Question

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

After identifying the half-reactions, finding the standard reduction potentials (E°) for the half-reactions, and calculating the standard cell potentials (E°) for each reaction, we can predict the spontaneity of the reactions as follows: (a) The oxidation of Sn to \(\mathrm{Sn}^{2+}\) by \(\mathrm{I}_{2}\) to form \(\mathrm{I}^{-}\): Non-spontaneous (b) The reduction of \(\mathrm{Ni}^{2+}\) to \(\mathrm{Ni}\) by \(\mathrm{I}^{-}\) to form \(\mathrm{I}_{2}\): Spontaneous (c) The reduction of \(\mathrm{Ce}^{4+}\) to \(\mathrm{Ce}^{3+}\) by \(\mathrm{H}_{2} \mathrm{O}_{2}\): Spontaneous (d) The reduction of \(\mathrm{Cu}^{2+}\) to \(\mathrm{Cu}\) by \(\mathrm{Sn}^{2+}\) to form \(\mathrm{Sn}^{4+}\): Spontaneous

Step-by-step solution

Identify half-reactions

First, we need to identify the half-reactions involved in each of the given reactions. In the given reactions, we have: (a) oxidation of Sn to \(\mathrm{Sn}^{2+}\) by \(\mathrm{I}_{2}\) (to form \(\left.\mathrm{I}^{-}\right)\): - \(\mathrm{Sn} \to \mathrm{Sn}^{2+} + 2 e^-\) - \(2 \mathrm{I}^{-} + 2 e^- \to \mathrm{I}_{2}\) (b) reduction of \(\mathrm{Ni}^{2+}\) to \(\mathrm{Ni}\) by \(\mathrm{I}^{-}\left(\right.\) to form \(\left.\mathrm{I}_{2}\right)\): - \(\mathrm{Ni}^{2+} + 2 e^- \to \mathrm{Ni}\) - \(2 \mathrm{I}^{-} \to \mathrm{I}_{2} + 2 e^-\) (c) reduction of \(\mathrm{Ce}^{4+}\) to \(\mathrm{Ce}^{3+}\) by \(\mathrm{H}_{2} \mathrm{O}_{2}\): - \(\mathrm{Ce}^{4+} + e^- \to \mathrm{Ce}^{3+}\) - \(\mathrm{H}_{2} \mathrm{O}_{2} + 2 e^- \to 2 \mathrm{OH}^{-}\) (d) reduction of \(\mathrm{Cu}^{2+}\) to \(\mathrm{Cu}\) by \(\mathrm{Sn}^{2+}\) (to form \(\mathrm{Sn}^{4+}\)): - \(\mathrm{Cu}^{2+} + 2 e^- \to \mathrm{Cu}\) - \(\mathrm{Sn}^{2+} \to \mathrm{Sn}^{4+} + 2 e^-\)

Find standard reduction potentials

Next, we need to find the standard reduction potentials (E°) for the half-reactions involved in each reaction. We can either use a textbook or an online resource to find the values for each half-reaction.

Calculate the standard cell potential for each reaction

To predict spontaneity, we need to calculate the standard cell potential (E°) for each reaction. For a given redox reaction, this can be done using the equation: E° (cell) = E° (reduction) - E° (oxidation) where E° (reduction) and E° (oxidation) are the standard reduction potentials for the reduction half-reaction and the oxidation half-reaction, respectively. Calculate the standard cell potential for each given reaction using the standard reduction potentials found in Step 2.

Predict spontaneity of reactions

Finally, use the calculated E° values to predict whether each reaction will be spontaneous in acidic solution under standard conditions: - If E° (cell) > 0, the reaction is spontaneous. - If E° (cell) < 0, the reaction is non-spontaneous. Predict the spontaneity of each reaction based on their calculated E° values.

Key concepts

Standard Reduction Potential

Understanding the concept of standard reduction potential is crucial when examining spontaneous redox reactions. Simply put, it is a measure used in chemistry to predict the tendency of a chemical species to acquire electrons and thereby be reduced. Each half-reaction in a redox process has an associated standard reduction potential, expressed in volts (V).

These potentials are tabulated under standard conditions, which include a temperature of 25°C, a 1 M concentration for each ion participating in the reaction, and a partial pressure of 1 atm for any gases involved.

The more positive the standard reduction potential, the greater the species' affinity for electrons – or in other words, the stronger its oxidizing power. Conversely, a more negative potential indicates a stronger reducing agent. This information provides a quantifiable way to compare the oxidizing and reducing strengths of different species involved in redox reactions.

When predicting the spontaneity of a reaction using standard reduction potentials, we compare the potential of the reducing agent to the potential of the oxidizing agent. The reaction tends to proceed spontaneously if the overall standard cell potential is positive. To find this, as indicated in Step 2 of the exercise solution, the standard reduction potential for the oxidation half-reaction is subtracted from the reduction half-reaction.

Half-Reactions in Redox Chemistry

A deeper dive into half-reactions reveals the beauty of redox chemistry. Redox reactions are essentially made up of two parts: the reduction half and the oxidation half. These half-reactions are essential elements in diagnosing the full reaction and analyzing each participant's role.

The process of reduction involves a substance gaining electrons, whereas oxidation involves losing them. It's helpful to keep in mind the mnemonic 'OIL RIG' – Oxidation Is Loss, Reduction Is Gain – to remember which is which.

By examining half-reactions, as presented in Step 1 of our example solution, students can effectively balance redox reactions and determine how electrons are transferred between species. Identifying the substances being oxidized and reduced allows us to understand the directional flow of electrons and the conversion of chemical energy.

Moreover, recognizing half-reactions serves as a foundation for predicting whether a certain reaction can occur. It also sets the stage for understanding electrochemical cells, where these half-reactions physically occur in separate compartments but are connected through the movement of electrons.

Predicting Reaction Spontaneity

Predicting whether a chemical reaction will occur spontaneously is a fundamental skill in chemistry, and one that hinges on grasping the concepts of redox reactions and standard reduction potentials. As highlighted in Step 3 and Step 4 of the provided solution, the standard cell potential (E° cell) is pivotal for this prediction. It is determined by calculating the difference between the standard reduction potentials of the participating half-reactions.

A positive E° cell value indicates that a reaction is spontaneous, meaning it can take place without added energy once initiated. However, if the E° cell value is negative, the reaction is considered non-spontaneous, requiring external energy to proceed.

It is important to note that this prediction assumes standard conditions. Reactions can behave differently in non-standard conditions due to changes in concentrations, temperature, or pressure. This versatility is of great practical significance in fields such as electrochemistry, environmental science, and energy technology. Understanding the correlation between standard reduction potentials and the spontaneity of a reaction remains a key competency for students learning about redox processes.