Consider a cell based on the following half-reactions: Au^3++3 e^- ⟶Au 𝒞^∘=1.50 V Fe^3++e

step 1 Okay, so we are given this two half cell equations for a cell like this. E0 is equal to 1 .5 vol

Consider a cell based on the following half-reactions:...

Consider a cell based on the following half-reactions: $$\begin{aligned}\mathrm{Au}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au} & \mathscr{C}^{\circ}=1.50 \mathrm{~V} \\ \mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+} & \mathscr{C}^{\circ}=0.77 \mathrm{~V} \end{aligned}$$ a. Draw this cell under standard conditions, labeling the anode, the cathode, the direction of electron flow, and the concentrations, as appropriate. b. When enough $\mathrm{NaCl}(s)$ is added to the compartment containing gold to make the $\left[\mathrm{Cl}^{-}\right]=0.10 M$, the cell potential is observed to be $0.31 \mathrm{~V}$. Assume that $\mathrm{Au}^{3+}$ is reduced and assume that the reaction in the compartment containing gold is $$\mathrm{Au}^{3+}(a q)+4 \mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{AuCl}_{4}^{-}(a q)$$ Calculate the value of $K$ for this reaction at $25^{\circ} \mathrm{C}$.

Consider a cell based on the following half-reactions:
$$\begin{aligned}\mathrm{Au}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au} & \mathscr{C}^{\circ}=1.50 \mathrm{~V} \\
\mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+} & \mathscr{C}^{\circ}=0.77 \mathrm{~V}
\end{aligned}$$
a. Draw this cell under standard conditions, labeling the anode, the cathode, the direction of electron flow, and the concentrations, as appropriate.
b. When enough $\mathrm{NaCl}(s)$ is added to the compartment containing gold to make the $\left[\mathrm{Cl}^{-}\right]=0.10 M$, the cell potential is observed to be $0.31 \mathrm{~V}$. Assume that $\mathrm{Au}^{3+}$ is reduced and assume that the reaction in the compartment containing gold is
$$\mathrm{Au}^{3+}(a q)+4 \mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{AuCl}_{4}^{-}(a q)$$
Calculate the value of $K$ for this reaction at $25^{\circ} \mathrm{C}$.

Key Concepts

Equilibrium Constant Determination from Electrochemical Data

This concept connects cell potential measurements with equilibrium constants for a reaction. By measuring the cell potential under non-standard conditions and applying the Nernst equation, one can deduce the relationship between the cell potential, the reaction’s equilibrium position, and hence calculate the equilibrium constant. This is particularly useful when the reaction involves complex formation or other equilibria that shift the concentrations of reactive species.

Nernst Equation

The Nernst equation relates the cell potential under non-standard conditions to the standard cell potential, temperature, number of electrons transferred, and the reaction quotient. This equation is fundamental in electrochemistry as it allows the calculation of cell potential when concentrations deviate from standard state, providing insight into the effect of ionic concentrations on the cell's behavior.

Redox Half-Reactions

Redox half-reactions break down the overall redox process into two separate processes: oxidation (loss of electrons) and reduction (gain of electrons). Each half-reaction is written with its specific electron transfer, and when combined, they give the complete redox reaction. Understanding these half-reactions helps in identifying the roles of species in the cell and accurately determining which electrode is the anode or cathode.

Standard Electrode Potentials

Standard electrode potentials serve as a reference to predict the direction of redox reactions under standard conditions. They are measured under specific conditions (1 M concentration of solutions, 1 atm pressure, and 25°C) and indicate the tendency of a species to be reduced. These values allow for comparison between half-reactions to determine the spontaneous direction of electron flow in the cell.

Electrochemical Cell Construction

This concept involves the structure and design of cells where oxidation and reduction occur in separate compartments. An electrochemical cell includes two electrodes (anode and cathode), a salt bridge or membrane to maintain ionic balance, and connections for electron flow. Proper labeling and understanding of the different compartments and their roles are essential for understanding how the cell operates under various conditions.

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