Consider the galvanic cell based on the following...

Consider the galvanic cell based on the following half-reactions: $$\begin{array}{ll}\mathrm{Au}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au} & \mathscr{E}^{\circ}=1.50 \mathrm{~V} \\ \mathrm{Tl}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Tl} & \mathscr{E}^{\circ}=-0.34 \mathrm{~V} \end{array}$$ a. Determine the overall cell reaction and calculate $\mathscr{E}_{\mathrm{ccll}}^{\circ}$ b. Calculate $\Delta G^{\circ}$ and $K$ for the cell reaction at $25^{\circ} \mathrm{C}$. c. Calculate $\mathscr{E}_{\text {cell }}$ at $25^{\circ} \mathrm{C}$ when $\left[\mathrm{Au}^{3+}\right]=1.0 \times 10^{-2} M$ and $\left[\mathrm{Tl}^{+}\right]=1.0 \times 10^{-4} \mathrm{M}$

Consider the galvanic cell based on the following half-reactions:
$$\begin{array}{ll}\mathrm{Au}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au} & \mathscr{E}^{\circ}=1.50 \mathrm{~V} \\
\mathrm{Tl}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Tl} & \mathscr{E}^{\circ}=-0.34 \mathrm{~V}
\end{array}$$
a. Determine the overall cell reaction and calculate $\mathscr{E}_{\mathrm{ccll}}^{\circ}$
b. Calculate $\Delta G^{\circ}$ and $K$ for the cell reaction at $25^{\circ} \mathrm{C}$.
c. Calculate $\mathscr{E}_{\text {cell }}$ at $25^{\circ} \mathrm{C}$ when $\left[\mathrm{Au}^{3+}\right]=1.0 \times 10^{-2} M$ and $\left[\mathrm{Tl}^{+}\right]=1.0 \times 10^{-4} \mathrm{M}$

Key Concepts

Nernst Equation

The Nernst equation is used to calculate the cell potential under non-standard conditions by accounting for the actual concentrations of the reacting species. It relates the cell potential to the standard cell potential, temperature, the number of electrons transferred, and the reaction quotient. This equation is essential for understanding how deviation from standard conditions affects the performance of an electrochemical cell.

Galvanic Cells

Galvanic cells are electrochemical cells that convert chemical energy into electrical energy through spontaneous redox reactions. In these cells, oxidation occurs at the anode and reduction occurs at the cathode, and the overall cell reaction is determined by combining the half-reactions while ensuring that electrons are balanced. Understanding galvanic cells is essential to analyze and calculate cell potentials, Gibbs free energy changes, and equilibrium constants.

Standard Reduction Potentials

Standard reduction potentials are measures of the tendency of a chemical species to gain electrons and be reduced, measured under standard conditions. They allow us to predict the direction of electron flow by comparing the potentials of the two half-reactions involved in a galvanic cell. The standard cell potential is calculated by taking the difference between the reduction potential of the cathode and that of the anode.

Gibbs Free Energy

Gibbs free energy (?G°) quantifies the maximum reversible work that can be performed by a chemical reaction at constant temperature and pressure. In the context of electrochemistry, ?G° is directly related to the standard cell potential (E°cell) by the equation ?G° = -nFE°cell, where n is the number of electrons transferred and F is Faraday’s constant. This relationship helps determine the spontaneity of the cell reaction.

Equilibrium Constant

The equilibrium constant (K) for a redox reaction in an electrochemical cell is related to the standard cell potential through the equation ?G° = -RT ln K, linking chemical thermodynamics with electrochemistry. This relationship allows the determination of the position of equilibrium from electrochemical measurements and shows how a large positive E°cell corresponds to a large equilibrium constant, indicating reaction favorability.

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