Problem 99 - Chemistry: The Central Science in SI Units, Global Edition

Question

Predict whether the following reactions will be spontaneous in acidic solution under standard conditions: (a) oxidation of \(\mathrm{Cu}\) to \(\mathrm{Cu}^{2+}\) by \(\mathrm{I}_{2}\) (to form \(\mathrm{I}^{-}\) ), \((\mathbf{b})\) reduction of \(\mathrm{Fe}^{2+}\) to \(\mathrm{Fe}\) by \(\mathrm{H}_{2}\) (to form \(\mathrm{H}^{+}\) ), \(\left(\mathbf{c}\right.\) ) reduction of \(\mathrm{I}_{2}\) to \(\mathrm{I}^{-}\) by \(\mathrm{H}_{2} \mathrm{O}_{2},(\mathbf{d})\) reduction of \(\mathrm{Ni}^{2+}\) to \(\mathrm{Ni}\) by \(\mathrm{Sn}^{2+}\left(\right.\) to form \(\left.\mathrm{Sn}^{4+}\right)\).

Step-by-Step Solution

Answer

Among the four reactions, only the oxidation of Cu to Cu²⁺ by I₂ to form I⁻ (a) is spontaneous in acidic solution under standard conditions. Eº_cell for this reaction is positive (0.20 V). The other reactions (b, c, and d) have negative Eº_cell values, indicating that they are not spontaneous under the given conditions.

Step 1: Recall the standard potentials for the reactions under consideration

: To predict whether a given reaction will be spontaneous in acidic solution under standard conditions, we can refer to standard reduction potential tables. (a) Cu to Cu²⁺ and I₂ to I⁻. Eº(Cu²⁺/Cu) = +0.34 V Eº(I₂/I⁻) = +0.54 V (b) Fe²⁺ to Fe and H₂ to H⁺. Eº(Fe²⁺/Fe) = -0.44 V Eº(H₂/H⁺) = 0 V (since hydrogen is the reference) (c) I₂ to I⁻ and H₂O₂ to H₂O. Eº(I₂/I⁻) = +0.54 V Eº(H₂O₂/H₂O) = +1.78 V (d) Ni²⁺ to Ni and Sn²⁺ to Sn⁴⁺. Eº(Ni²⁺/Ni)= -0.26 V Eº(Sn⁴⁺/Sn²⁺) = +0.15 V

Step 2: Calculate the overall cell potential for each reaction

: (a) Eº_cell = Eº(I₂/I⁻) - Eº(Cu²⁺/Cu) = 0.54 V - 0.34 V = 0.20 V Since Eº_cell is positive, the reaction is spontaneous. (b) Eº_cell = Eº(Fe²⁺/Fe) - Eº(H₂/H⁺) = -0.44 V - 0 V = -0.44 V Since Eº_cell is negative, the reaction is not spontaneous. (c) Eº_cell = Eº(I₂/I⁻) - Eº(H₂O₂/H₂O) = 0.54 V - 1.78 V = -1.24 V Since Eº_cell is negative, the reaction is not spontaneous. (d) Eº_cell = Eº(Ni²⁺/Ni) - Eº(Sn⁴⁺/Sn²⁺) = -0.26 V - 0.15 V = -0.41 V Since Eº_cell is negative, the reaction is not spontaneous. In conclusion, among the four reactions, only the first reaction (oxidation of Cu to Cu²⁺ by I₂ to form I⁻) is spontaneous in acidic solution under standard conditions.

Key Concepts

Standard Reduction Potential

Standard reduction potentials ( E° ) are essential in determining the likelihood of a chemical reaction occurring under standard conditions (25°C, 1 atm, and 1 M concentrations). A standard reduction potential is measured in volts and indicates a substance's ability to gain electrons, essentially how eagerly it wants to be reduced.

In electrochemistry, every substance has a specific reduction potential, which can be found in standard reduction potential tables. These tables list various chemical reactions and their respective E° values.

Here is how you can utilize them:

• A higher E° value means a greater tendency to gain electrons and be reduced.
• If comparing two half-reactions, the one with the higher E° value will act as the cathode (reduction site) in a galvanic cell.

By using standard reduction potentials, you can calculate the overall cell potential ( E°_cell ) of a redox reaction, which determines if the reaction is spontaneous, as positive overall cell potentials indicate spontaneous reactions.

Spontaneous Reaction

A spontaneous reaction is one that occurs without needing additional energy once started. In electrochemistry, whether a reaction is spontaneous is determined using standard reduction potentials.

When you calculate the overall cell potential ( E°_cell ) of a reaction, look for:

• A positive E°_cell indicates a spontaneous reaction.
• A negative E°_cell means the reaction is non-spontaneous, and an additional energy input is needed to start it.

To find E°_cell , subtract the E° of the oxidation reaction from the E° of the reduction reaction. Redox reactions are the heart of electrochemical cells, and understanding whether they are spontaneous is crucial for predicting the behavior of these cells in real-world applications.

Oxidation

Oxidation is a chemical process where a substance loses electrons. In redox reactions, it occurs alongside reduction, which is the gain of electrons by another substance.

Remember:

• The substance that loses electrons is oxidized and termed the reducing agent or reductant.
• Every oxidation must be paired with a reduction, as electrons cannot exist free in solutions.

In an oxidation process, the oxidized substance's oxidation state increases.

For example, in the reaction highlighted in the solution, copper ( Cu ) is oxidized to copper ions ( Cu^{2+} ). This is essential to forming a complete redox reaction, where Iodine goes to I⁻ , paired with the reduction half to complete the loop of electron transfer. Understanding these electron transfers helps predict the pathway and feasibility of chemical processes.