If an iron (III) complex with the formula [Fe(NH₃)ₓ(CN)_y]⁻ has no electron in its e_g orbital, then the value of x+y is

Solution

Chemistry ma’am · 4 steps

An empty e_g set in d⁵ means a low-spin octahedral complex, so it needs six ligands.

1. Count d electrons. Iron has the configuration [Ar] 3d⁶ 4s². Fe³⁺ loses both 4s electrons and one 3d electron, so it is d⁵.
2. Read the eg condition. The labels t_(2g) and e_g belong to an octahedral field. To keep all 5 electrons out of e_g, they must pair up in t_(2g) as t_(2g)⁵ e_g⁰. That is low spin, and the strong-field CN⁻ ligands make the splitting large enough for it. Octahedral means x + y = 6.
3. Check the charge. NH₃ is neutral and each CN⁻ carries -1. Set the charges equal to the overall charge.

   (+3) + x(0) + y(-1) = -1 ⇒ y = 4, x = 6 - 4 = 2

4. So. The complex is [Fe(NH₃)₂(CN)₄]⁻, with x + y = 6. The answer is (a).

The idea to keep. When a question names t_(2g) and e_g, think octahedral and six ligands. Then use the charge balance to split those six between the ligand types.

Answer from the NTA final answer key. Solution by PrepWiser.