Consider the galvanic cell based on the following halfreactions: $$ \begin{array}{ll} \mathrm{Au}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Au} & \mathscr{E}^{\circ}=1.50 \mathrm{~V} \\ \mathrm{Tl}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Tl} & \mathscr{E}^{\circ}=-0.34 \mathrm{~V} \end{array} $$

Short Answer

Expert verified
The overall cell potential for the galvanic cell based on the given half-reactions is \(E_{cell}^° = 1.84\,\text{V}\), with gold (Au) acting as the cathode and thallium (Tl) as the anode.

Step by step solution

01

Identify the cathode and the anode

First, determine which half-reaction is taking place at the cathode (reduction) and which is taking place at the anode (oxidation). The substance with the higher standard reduction potential value will act as the cathode, as it has a stronger tendency to gain electrons and undergo reduction. In this case, gold (Au) has a higher standard reduction potential (\(\mathscr{E}^\circ = 1.50 V\)) than thallium (Tl), which has a standard reduction potential of \(\mathscr{E}^\circ = -0.34 V\). Thus, the cathode half-reaction is: $$ \mathrm{Au}^{3+} + 3 \mathrm{e}^{-} \longrightarrow \mathrm{Au}; \quad \mathscr{E}^{\circ} = 1.50 \mathrm{~V} $$ And the anode half-reaction is: $$ \mathrm{Tl}^{+} + \mathrm{e}^{-} \longrightarrow \mathrm{Tl}; \quad \mathscr{E}^{\circ} = -0.34 \mathrm{~V} $$
02

Calculate the overall cell potential

Now that we have identified the cathode and the anode, we can use their respective standard reduction potentials to calculate the overall cell potential: $$ E_{cell}^° = E_{cathode}^° - E_{anode}^° = E_{Au}^° - E_{Tl}^° $$ Plug in the given values for the standard reduction potentials and calculate the cell potential: $$ E_{cell}^° = 1.50\,\text{V} - (-0.34\,\text{V}) = 1.50\,\text{V} + 0.34\,\text{V} = 1.84\,\text{V} $$ Therefore, the overall cell potential for this galvanic cell is \(1.84\,\text{V}\).

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Most popular questions from this chapter

The Ostwald process for the commercial production of nitric acid involves the following three steps: $$ \begin{aligned} 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{NO}_{2}(g) \\ 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow 2 \mathrm{HNO}_{3}(a q)+\mathrm{NO}(g) \end{aligned} $$ a. Which reactions in the Ostwald process are oxidationreduction reactions? b. Identify each oxidizing agent and reducing agent.

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What is electrochemistry? What are redox reactions? Explain the difference between a galvanic and an electrolytic cell.

An electrochemical cell is set up using the following unbalanced reaction: $$ \mathrm{M}^{a+}(a q)+\mathrm{N}(s) \longrightarrow \mathrm{N}^{2+}(a q)+\mathrm{M}(s) $$ The standard reduction potentials are: $$ \begin{array}{ll} \mathrm{M}^{a+}+a \mathrm{e}^{-} \longrightarrow \mathrm{M} & \mathscr{E}^{\circ}=0.400 \mathrm{~V} \\ \mathrm{~N}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{N} & \mathscr{E}^{\circ}=0.240 \mathrm{~V} \end{array} $$ The cell contains \(0.10 \mathrm{M} \mathrm{N}^{2+}\) and produces a voltage of \(0.180 \mathrm{~V}\). If the concentration of \(\mathrm{M}^{a+}\) is such that the value of the reaction quotient \(Q\) is \(9.32 \times 10^{-3}\), calculate \(\left[\mathrm{M}^{a+}\right]\). Calculate \(w_{\max }\) for this electrochemical cell.

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