Which of the following reduce silver nitrate to silver?

Pyrophosphorous acid

The correct answer is option 3. Pyrophosphorous acid.

Let us explore the chemical properties and oxidation states of the given acids to understand why pyrophosphorous acid \((H_4P_2O_5)\) is the only one that can reduce silver nitrate \((AgNO_3)\) to metallic silver \((Ag)\).

Understanding Oxidation States and Reducing Ability

Oxidation State: The oxidation state of an element in a compound indicates the degree of oxidation (loss of electrons) or reduction (gain of electrons) of that element.

Reducing Agent: A substance that reduces another substance by donating electrons to it is called a reducing agent. In the process, the reducing agent itself gets oxidized (its oxidation state increases).

Examining Each Acid

1. Orthophosphoric Acid \((H_3PO_4)\)

Orthophosphoric acid has the formula \(H_3PO_4\).

Oxidation State of Phosphorus: In \(H_3PO_4\), phosphorus has an oxidation state of +5.

Calculation:

Hydrogen: \(+1\) each (3 hydrogens, so total +3).

Oxygen: \(-2\) each (4 oxygens, so total \(-8\)).

Phosphorus must balance the charges: \(x + 3 - 8 = 0 \rightarrow x = +5\).

Since phosphorus is in its maximum oxidation state of +5, it cannot be further oxidized and hence cannot act as a reducing agent. Therefore, \(H_3PO_4\) cannot reduce \(AgNO_3\) to silver.

2. Pyrophosphoric Acid \((H_4P_2O_7)\)

Pyrophosphoric acid has the formula \(H_4P_2O_7\).

Oxidation State of Phosphorus: In \(H_4P_2O_7\), phosphorus also has an oxidation state of +5.

Calculation:

Hydrogen: \(+1\) each (4 hydrogens, so total +4).

Oxygen: \(-2\) each (7 oxygens, so total \(-14\)).

For 2 phosphorus atoms to balance: \(2x + 4 - 14 = 0 \rightarrow 2x = +10 \rightarrow x = +5\).

Similar to orthophosphoric acid, phosphorus in pyrophosphoric acid is also in its highest oxidation state. It cannot act as a reducing agent and hence cannot reduce \(AgNO_3\).

3. Pyrophosphorous Acid \((H_4P_2O_5)\)

Pyrophosphorous acid has the formula \(H_4P_2O_5\).

Oxidation State of Phosphorus: In \(H_4P_2O_5\), phosphorus has an oxidation state of +3.

Calculation:

Hydrogen: \(+1\) each (4 hydrogens, so total +4).

Oxygen: \(-2\) each (5 oxygens, so total \(-10\)).

For 2 phosphorus atoms to balance: \(2x + 4 - 10 = 0 \rightarrow 2x = +6 \rightarrow x = +3\).

Phosphorus in pyrophosphorous acid has an oxidation state of +3, which is lower than its maximum possible state of +5. This means that pyrophosphorous acid can donate electrons (act as a reducing agent) and be oxidized to a higher oxidation state, like +5. Hence, pyrophosphorous acid can reduce \(AgNO_3\) to metallic silver \(Ag\), while it itself gets oxidized.

4. Metaphosphoric Acid \((HPO_3)\)

Metaphosphoric acid has the formula \(HPO_3\).

Oxidation State of Phosphorus: In \(HPO_3\), phosphorus has an oxidation state of +5.

Calculation:

Hydrogen: \(+1\).

Oxygen: \(-2\) each (3 oxygens, so total \(-6\)).

Phosphorus must balance the charges: \(x + 1 - 6 = 0 \rightarrow x = +5\).

Like the other acids with phosphorus in the +5 oxidation state, metaphosphoric acid cannot be further oxidized, and therefore cannot act as a reducing agent. It cannot reduce \(AgNO_3\).

Overall Conclusion

Only pyrophosphorous acid \((H_4P_2O_5)\), where phosphorus is in the +3 oxidation state, has the potential to reduce silver nitrate to silver. The other acids have phosphorus in the +5 oxidation state, which is the highest oxidation state for phosphorus, making them incapable of acting as reducing agents.

Thus, the correct answer is option 3. Pyrophosphorous acid