Find the magnetic moment of the complex

Question: Consider the following complex ions, P, Q and R 

P = [FeF₆]^3-, Q = [V(H₂O)₆]²⁺, and R = [Fe(H₂O)₆]²⁺

What is the correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.)?

A) R<Q<P

B)  Q<R<P

C)  R<P<Q

D) Q<P<R

Solution:

The formula used to calculate the spin-only magnetic moment can be written as:

μ= √n(n+2) B.M.

Where n = no. of unpaired electron

 

So first let us find out number of unpaired electron in each complex.

 

1)   P = [FeF₆]^3-

Charge on Fe in the complex: [FeF₆]^3-    

                                                                                     X + (1x6) = -3

                                                        = +3

So number of unpaired electron in Fe⁺³ = 3s², 3p⁶, 3d⁵, 4s⁰            

                                                                      = 5

Magnetic moment = √5 (5+2)

                                         =√35 B.M.

 

2)   Q = [V(H₂O)₆]²⁺

Charge on Fe in the complex: X + (0x6) = +2

                                                 = +2

So number of unpaired electron in V⁺² = 3s², 3p⁶, 3d³,           

                                                                     = 3

Magnetic moment = √3 (3+2)

                                         =√15 B.M.

 

3)   R = [Fe(H₂O)₆]²⁺

Charge on Fe in the complex: X + (0x6) = +2

                                                    = +2

So number of unpaired electron in Fe⁺² = 3s², 3p⁶, 3d⁶         

                                                                     = 4

Magnetic moment = √4 (4+2)

                                         =√24 B.M.

So the correct order of the complex ions, according to their spin-only magnetic moment values is P > R > Q

Thus option B is correct.