Which one of the following does not correctly represent the correct order of the property indicated against it?

$Ti <V<Cr<Mn$: increasing melting point

The correct answer is Option (3) → $Ti <V<Cr<Mn$: increasing melting point.

Let us break down each statement regarding the properties of titanium (Ti), vanadium (V), chromium (Cr), and manganese (Mn) in detail to identify which one is incorrect.

1. Increasing Number of Oxidation States: Ti < V < Cr < Mn

Oxidation State:

Titanium (Ti): Common oxidation states are +3 and +4.

Vanadium (V): Exhibits oxidation states ranging from +2 to +5.

Chromium (Cr): Shows oxidation states from +2 to +6.

Manganese (Mn): Can have oxidation states from +2 to +7

As we move from Ti to Mn, the ability to exhibit multiple oxidation states increases. Hence, this statement is correct as it accurately reflects the increasing capability of these elements to form various oxidation states.

2. Increasing Magnetic Moment: Ti³⁺ < V³⁺ < Cr³⁺ < Mn³⁺

Magnetic Moment Calculation:

\(Ti^{3+}\) (Titanium): Has a \(d^1\) configuration (1 unpaired electron). Magnetic moment \(= \sqrt{n(n+2)} = \sqrt{1(1+2)} = \sqrt{3} \approx 1.73\) BM.

\(V^{3+}\) (Vanadium): Has a \(d^2\) configuration (2 unpaired electrons). Magnetic moment \(= \sqrt{2(2+2)} = \sqrt{8} \approx 2.83\) BM.

\(Cr^{3+}\) (Chromium): Has a \(d^3\) configuration (3 unpaired electrons). Magnetic moment \(= \sqrt{3(3+2)} = \sqrt{15} \approx 3.87\) BM.

\(Mn^{3+}\) (Manganese): Has a \(d^4\) configuration (4 unpaired electrons). Magnetic moment \(= \sqrt{4(4+2)} = \sqrt{24} \approx 4.90\) BM.

The magnetic moment increases with the number of unpaired electrons. Therefore, the order given is correct.

3. Increasing Melting Point: Ti < V < Cr < Mn

Melting Points:

Titanium (Ti): Melting point = 1668 °C

Vanadium (V): Melting point = 1910 °C

Chromium (Cr): Melting point = 1907 °C

Manganese (Mn): Melting point = 1246 °C

The trend in melting points does not follow the order Ti < V < Cr < Mn. In fact, Cr has a higher melting point than Mn. The correct order should be Ti < Mn < Cr < V. Therefore, this statement is not correct.

4. Increasing Second Ionization Enthalpy: Ti < V < Mn < Cr

Ionization Enthalpy:

Second ionization enthalpy refers to the energy required to remove the second electron from an atom. Generally, as you move across the period from left to right, the ionization enthalpies increase due to the increasing nuclear charge, which makes it harder to remove electrons.

As we go from Ti to Cr, the second ionization enthalpy increases due to higher nuclear charge and more stability in filled or half-filled orbitals. Therefore, this order is also correct.

Conclusion

The incorrect statement among the options is: Ti < V < Cr < Mn: increasing melting point.

This statement fails because it inaccurately represents the actual trend in melting points, where chromium has a higher melting point than manganese. Thus, the correct order based on melting points is Ti < Mn < Cr < V.