Step 1: Understanding the complex.
Potassium trioxalato aluminate (III) consists of potassium ions (K\(^+\)) and the complex ion [Al(C\(_2\)O\(_4\))\(_3\)]\(^{3-}\), where the aluminum ion is coordinated with three oxalate (C\(_2\)O\(_4\))\(^{2-}\) ligands. The formula is K\(_3\)[Al(C\(_2\)O\(_4\))\(_3\)].
Step 2: Analyzing the options. (A) K\(_4\)[Al(C\(_2\)O\(_4\))\(_3\)]: Incorrect — The charge on the complex would not balance. (B) K\(_3\)Al(C\(_2\)O\(_4\))\(_3\): Incorrect — The correct formula should have the complex ion in brackets. (C) Al\(_3\)[K\(_3\)(C\(_2\)O\(_4\))\(_3\)]: Incorrect — This formula does not represent the correct stoichiometry of the ions. (D) K\(_3\)[Al(C\(_2\)O\(_4\))\(_3\)]: Correct — This is the correct formula for potassium trioxalato aluminate (III).
Step 3: Conclusion.
The correct answer is (D) K\(_3\)[Al(C\(_2\)O\(_4\))\(_3\)].