Problem 79 - Introductory Chemistry Atoms First

Question

Using the EMF series on page 391, decide which of the following redox reactions is spontaneous. Explain your answer. (a) \(3 \mathrm{Ag}+\mathrm{Au}^{3+} \rightarrow \mathrm{Au}+3 \mathrm{Ag}^{+}\) (b) \(\mathrm{Au}+3 \mathrm{Ag}^{+} \rightarrow 3 \mathrm{Ag}+\mathrm{Au}^{3+}\)

Step-by-Step Solution

Answer

Reaction (a) is spontaneous with an E° value of +0.70 V, while reaction (b) is not spontaneous with an E° value of -0.70 V. This is determined by calculating the standard cell potential (E°) for each reaction using the EMF series table and the equation E° = E°(cathode) - E°(anode). A positive E° indicates a spontaneous reaction, and a negative E° indicates a non-spontaneous reaction.

Step 1: Identify the half-reactions

First, we need to identify the half-reactions involved in each redox reaction. The given redox reactions are: (a) \( 3 \mathrm{Ag}+\mathrm{Au}^{3+} \rightarrow \mathrm{Au}+3 \mathrm{Ag}^{+} \) (b) \( \mathrm{Au}+3 \mathrm{Ag}^{+} \rightarrow 3 \mathrm{Ag}+\mathrm{Au}^{3+} \) For (a), the half-reactions are: (i) Oxidation: \( \mathrm{Ag} \rightarrow \mathrm{Ag}^{+} + e^- \) (ii) Reduction: \( \mathrm{Au}^{3+} + 3e^- \rightarrow \mathrm{Au} \) For (b), the half-reactions are: (i) Oxidation: \( \mathrm{Au} \rightarrow \mathrm{Au}^{3+} + 3e^- \) (ii) Reduction: \( \mathrm{Ag}^{+} + e^- \rightarrow \mathrm{Ag}\)

Step 2: Determine E° values from the EMF series

Now we need to find the standard reduction potentials for each half-reaction from the EMF series table on page 391: For (a): - For silver: E°(Ag⁺/Ag) = +0.80 V - For gold: E°(Au³⁺/Au) = +1.50 V For (b): - For gold: E°(Au³⁺/Au) = +1.50 V - For silver: E°(Ag⁺/Ag) = +0.80 V

Step 3: Calculate E° for the reactions using E°(cathode) - E°(anode)

For each reaction, we will determine the E° by using the E° values of the half-reactions. For (a): - E° = E°(Au³⁺/Au) - E°(Ag⁺/Ag) = (+1.50 V) - (+0.80 V) = +0.70 V For (b): - E° = E°(Ag⁺/Ag) - E°(Au³⁺/Au) = (+0.80 V) - (+1.50 V) = -0.70 V

Step 4: Determine the spontaneity

Finally, we can determine the spontaneity of the reactions based on their E° values. For (a): As E° = +0.70 V is positive, reaction (a) is spontaneous. For (b): As E° = -0.70 V is negative, reaction (b) is not spontaneous and is not favored.

Key Concepts

EMF series

The EMF series, also known as the electromotive force series, is an arrangement of elements according to their standard electrode potentials. This series helps in determining the tendency of a chemical species to gain or lose electrons, which is crucial in predicting the direction of redox reactions. Each element or compound is listed with its standard reduction potential in volts.

• Elements at the top are more easily reduced and have higher positive potentials.
• Elements at the bottom are more easily oxidized and have lower negative or less positive potentials.

When comparing two substances, the one with the higher potential acts as a stronger oxidizing agent, and the one with the lower potential serves as a stronger reducing agent. The positioning within the EMF series can predict whether a redox reaction between two substances will be spontaneous. This is achieved by calculating the difference in their standard reduction potentials.

Standard Reduction Potentials

The concept of standard reduction potentials, denoted by E°, is pivotal in electrochemistry, specifically in redox reactions. It measures the tendency of a species to gain electrons and be reduced. The values are determined under standard conditions, which include a concentration of one molar for each ion, a pressure of one atmosphere, and a temperature of 25°C.
Some main highlights regarding standard reduction potentials:

• They are tabulated in the EMF series, which provides a comprehensive view of different elements and their potentials.
• The more positive the E°, the greater the species' affinity to attract electrons and be reduced.
• Conversely, a less positive (or more negative) E° suggests a strong tendency to lose electrons and be oxidized.

Understanding these potentials allows us to predict the flow of electrons between species in a reaction, which is essential for determining the feasibility and spontaneity of the redox processes.

Spontaneity of Reactions

In redox chemistry, the spontaneity of reactions is evaluated using the concept of standard electrode potentials. A spontaneous reaction is one that proceeds without needing an external energy source. The spontaneity of a reaction can be predicted based on the sign of its calculated electromotive force (EMF).
To determine if a redox reaction is spontaneous:

• First, identify the anode and cathode of the reaction.
• Calculate the potential difference (EMF) using: \[E^°_{cell} = E^°_{{cathode}} - E^°_{{anode}}\]
• If the result, E°, is positive, then the reaction is spontaneous.
• If the result is negative, the reaction is not spontaneous and requires energy input.

Thus, by correctly determining the cathode and anode and evaluating the potentials, one predicts whether a redox process will occur naturally.

Oxidation and Reduction Half-Reactions

Redox reactions consist of oxidation and reduction half-reactions, where one species loses electrons (oxidation) and another gains electrons (reduction). Recognizing these half-reactions is fundamental to understanding how electrons are transferred in a chemical reaction.
Here’s how to break it down:

• Oxidation half-reaction: This involves the loss of electrons. For example, in the reaction of silver, it can be written as: \[ \text{Ag} \rightarrow \text{Ag}^+ + e^- \]
• Reduction half-reaction: Here, electrons are gained. Using gold as an example: \[ \text{Au}^{3+} + 3e^- \rightarrow \text{Au} \]

By writing these half-reactions, one can easily calculate the standard potentials for each and predict the direction of electron flow. This method not only simplifies complex reactions but also helps in determining reaction spontaneity.