Question

Hydrazine has been employed as a reducing agent for metals. Using standard reduction potentials, predict whether the following metals can be reduced to the metallic state by hydrazine under standard conditions in acidic solution: (a) \(\mathrm{Fe}^{2+},(\mathrm{b}) \mathrm{Sn}^{2+},(\mathrm{c}) \mathrm{Cu}^{2+}\), (d) \(\mathrm{Ag}^{+},(\mathrm{e}) \mathrm{Cr}^{3+}\).

Short answer

Hydrazine can reduce \(Fe^{2+}\), \(Sn^{2+}\), \(Cu^{2+}\), and \(Cr^{3+}\) ions to their metallic states under standard conditions in acidic solution, based on their positive ΔE° values (0.32 V, 0.624 V, 0.423 V, and 0.016 V, respectively). However, it cannot reduce \(Ag^+\) ions to metallic silver, as the ΔE° value is negative (-0.838 V).

Step-by-step solution

(a) Iron

: 1. Balanced half-cell reduction reaction for iron (Fe²⁺): \(Fe^{2+} + 2e^- \rightarrow Fe\) E° = -0.440 V 2. Combine half-cell reactions and balance the overall reaction: \(N_2H_4 + 4H^+ + 2Fe^{2+} \rightarrow 2NH_4^+ + 2Fe\) 3. Calculate ΔE°: ΔE° = -(-0.440) - (-0.76) = 0.32 V 4. Since ΔE° > 0, hydrazine can reduce \(Fe^{2+}\) ions to metallic iron.

(b) Tin

: 1. Balanced half-cell reduction reaction for tin (Sn²⁺): \(Sn^{2+} + 2e^- \rightarrow Sn\) E° = -0.136 V 2. Combine half-cell reactions and balance the overall reaction: \(N_2H_4 + 4H^+ + 2Sn^{2+} \rightarrow 2NH_4^+ + 2Sn\) 3. Calculate ΔE°: ΔE° = -(-0.136) - (-0.76) = 0.624 V 4. Since ΔE° > 0, hydrazine can reduce \(Sn^{2+}\) ions to metallic tin.

(c) Copper

: 1. Balanced half-cell reduction reaction for copper (Cu²⁺): \(Cu^{2+} + 2e^- \rightarrow Cu\) E° = 0.337 V 2. Combine half-cell reactions and balance the overall reaction: \(N_2H_4 + 4H^+ + 2Cu^{2+} \rightarrow 2NH_4^+ + 2Cu\) 3. Calculate ΔE°: ΔE° = -(0.337) - (-0.76) = 0.423 V 4. Since ΔE° > 0, hydrazine can reduce \(Cu^{2+}\) ions to metallic copper.

(d) Silver

: 1. Balanced half-cell reduction reaction for silver (Ag⁺): \(Ag^+ + e^- \rightarrow Ag\) E° = 0.799 V 2. Combine half-cell reactions and balance the overall reaction: \(N_2H_4 + 4H^+ + 4Ag^+ \rightarrow 2NH_4^+ + 4Ag\) 3. Calculate ΔE°: ΔE° = -2(0.799) - (-0.76) = -0.838 V 4. Since ΔE° < 0, hydrazine cannot reduce \(Ag^+\) ions to metallic silver.

(e) Chromium

: 1. Balanced half-cell reduction reaction for chromium (Cr³⁺): \(Cr^{3+} + 3e^- \rightarrow Cr\) E° = -0.744 V 2. Combine half-cell reactions and balance the overall reaction: \(2N_2H_4 + 8H^+ + Cr^{3+} \rightarrow 4NH_4^+ + Cr\) 3. Calculate ΔE°: ΔE° = -(-0.744) - (-0.76) = 0.016 V 4. Since ΔE° > 0, hydrazine can reduce \(Cr^{3+}\) ions to metallic chromium. In conclusion, hydrazine can reduce \(Fe^{2+}\), \(Sn^{2+}\), \(Cu^{2+}\), and \(Cr^{3+}\) ions to their metallic states, but not \(Ag^+\) ions.

Key concepts

Standard Reduction Potentials

Understanding standard reduction potentials is crucial when analyzing redox reactions in electrochemistry. Reduction potential, measured in volts (V), indicates how likely a substance is to gain electrons, thus being reduced. In more technical terms, it's the measurement of the tendency of a chemical species to acquire electrons and be reduced.

A half-cell’s reduction potential is compared to the standard hydrogen electrode (SHE), which is arbitrarily set at 0 volts. When we look at different substances, a positive standard reduction potential means a substance is more likely to be reduced (gain electrons) than the hydrogen ion, whereas a negative value means it's less likely.

In the given exercise, for example, the reduction of copper has a positive E° value, indicating that it is relatively easy to reduce compared to hydrogen. Conversely, chromium has a negative E° value, suggesting it is less eager to gain electrons. However, when coupled with an appropriate reducing agent like hydrazine, these metals can still undergo reduction.

Metallic State Reduction

Metallic state reduction involves the process of reducing metal ions from their oxidized state in a solution to a solid metal. This is typically done using a reducing agent that donates electrons to the metal ions. Hydrazine, with the chemical formula \(N_2H_4\), is one such reducing agent and plays a key role in this type of chemical reaction.

In the context of the presented exercise, metals like iron and tin, which have positive standard reduction potentials when coupled with hydrazine, readily accept electrons and are reduced to their solid, metallic state. It's important to note that the capability of hydrazine to reduce a metal ion depends not only on the metal's reduction potential but also on the potential of the reducing agent itself.

Electrochemistry

Electrochemistry is the study of chemical processes that cause electrons to move. This movement of electrons generates electricity, which is why electrochemistry is central to the design of batteries and electroplating processes.

The core of electrochemistry is the redox reaction, where oxidation (loss of electrons) and reduction (gain of electrons) occur. The behavior of these reactions can be predicted using standard reduction potentials, as demonstrated in the exercise. When we calculate the difference in standard potentials between the reducing agent (in this case, hydrazine) and the metal ion, we are able to predict if the reaction is thermodynamically favorable – as indicated by a positive combined standard potential.

Half-Cell Reactions

A half-cell reaction is one half of a redox reaction, where either oxidation or reduction occurs. Every electrochemical cell consists of two half-cells: the anode half-cell, where oxidation happens, and the cathode half-cell, where reduction takes place. Each half-cell has its own distinct standard reduction potential.

By looking at the standard reduction potential of these half-cells, as done for the metals and hydrazine in the exercise, we are able to predict if the overall reaction will proceed spontaneously. For a redox reaction to occur, electrons must flow from the anode to the cathode. If the computed cell potential (\(\Delta E°\)) is positive, the reaction is spontaneous and will proceed under the standard conditions. This is the case for the reduction of iron, tin, copper, and chromium by hydrazine in the given exercise – each of these metals displayed a positive potential when reacted with hydrazine.