Problem 4 How is the change in standard re... [FREE SOLUTION]

Chapter 10: Problem 4

How is the change in standard reduction potential \(\left(\Delta E^{\circ}\right)\) determined for a redox reaction, and how is it related to the change in standard free energy \(\Delta G^{\circ \prime}\) for the same reaction?

Short Answer

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Answer: The change in standard reduction potential (\(\Delta E^{\circ}\)) is directly related to the change in standard free energy (\(\Delta G^{\circ \prime}\)) for a redox reaction. The relationship between the two is given by the equation: \(\Delta G^{\circ \prime} = -nF\Delta E^{\circ}\), where \(n\) is the number of moles of electrons transferred in the reaction, \(F\) is the Faraday constant, and \(\Delta E^{\circ}\) is the change in standard reduction potential. A more positive standard reduction potential corresponds to a more negative \(\Delta G^{\circ \prime}\), which indicates a spontaneous reaction, while a more negative standard reduction potential corresponds to a more positive \(\Delta G^{\circ \prime}\), indicating a non-spontaneous reaction.

Step by step solution

Define Standard Reduction Potential

The standard reduction potential is a measure of the tendency of a chemical species to acquire electrons and be reduced. It is measured in volts (V) and is defined under standard conditions, which include a concentration of 1 M, a pressure of 1 atm, and a temperature of 298 K. The standard reduction potentials for half-reactions can be looked up in a table, where their values are given relative to the standard hydrogen electrode (SHE), which has a potential of 0 V.

Define Standard Free Energy

Standard free energy (\(\Delta G^{\circ \prime}\)) represents the maximum amount of work that can be done by a chemical reaction under standard conditions. Free energy change is a measure of the energy available to do work, and the sign of \(\Delta G^{\circ \prime}\) determines if a reaction is spontaneous or not. When \(\Delta G^{\circ \prime} < 0\), the reaction is spontaneous, and when \(\Delta G^{\circ \prime} > 0\), the reaction is non-spontaneous.

Understand the Relationship between Standard Reduction Potential and Standard Free Energy

There is a direct relationship between the standard reduction potential and the change in standard free energy of a redox reaction. The more positive the standard reduction potential, the more likely the substance will be reduced and release energy in the form of work rather than heat, which results in a negative value for \(\Delta G^{\circ \prime}\). Conversely, the more negative the standard reduction potential, the less likely the substance will be reduced, and the reaction will require energy input or have a positive \(\Delta G^{\circ \prime}\).

Determine the Change in Standard Reduction Potential for a Redox Reaction

To find the change in standard reduction potential (\(\Delta E^{\circ}\)) for a redox reaction, we need to first identify the half-reactions involved. Next, look up the standard reduction potentials for the relevant half-reactions in a table. Finally, calculate \(\Delta E^{\circ}\) as follows: \(\Delta E^{\circ} = E^{\circ}_{cathode} - E^{\circ}_{anode}\) where \(E^{\circ}_{cathode}\) is the standard reduction potential of the half-reaction occurring at the cathode (reduction), and \(E^{\circ}_{anode}\) is the standard reduction potential of the half-reaction occurring at the anode (oxidation).

Relate Change in Standard Reduction Potential to Change in Standard Free Energy

The relationship between the change in standard reduction potential (\(\Delta E^{\circ}\)) and the change in standard free energy (\(\Delta G^{\circ \prime}\)) is given by the following equation: \(\Delta G^{\circ \prime} = -nF\Delta E^{\circ}\) where \(n\) is the number of moles of electrons transferred in the redox reaction, \(F\) is the Faraday constant (\(\approx 96,485 \,\text{C/mol}\)), and \(\Delta E^{\circ}\) is the change in standard reduction potential. By using this equation, we can determine the change in standard free energy for a redox reaction, knowing the change in standard reduction potential and the number of moles of electrons transferred.

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How is the change in standard reduction potential \(\left(\Delta E^{\circ}\right)\) determined for a redox reaction, and how is it related to the change in standard free energy \(\Delta G^{\circ \prime}\) for the same reaction?

Short Answer

Step by step solution

Define Standard Reduction Potential

Define Standard Free Energy

Understand the Relationship between Standard Reduction Potential and Standard Free Energy

Determine the Change in Standard Reduction Potential for a Redox Reaction

Relate Change in Standard Reduction Potential to Change in Standard Free Energy

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