.

Its corresponding anion is peroxodisulphate: $\mathrm{S_2O_8^{2-}}$

Electrolytic formation of peroxodisulphate

In electrolysis, peroxodisulphate is formed at the anode by oxidation of hydrogen sulphate / sulphate species in concentrated sulphuric acid.

The anodic reaction is commonly written as: $2\,\mathrm{HSO_4^-} \rightarrow \mathrm{S_2O_8^{2-}} + 2\,\mathrm{H^+} + 2e^-$

In strongly acidic medium, this gives peroxodisulphuric acid.

Why concentrated sulphuric acid is required

• High concentration of sulphate/bisulphate ions favors coupling to form the peroxide linkage $(-O-O-)$.
• In dilute aqueous solutions, water is preferentially oxidized at the anode, producing oxygen instead of $\mathrm{S_2O_8^{2-}}$.

Check each option

A: Concentrated solution of sulphuric acid
Yes. This is the standard electrolyte used for preparing $\mathrm{H_2S_2O_8}$ by electrolysis.

B: Dilute solution of sodium sulphate
No. In dilute solution, oxidation of water to $\mathrm{O_2}$ is favored.

C: Acidified dilute solution of sodium sulphate
No. Even though acidic, it is still dilute; oxygen evolution dominates rather than peroxodisulphate formation.

D: Dilute solution of sulphuric acid
No. Again, dilute medium favors oxygen evolution.

Final answer

Therefore, the correct option is: $\boxed{\text{A}}$