Consider the hydrated ions of

Question:

Consider the hydrated ions of $\mathrm{Ti}^{2+}, \mathrm{V}^{2+}, \mathrm{Ti}^{3+}$, and $\mathrm{Sc}^{3+}$.

The correct order of their spin-only magnetic moments is :

  1. $\mathrm{V}^{2+}<\mathrm{Ti}^{2+}<\mathrm{Ti}^{3+}<\mathrm{Sc}^{3+}$

  2. $\mathrm{Sc}^{3+}<\mathrm{Ti}^{3+}<\mathrm{Ti}^{2+}<\mathrm{V}^{2+}$

  3. $\mathrm{Ti}^{3+}<\mathrm{Ti}^{2+}<\mathrm{Sc}^{3+}<\mathrm{V}^{2+}$

  4. $\mathrm{Sc}^{3+}<\mathrm{Ti}^{3+}<\mathrm{V}^{2+}<\mathrm{Ti}^{2+}$


Correct Option: , 2

Solution:

Electronic configuration of the given transition metal ions are :

$\mathrm{Sc}^{3+}(\mathrm{Z}=21) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}$

$\mathrm{Ti}^{2+}(\mathrm{Z}=22) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{2}$

$\mathrm{Ti}^{3+}(\mathrm{Z}=22) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{1}$

$\mathrm{~V}^{2+}(\mathrm{Z}=23) 1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{3}$

Since, magnetic moment is directly proportional to the number of unpaired electrons. The correct increasing order of magnetic moment is $\mathrm{Sc}^{3+}<\mathrm{Ti}^{3+}<\mathrm{Ti}^{2+}<\mathrm{V}^{2+}$ because they have $0,1,2$ and 3 unpaired electrons respectively.

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