Step 1: Understanding the Question:
The question asks us to identify the specific laboratory or industrial electrochemical setup that yields ultra-pure hydrogen gas (purity $\gt 99.5\%$).
Step 2: Key Formula or Approach:
While normal hydrogen gas can be evolved via standard acid-metal reactions or the electrolysis of acidified water, high-purity dihydrogen requires a highly stable alkaline electrolyte combined with inert, non-corrosive electrodes to prevent secondary chemical contamination.
Step 3: Detailed Explanation:
Let's evaluate the options to determine why option (D) is structurally superior:
Pure water (Option B) is an extremely poor electrical conductor due to its low autoionization, rendering regular electrolysis impossible without adding an ionic promoter.
Using reactive electrodes like Zinc (Option A) or Cadmium (Option C) introduces heavy metal ions into the solution, causing electrode degradation and chemical impurities in the evolved gas stream.
The standard textbook method for preparing highly pure dihydrogen gas involves the electrolysis of a warm aqueous solution of barium hydroxide, $\text{Ba(OH)}_2$, using nickel (Ni) electrodes. Barium hydroxide offers high ionic mobility when warm, and the robust nickel electrodes possess an exceptionally low overpotential for hydrogen evolution while remaining perfectly stable against alkaline corrosion. This ensures that the gas generated at the cathode is clean and free of volatile chemical impurities.
Step 4: Final Answer:
Pure dihydrogen is obtained via the electrolysis of warm barium hydroxide using nickel electrodes, which corresponds to option (D).