Question

Predict whether the following reactions will be spontaneous in acidic solution under standard conditions: (a) oxidation of \(\mathrm{Sn}\) to \(\mathrm{Sn}^{2+}\) by \(\mathrm{I}_{2}\) (to form \(\mathrm{I}^{-}\) ), (b) reduction of \(\mathrm{Ni}^{2+}\) to \(\mathrm{Ni}\) by \(\mathrm{I}^{-}\) (to form \(\mathrm{I}_{2}\) ), (c) reduction of \(\mathrm{Ce}^{4+}\) to \(\mathrm{Ce}^{3+}\) by \(\mathrm{H}_{2} \mathrm{O}_{2},\) (d) reduction of \(\mathrm{Cu}^{2+}\) to \(\mathrm{Cu}\) by \(\mathrm{Sn}^{2+}\) (to form \(\mathrm{Sn}^{4+}\) ).

Short answer

In acidic solution under standard conditions, the spontaneity of the given reactions is as follows: (a) The oxidation of Sn to Sn²⁺ by I₂ (to form I⁻) is spontaneous with E° = 0.68 V. (b) The reduction of Ni²⁺ to Ni by I⁻ (to form I₂) is non-spontaneous with E° = -0.79 V. (c) The reduction of Ce⁴⁺ to Ce³⁺ by H₂O₂ is non-spontaneous with E° = -0.15 V. (d) The reduction of Cu²⁺ to Cu by Sn²⁺ (to form Sn⁴⁺) is spontaneous with E° = 0.19 V.

Step-by-step solution

Determine the Standard Reduction Potentials for Each Half-Reaction

Look up the standard reduction potentials for each half-reaction in a table. These values are generally provided in textbooks or can be found online.

Calculate the E° value for the cell

For each reaction, plug in the values of standard reduction potentials (E°) into the formula: \[ E°_{cell} = E°_{cathode} - E°_{anode} \]

Determine the spontaneity of the reaction

Compare the calculated E° values with 0 to determine the spontaneity of each reaction: - If E° > 0, the reaction is spontaneous - If E° < 0, the reaction is non-spontaneous Using the standard reduction potentials and the above steps, let's predict the spontaneity of the given reactions in acidic solution under standard conditions: (a) Oxidation of Sn to Sn²⁺ by I₂ (to form I⁻): E°(Sn²⁺/Sn) = -0.14 V (This is the anode) E°(I₂/I⁻) = 0.54 V (This is the cathode) E°(cell) = 0.54 - (-0.14) = 0.68 V Since E° > 0, the reaction is spontaneous. (b) Reduction of Ni²⁺ to Ni by I⁻ (to form I₂): E°(Ni²⁺/Ni) = -0.25 V (This is the cathode) E°(I₂/I⁻) = 0.54 V (This is the anode) E°(cell) = -0.25 - 0.54 = -0.79 V Since E° < 0, the reaction is non-spontaneous. (c) Reduction of Ce⁴⁺ to Ce³⁺ by H₂O₂: E°(Ce⁴⁺/Ce³⁺) = 1.61 V (This is the cathode) E°(H₂O₂/H₂O) = 1.76 V (This is the anode) E°(cell) = 1.61 - 1.76 = -0.15 V Since E° < 0, the reaction is non-spontaneous. (d) Reduction of Cu²⁺ to Cu by Sn²⁺ (to form Sn⁴⁺): E°(Cu²⁺/Cu) = 0.34 V (This is the cathode) E°(Sn⁴⁺/Sn²⁺) = 0.15 V (This is the anode) E°(cell) = 0.34 - 0.15 = 0.19 V Since E° > 0, the reaction is spontaneous.

Key concepts

Standard Reduction Potentials

Understanding standard reduction potentials is crucial when predicting the spontaneity of redox reactions. A reduction potential is a measure of the tendency of a chemical species to acquire electrons and thereby be reduced. Each half-reaction has a standard reduction potential (\( E^\text{o} \) value), which are typically found in electrochemistry tables and indicate the ease with which a species is reduced.

The standard reduction potentials are measured under standard conditions, which is typically 25°C, 1 M concentration for each ion participating in the reaction, and a pressure of 1 atm for any gases that are involved.

In a redox reaction, the substance that has the higher (more positive) standard reduction potential will tend to undergo reduction (gain electrons), while the other substance with the lower standard reduction potential will tend to get oxidized (lose electrons). The difference in potential (\( E^\text{o}_\text{cell} \) value) can be calculated using the formula: \[ E^\text{o}_\text{cell} = E^\text{o}_\text{cathode} - E^\text{o}_\text{anode} \]
If this value is positive (\( E^\text{o}_\text{cell} > 0 \) ), the redox reaction is considered to be spontaneous under standard conditions. Conversely, if the value is negative (\( E^\text{o}_\text{cell} < 0 \) ), the reaction is non-spontaneous.

Electrochemistry

Electrochemistry is the branch of chemistry that deals with the relationship between electrical energy and chemical changes, which is at the core of redox reactions. It's primarily concerned with how chemical energy is converted to electrical energy and vice versa.

In the context of spontaneous reactions, electrochemistry provides us with the tools to quantify and predict the flow of electrons, which are the source of the chemical changes. The standard reduction potentials are a key concept within electrochemistry that enables these predictions. By understanding the flow of electrons, we can harness these reactions to do useful work, for example in batteries or corrosion prevention.

The principles of electrochemistry are used to develop sensors, electroplating techniques, and electrochemical cells, where chemical energy is transformed into electrical energy as a means of power generation. Understanding how electrochemical gradients work allows scientists and engineers to innovate in power storage and generation technologies.

Galvanic Cells

Galvanic cells, also known as voltaic cells, are the physical structures that allow for spontaneous redox reactions to be harnessed for electrical energy. These cells are designed to separate the oxidation and reduction reactions into different compartments, connected by a salt bridge and an external circuit.

The anode is the electrode where oxidation occurs, while the cathode is the electrode where reduction takes place. Electrons flow from the anode to the cathode through an external circuit, thereby generating an electric current that can be used to do work. The salt bridge allows for the flow of ions to maintain a charge balance as the redox reaction proceeds.

In a galvanic cell, the spontaneous reaction's electrical potential can be measured using a voltmeter and is a direct result of the differences in standard reduction potentials of the electrodes. When dealing with exercises involving spontaneous reactions, it's often helpful to visualize the reaction occurring within a galvanic cell to understand better where oxidation and reduction are taking place and the direction of electron flow.