Read the passage given and answer the question.

The transition elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example, exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at extreme ends stems from either too few electrons to lose or share (Sc, Ti) on too many d-electrons (hence fewer orbitals available in which to share electrons with others) for higher valence (Cu, Zn). Thus early in the early series scandium (II) is virtually unknown and titanium (IV) is more stable than Ti(III) or Ti(II). At the other end, the only oxidation state of zinc is +2 (no d electrons are involved). The maximum oxidation states of reasonable stability correspond in value to the sum as s- and d-electrons upto  manganese \((Ti^{IV}O_2, V^VO_2^+, Cr^{VI}O_4^{2}, Mn^{VII}O_4 )\) followed by a rather abrupt decrease in stability of higher oxidation states, so that the typical species to follow are \(Fe^{II, III}\), \(Co^{II, III}\), \(Cu^{I, II}\), \(Zn^{II}\).

The variability of oxidation states, a characteristic of transition elements, arises out of incomplete filling of d-orbitals in such a way that their oxidation states differ from each other by unity, e.g., \(V^{II}\), \(V^{III}\), \(V^{IV}\), \(V^V\). This is in contrast with the variability of oxidation states of non transition elements where oxidation states normally differ by a unit or two.

An interesting feature in the variability of oxidation states of the d-block elements is noticedamong the groups (groups 4 through 10). Although in the p-block, the lower oxidation states are favoured by the heavier members (due to inert pair effect), the opposite is true in the groups of d-block. For example, in group 6, \(Mo^{(VI)}\) and \(W^{(VI)}\) are found to be more stable than \(Cr^{(VI)}\). The \(Cr^{(VI)}\) in the form of dichromate in acidic medium is a strong agent, whereas \(MoO_3\) and \(WO_3\) are not.

Low oxidation states are found when a complex compound has ligands capable of \(\pi \)-acceptor character in addition to the \(\sigma \)-bonding. For example, in \(Ni(CO)_4\) and \(Fe(CO)_5\), the oxidation state of nickel and iron is zero.

Most acidic species among the following is:

\(Mn_2O_7\)

The correct answer is option 1. \(Mn_2O_7\).

Metal oxides can either be basic, amphoteric, or acidic, depending on the oxidation state of the metal and the nature of the metal-oxygen bond:

Basic Oxides: These are generally formed by metals in lower oxidation states. They tend to donate \( OH^- \) ions in water, making the solution basic.

Amphoteric Oxides: These oxides can act as either an acid or a base, depending on the conditions.

Acidic Oxides: These are typically formed by non-metals or metals in high oxidation states. They tend to form acids when dissolved in water, releasing \( H^+ \) ions.

Oxidation State and Acidity

The acidity of a metal oxide generally increases with the oxidation state of the metal. This is because:

Higher oxidation states lead to stronger polar covalent bonds between the metal and oxygen. The oxygen in such compounds has a greater tendency to draw electron density towards itself, weakening the metal-oxygen bond. When the metal-oxygen bond is weakened, the oxide is more likely to release \( O_2^- \) ions or combine with water to produce acidic solutions, which release \( H^+ \) ions.

Oxidation States of Manganese in the Given Oxides

Let us calculate and understand the oxidation state of manganese in each of the given oxides:

1. \(Mn_2O_7\):

Oxidation state of Mn: \(+7\)

\(\text{Let the oxidation state of Mn be } x\)

\(2x + 7(-2) = 0 \Rightarrow 2x - 14 = 0 \Rightarrow x = +7\)

2. \(MnO_2\):

Oxidation state of Mn: \(+4\)

\(x + 2(-2) = 0 \Rightarrow x - 4 = 0 \Rightarrow x = +4\)

3. \(MnO\):

Oxidation state of Mn: \(+2\)

\(x + (-2) = 0 \Rightarrow x = +2\)

4. \(Mn_2O_3\):

Oxidation state of Mn: \(+3\)

\(2x + 3(-2) = 0 \Rightarrow 2x - 6 = 0 \Rightarrow x = +3\)

Comparing the Acidity

Now that we know the oxidation states, let's rank the oxides in terms of acidity:

\(Mn_2O_7\) (Oxidation state \(+7\)):

Manganese is in its highest possible oxidation state. \(Mn_2O_7\) is a highly covalent oxide and is known to be strongly acidic. It reacts with water to form \(HMnO_4\) (permanganic acid), which is a strong acid.

\(MnO_2\) (Oxidation state \(+4\)):

Manganese is in a moderate oxidation state. \(MnO_2\) is amphoteric, meaning it can react with both acids and bases, but it is less acidic than \(Mn_2O_7\).

\(Mn_2O_3\) (Oxidation state \(+3\)):

Manganese is in a lower oxidation state. \(Mn_2O_3\) is also amphoteric but leans more towards being basic compared to \(MnO_2\), making it less acidic.

\(MnO\) (Oxidation state \(+2\)):

Manganese is in its lowest oxidation state among the options. \(MnO\) is a basic oxide and does not exhibit acidic properties.

Conclusion

\(Mn_2O_7\), with manganese in the \(+7\) oxidation state, is the most acidic oxide among the given options. This is because the high oxidation state of manganese leads to a very polar Mn-O bond, resulting in a strong tendency to form acidic solutions when dissolved in water.

The correct answer is option 1: \(Mn_2O_7\).