Question

Use tabulated electrode potentials to calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) for each reaction at \(25^{\circ} \mathrm{C}\) $$\begin{array}{l}{\text { a. } 2 \mathrm{Fe}^{3+}(a q)+3 \mathrm{Sn}(s) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{Sn}^{2+}(a q)} \\ {\text { b. } \mathrm{O}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)+2 \mathrm{Cu}(s) \longrightarrow 4 \mathrm{OH}^{-}(a q)+2 \mathrm{Cu}^{2+}(a q)}\end{array}$$ $${ c. } \operatorname{Br}_{2}(l)+2 \mathrm{I}^{-2}(a q) \longrightarrow 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)$$

Short answer

Calculate the number of moles of electrons transferred for each reaction (n), find the standard cell potential (E°) for each, and use the Gibbs Free Energy equation \(\Delta G_{\mathrm{rxn}}^{\circ} = -nFE^{\circ}\) to solve for \(\Delta G_{\mathrm{rxn}}^{\circ}\).

Step-by-step solution

Understand the Gibbs Free Energy Equation

To calculate the Gibbs Free Energy change \(\Delta G_{\mathrm{rxn}}^{\circ}\) for a reaction, use the equation \(\Delta G_{\mathrm{rxn}}^{\circ} = -nFE^{\circ}\), where \(n\) is the number of moles of electrons transferred in the reaction, \(F\) is the Faraday constant (96485 C/mol), and \(E^{\circ}\) is the standard cell potential in volts.

Determine the Standard Cell Potential (\(E^\circ\)) for Each Reaction

Use tabulated standard electrode potentials to find the \(E^{\circ}\) values for the half-reactions involved. The cell potential for the overall reaction is the difference between the electrode potentials for the reduction and oxidation half-reactions.

Calculate \(E^\circ\) for Reaction a

Identify the half-reactions: \(2\mathrm{Fe}^{3+} + 2e^- \rightarrow 2\mathrm{Fe}\) and \(\mathrm{Sn} \rightarrow \mathrm{Sn}^{2+} + 2e^-\). Look up their standard electrode potentials and calculate \(E^{\circ}\) for the complete reaction.

Calculate \(E^\circ\) for Reaction b

Identify the half-reactions: \(\mathrm{O}_2 + 4\mathrm{H}^+ + 4e^- \rightarrow 2\mathrm{H}_2\mathrm{O}\) and \(\mathrm{Cu} \rightarrow \mathrm{Cu}^{2+} + 2e^-\). Look up their standard electrode potentials and calculate \(E^{\circ}\) for the complete reaction.

Calculate \(E^\circ\) for Reaction c

Identify the half-reactions: \(\mathrm{Br}_2 + 2e^- \rightarrow 2\mathrm{Br}^-\) and \(2\mathrm{I}^- \rightarrow \mathrm{I}_2 + 2e^-\). Look up their standard electrode potentials and calculate \(E^{\circ}\) for the complete reaction.

Calculate the Number of Moles of Electrons Transferred (\(n\))

Determine the value of \(n\) for each reaction by examining the balanced chemical equations and identifying how many electrons are transferred in each reaction.

Calculate \(\Delta G_{\mathrm{rxn}}^{\circ}\) for Each Reaction

With the calculated values of \(E^{\circ}\) and \(n\), use the \(\Delta G_{\mathrm{rxn}}^{\circ}\) equation to find the change in Gibbs Free Energy for each reaction. Substitute the Faraday constant (\(F = 96485 C/mol\)) and the values you found into the equation and solve for \(\Delta G_{\mathrm{rxn}}^{\circ}\).

Key concepts

Electrode Potentials

Electrode potentials, also known as standard reduction potentials, are a measure of the tendency of a chemical species to be reduced. In simpler terms, they tell us how likely an element or compound is to gain electrons and form a bond. These potentials are measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C temperature) and are given the symbol \(E^{\text{\circ}}\).

When dealing with redox (reduction-oxidation) reactions, we split the reaction into two half-reactions: one for oxidation (loss of electrons) and one for reduction (gain of electrons). Each half-reaction has its own electrode potential, and the overall cell potential can be calculated by subtracting the potential of the oxidation half-reaction from that of the reduction half-reaction. By referencing a table of standard electrode potentials, students can find the \(E^{\text{\circ}}\) values they need to calculate the standard cell potential for a redox reaction.

Standard Cell Potential

The standard cell potential (\(E^{\text{\circ}}\)) provides insight into the voltage that can be expected from an electrochemical cell when no current is drawn from it. If \(E^{\text{\circ}}\) is positive, it indicates that the reaction should proceed spontaneously as written (under standard conditions). Conversely, if \(E^{\text{\circ}}\) is negative, the reaction is non-spontaneous.

To calculate the standard cell potential for a full reaction, we identify and combine the \(E^{\text{\circ}}\) values of the two half-reactions. This process helps us to gather all the pieces needed to solve the bigger puzzle—how much energy will be released or consumed during a chemical reaction.

Faraday Constant

The Faraday constant (\(F\)) is fundamental in the study of electrochemistry and represents the total electric charge carried by one mole of electrons, approximately 96485 coulombs per mole (C/mol). This number is named after the famous scientist Michael Faraday.

The Faraday constant allows us to translate between the macroscopic world that we observe and the microscopic world of atoms and electrons. When solving problems related to Gibbs Free Energy calculations, the Faraday constant is used to convert the standard cell potential \(E^{\text{\circ}}\) into an energy value that tells us about the feasibility and energy changes of the overall reaction.

Redox Reactions

Redox reactions are chemical processes where oxidation and reduction occur simultaneously. Oxidation refers to the loss of electrons by a molecule, atom, or ion, while reduction is the gain of electrons. In redox reactions, electrons are transferred from one substance to another, and this transfer is what drives the chemical reactions in batteries, biological systems, and industrial processes.

The balancing of redox reactions can be complex, but it's crucial for correctly identifying the stoichiometry of a reaction, which is necessary when calculating the Gibbs Free Energy change. This challenge can be defeated by meticulously counting the number of electrons lost and gained, ensuring that they are equal on both sides of the reaction equation.