Question

Which of the following reactions is/are spontaneous at standard conditions? (a) \(\mathrm{Zn}(s)+2 \mathrm{Fe}^{3+} \longrightarrow \mathrm{Zn}^{2+}(a q)+2 \mathrm{Fe}^{2+}(a q)\) (b) \(\mathrm{Cu}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Cu}^{2+}(a q)+\mathrm{H}_{2}(g)\) (c) \(2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q)\)

Short answer

(a) Zn(s) + Fe³⁺(aq) → Zn²⁺(aq) + Fe(s) (b) Cu(s) + 2H⁺(aq) → Cu²⁺(aq) + H₂(g) (c) 2Br⁻(aq) + I₂(s) → Br₂(l) + 2I⁻(aq) Answer: Reactions (b) and (c) are spontaneous at standard conditions, while reaction (a) is non-spontaneous.

Step-by-step solution

For each reaction, determine the half-reactions involved and their standard reduction potentials.

Using the standard reduction potentials table, we can find the reduction and oxidation half-reactions with their corresponding standard reduction potentials: (a) Zn(s) → Zn²⁺(aq) + 2e⁻ (oxidation) E° = -0.76 V Fe³⁺(aq) + 3e⁻ → Fe(s) (reduction) E° = +0.036 V (b) Cu(s) → Cu²⁺(aq) + 2e⁻ (oxidation) E° = +0.34 V 2H⁺(aq) + 2e⁻ → H₂(g) (reduction) E° = 0 V (c) 2Br⁻(aq) → Br₂(l) + 2e⁻ (oxidation) E° = +1.09 V I₂(s) + 2e⁻ → 2I⁻(aq) (reduction) E° = +0.54 V

Calculate the cell potentials for each reaction.

To find the cell potentials (E°ₜₒₜₐₗ) for each reaction, sum the standard reduction potentials of the oxidation half-reaction and the reduction half-reaction. For (a): E°ₜₒₜₐₗ = (-0.76 V) + (+0.036 V) = -0.72 V For (b): E°ₜₒₜₐₗ = (+0.34 V) + (0 V) = +0.34 V For (c): E°ₜₒₜₐₗ = (+1.09 V) + (-0.54 V) = +0.55 V

Determine the spontaneity of each reaction based on the calculated cell potentials.

A positive cell potential indicates a spontaneous reaction, while a negative cell potential suggests a non-spontaneous reaction: (a) E°ₜₒₜₐₗ = -0.72 V (non-spontaneous reaction) (b) E°ₜₒₜₐₗ = +0.34 V (spontaneous reaction) (c) E°ₜₒₜₐₗ = +0.55 V (spontaneous reaction) So, reactions (b) and (c) are spontaneous at standard conditions, while reaction (a) is non-spontaneous.

Key concepts

Standard Reduction Potentials

Understanding standard reduction potentials is crucial for predicting whether a chemical reaction is spontaneous. These potentials, symbolized as E°, are measures of the tendency of a species to gain electrons and reduce. Given in volts (V), they are determined under standard conditions, which include a temperature of 298 K (25°C), a pressure of 1 atm, and 1M concentrations for all solutions.

The more positive the reduction potential, the greater the species' ability to gain electrons. Conversely, a more negative reduction potential suggests a lower tendency to undergo reduction. A handy reference is the standard reduction potentials table, which lists various half-reactions and their associated potentials. This table is vital for comparing different species' behavior as either oxidizing or reducing agents and predicting reaction outcomes.

Half-Reactions

In electrochemistry, half-reactions split the overall chemical reaction into two separate parts: oxidation and reduction. These half-reactions show explicitly what happens to each reactant as it loses or gains electrons.

Oxidation Half-Reaction:

This part details the loss of electrons by a reactant, which increases its oxidation state. For instance, Zn(s) → Zn²⁺(aq) + 2e⁻ is an oxidation half-reaction, with zinc metal losing two electrons.

Reduction Half-Reaction:

Here, a reactant gains electrons, decreasing its oxidation state, such as Fe³⁺(aq) + 3e⁻ → Fe(s), showing iron ions gaining electrons to form iron metal. Analyzing these half-reactions and their potentials helps us calculate the overall cell potential and assess the spontaneity of the full reaction.

Cell Potential

The cell potential, denoted as E°ₜₒₜₐₗ, is the driving force of an electrochemical cell and indicates whether a reaction will proceed on its own. It is calculated by adding the standard reduction potential of the cathode (reduction half-reaction) and the negative standard reduction potential of the anode (oxidation half-reaction).

Positive cell potentials imply that the reaction may spontaneously proceed under standard conditions, while negative values suggest non-spontaneity. For example, in reaction (b) from the exercise, the cell potential was positive (+0.34 V), signifying a spontaneous reaction. The determination of cell potential is a powerful tool for understanding electrochemical processes and for designing batteries and electrochemical cells.

Oxidation and Reduction

The principles of oxidation and reduction are paramount in redox reactions. Oxidation corresponds to the loss of electrons by a substance, while reduction is the gain of electrons. These two processes always occur simultaneously, as the electrons lost by the oxidized species are gained by the reducing species.

Oxidizing Agent:

This is a substance that gets reduced by accepting electrons during a reaction, causing another substance to be oxidized. It has a higher, more positive standard reduction potential.

Reducing Agent:

Conversely, a reducing agent donates electrons and gets oxidized, possessing a lower, more negative standard reduction potential. The interplay between oxidizing and reducing agents, reflected in their standard reduction potentials, determines the direction and spontaneity of a reaction.