Which of the following cannot as an oxidising agent?

The correct answer is N^3-.

An oxidising agent is a substance that oxidises other substances by gaining electrons itself. Consequently, the central atom in an oxidising agent must undergo reduction (a decrease in its oxidation state) during a chemical reaction.
For an atom or ion to act as an oxidising agent, it must be in an oxidation state that can be reduced to a lower (more negative or less positive) state. This is possible when the element is not already in its lowest possible oxidation state.

Let us determine the oxidation states of the central elements in each of the given options:

1. In MnO₄^- (Permanganate ion):
The oxidation state of Manganese (Mn) is +7. This is the maximum possible oxidation state for manganese (Group 7 transition metal). While it cannot be oxidised further (cannot act as a reducing agent), it can easily gain electrons and be reduced to lower oxidation states like +6, +4, or +2. Thus, it acts as a very strong oxidising agent.

2. In SO₄^2- (Sulfate ion):
The oxidation state of Sulfur (S) is +6. This is the maximum possible oxidation state for sulfur (Group 16). Sulfur can be reduced to lower oxidation states (such as +4, 0, or -2). Therefore, it can act as an oxidising agent.

3. In BrO₃^- (Bromate ion):
The oxidation state of Bromine (Br) is +5. Since the maximum oxidation state of bromine is +7 and its lowest is -1, bromine in +5 state can be reduced to lower oxidation states (like 0 or -1). Hence, it can act as an oxidising agent.

4. In N^3- (Nitride ion):
The oxidation state of Nitrogen (N) is -3. Nitrogen is a Group 15 element, with a valence shell configuration of 2s²2p³. It can accommodate a maximum of 3 extra electrons to complete its octet, meaning its lowest possible oxidation state is -3.
Since nitrogen in N^3- is already in its lowest possible oxidation state, it cannot gain any more electrons to undergo reduction. Because it cannot be reduced, it cannot act as an oxidising agent. (Instead, it can only lose electrons and act as a reducing agent).

Therefore, N^3- cannot act as an oxidising agent.