The observed magnetic moment of the complex [Mn(N C S)₆)]^(x⁻) is 6.06 BM. The numerical value of x is __________.

Solution

Chemistry ma’am · 4 steps

Turn 6.06 BM into unpaired electrons first. That gives Mn's oxidation state, and then the charge follows.

1. Unpaired electrons. Use the spin-only formula μ = √n(n+2) BM. With n = 5, μ = √35 = 5.92 BM, the value closest to the observed 6.06 BM.

   Mn oxidation state	Configuration	Unpaired n	√n(n+2)
   +2	3d⁵	5	5.92 BM
   +3	3d⁴	4	4.90 BM
   +4	3d³	3	3.87 BM

2. Oxidation state. Five unpaired electrons means a high-spin 3d⁵ ion, which is Mn²⁺. This fits the ligand: thiocyanate bonded through N is a weak-field ligand, so the electrons stay unpaired.
3. Charge of complex. Each NCS⁻ carries -1. The overall charge is +2 + 6 × (-1) = -4, so the complex is [Mn(NCS)₆]⁴⁻.
4. So. x = 4.

The common slip: 2. Reporting the oxidation state of Mn instead of the charge on the complex gives 2. The six NCS⁻ ligands still add -6.

The idea to keep. Magnetic moment gives you the unpaired electrons, unpaired electrons give you the oxidation state, and the oxidation state plus the ligand charges give you the complex's charge.

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