Concept:
Electrolysis of aqueous sodium chloride solution (brine) is known as the
chlor-alkali process. During electrolysis, chloride ions are oxidized at the anode, while water is reduced at the cathode. Sodium ions remain in solution and combine with hydroxide ions to form sodium hydroxide.
Step 1: Write the reaction occurring at the anode.
Oxidation of chloride ions takes place at the anode:
\[\begin{aligned}
2Cl^- \rightarrow Cl_2 + 2e^-
\end{aligned}\]
Thus, chlorine gas is liberated at the anode.
Step 2: Write the reaction occurring at the cathode.
Water is reduced at the cathode:
\[\begin{aligned}
2H_2O + 2e^- \rightarrow H_2 + 2OH^-
\end{aligned}\]
Thus, hydrogen gas is evolved at the cathode.
Step 3: Identify the product remaining in the solution.
The sodium ions present in solution combine with hydroxide ions produced at the cathode:
\[\begin{aligned}
Na^+ + OH^- \rightarrow NaOH
\end{aligned}\]
Hence, sodium hydroxide is formed in the solution.
Step 4: Summarize the products formed.
\[
\begin{aligned}
\textbf{Anode} \quad & Cl_2 \\
\textbf{Cathode} \quad & H_2 \\
\textbf{Solution} \quad & NaOH
\end{aligned}
\]
Therefore, the products obtained are
\[\begin{aligned}
NaOH,\; H_2,\; Cl_2
\end{aligned}\]
\[\begin{aligned}
\boxed{NaOH,\; H_2,\; Cl_2}
\end{aligned}\]
Hence, option \(\mathbf{(D)}\) is correct.