Consider the galvanic cell based on the following...

Consider the galvanic cell based on the following half-reactions: $$\begin{array}{ll}\mathrm{Zn}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn} & \mathscr{E}^{\circ}=-0.76 \mathrm{~V} \\ \mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe} & \mathscr{E}^{\circ}=-0.44 \mathrm{~V} \end{array}$$ a. Determine the overall cell reaction and calculate $\mathscr{E}_{\mathrm{cell}}^{\circ}$ b. Calculate $\Delta G^{\circ}$ and $K$ for the cell reaction at $25^{\circ} \mathrm{C}$. c. Calculate $\mathscr{B}_{\text {coll }}$ at $25^{\circ} \mathrm{C}$ when $\left[\mathrm{Zn}^{2+}\right]=0.10 \mathrm{M}$ and $\left[\mathrm{Fe}^{2+}\right]=$ $1.0 \times 10^{-5} M$

Consider the galvanic cell based on the following half-reactions:
$$\begin{array}{ll}\mathrm{Zn}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn} & \mathscr{E}^{\circ}=-0.76 \mathrm{~V} \\
\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe} & \mathscr{E}^{\circ}=-0.44 \mathrm{~V}
\end{array}$$
a. Determine the overall cell reaction and calculate $\mathscr{E}_{\mathrm{cell}}^{\circ}$
b. Calculate $\Delta G^{\circ}$ and $K$ for the cell reaction at $25^{\circ} \mathrm{C}$.
c. Calculate $\mathscr{B}_{\text {coll }}$ at $25^{\circ} \mathrm{C}$ when $\left[\mathrm{Zn}^{2+}\right]=0.10 \mathrm{M}$ and $\left[\mathrm{Fe}^{2+}\right]=$ $1.0 \times 10^{-5} M$

Key Concepts

Galvanic Cell

A galvanic cell is an electrochemical cell that converts chemical energy into electrical energy through a spontaneous redox reaction. It consists of two half-cells where oxidation occurs at one electrode and reduction at the other. These cells are connected by an external circuit for electron flow and a salt bridge to maintain charge balance.

Half-Reactions

Half-reactions represent the separate oxidation and reduction processes in a redox reaction. Breaking a full reaction into half-reactions helps in balancing the number of electrons transferred and is essential for analyzing the individual contributions to the overall cell reaction.

Standard Reduction Potential

Standard reduction potentials are the voltages associated with reduction reactions measured under standard conditions. They provide a quantitative measure of the tendency of a chemical species to acquire electrons and be reduced, and they are used to predict which half-reaction will occur at the cathode and which at the anode.

Cell Potential Calculation

Calculating the overall cell potential involves taking the difference between the reduction potential at the cathode and that at the anode. This difference indicates the ability of the cell to do electrical work and is a key indicator of the spontaneity of the overall redox reaction.

Gibbs Free Energy

Gibbs free energy is a thermodynamic quantity that relates to the spontaneity of a reaction. In electrochemistry, the change in Gibbs free energy (?G°) can be calculated from the cell potential using the equation ?G° = -nFE°, linking electrical work to chemical energy changes.

Equilibrium Constant

The equilibrium constant quantifies the ratio of the concentrations (or activities) of products to reactants at equilibrium. It is intrinsically connected to the Gibbs free energy of the reaction through the relation ?G° = -RT ln K, allowing one to understand how far a reaction deviates from equilibrium.

Nernst Equation

The Nernst equation relates the cell potential under non-standard conditions to the standard cell potential and the reaction quotient. It allows the calculation of the cell voltage when concentrations of reactants and products differ from their standard values, thereby providing insight into the effect of concentration changes on cell performance.

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