Question

Consider the hydrated ions of \(\text{Ti}^{2+}\), \(\text{V}^{2+}\), \(\text{Ti}^{3+}\) and \(\text{Sc}^{3+}\). Identify the correct increasing order of their spin-only magnetic moment.

• A. \(\text{Sc}^{3+}\lt \text{Ti}^{3+}\lt \text{V}^{2+}\lt \text{Ti}^{2+}\)
• B. \(\text{Sc}^{3+}\lt \text{Ti}^{3+}\lt \text{Ti}^{2+}\lt \text{V}^{2+}\)
• C. \(\text{Ti}^{3+}\lt \text{Ti}^{2+}\lt \text{Sc}^{3+}\lt \text{V}^{2+}\)
• D. \(\text{V}^{2+}\lt \text{Ti}^{2+}\lt \text{Ti}^{3+}\lt \text{Sc}^{3+}\)

Hint:

Count unpaired d electrons in Sc3+, Ti3+, Ti2+ and V2+ and apply the spin-only formula.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Spin-only moment is \(\mu = \sqrt{n(n+2)}\) BM, which rises with the number n of unpaired electrons.

Step 2: Unpaired electrons
\(\text{Sc}^{3+}\): \(d^{0}\), n = 0, \(\mu = 0\).
\(\text{Ti}^{3+}\): \(d^{1}\), n = 1, \(\mu = 1.73\) BM.
\(\text{Ti}^{2+}\): \(d^{2}\), n = 2, \(\mu = 2.83\) BM.
\(\text{V}^{2+}\): \(d^{3}\), n = 3, \(\mu = 3.87\) BM.

Step 3: Order
\(\text{Sc}^{3+} \lt \text{Ti}^{3+} \lt \text{Ti}^{2+} \lt \text{V}^{2+}\), which is option (B).

Final Answer:
The increasing order is Sc3+, Ti3+, Ti2+, V2+. \[ \boxed{\text{(B) }\text{Sc}^{3+}<\text{Ti}^{3+}<\text{Ti}^{2+}<\text{V}^{2+}} \]