Chapter 21, Problem 21.151P

(a)

Interpretation Introduction

Interpretation:

The standard cell potential for the given cell has to be calculated.

Concept Introduction:

An electrochemical cell is a device in which a redox reaction is used to convert chemical energy into electrical energy. Such device is also known as the galvanic or voltaic cell.

Redox reaction: Redox reaction is a type of chemical reaction, where both the oxidation and reduction occur at the same time. In a redox reaction, one of the reactant is oxidized and the other is reduced simultaneously.

${\text{E}}^{\text{o}}{}_{\text{cell}}$-the cell potential measured at specified temperature conditions which is used to compare the potentials of different cells since, the ${\text{E}}_{\text{cell}}$ is affected by concentration changes as reaction proceeds and due to energy loss from heating of the cell and external circuit.

The Standard Gibb’s free energy change and the standard cell potential are related as followed:

$\text{Δ}°\text{G}\text{=}\text{-nFE}{°}_{\text{cell}}$

n - Number of electrons involved per equivalent of the net redox reaction in the cell

F - Faraday’s Constant (96500 C)

$\text{E}{°}_{\text{cell}}$ - Standard cell potential.

Explanation of Solution

The given information says that two voltaic cells are combined. The half reactions are depicted as follows,

  $\begin{array}{l}A{u}^{3+}\left(aq\right)+3e^{-}\rightleftharpoons Au\left(s\right)E^{\circ }=1.50V\\ \\ C{r}^{3+}\left(aq\right)+3e^{-}\rightleftharpoons Cr\left(s\right)E^{\circ }=-0.74V\\ \\ C{o}^{2+}\left(aq\right)+2e^{-}\rightleftharpoons Co\left(s\right)E^{\circ }=-0.28V\\ \\ Z{n}^{2+}\left(aq\right)+2e^{-}\rightleftharpoons Zn\left(s\right)E^{\circ }=-0.76V\end{array}$

Applying, the formula $E^{\circ }{}_{cell}=E^{\circ }{}_{cathode}-E^{\circ }{}_{anode}$, cell potential is determined as follows,

  $\begin{array}{l}{E}^{\circ }{}_{cell}=E^{\circ }{}_{cathode}-E^{\circ }{}_{anode}\\ \\ For\text{ cell Au/Cr}\Rightarrow E^{\circ }{}_{cell}=1.50V-\left(-0.74V\right)\\ =2.24\text{ V}\\ \\ For\text{ cell Co/Zn}\Rightarrow E^{\circ }{}_{cell}=-0.28V-\left(-0.76V\right)\\ =0.48\text{ V}\text{.}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The total cell potential when two given cells are connected in series has to be calculated.

Concept Introduction:

An electrochemical cell is a device in which a redox reaction is used to convert chemical energy into electrical energy. Such device is also known as the galvanic or voltaic cell.

Redox reaction: Redox reaction is a type of chemical reaction, where both the oxidation and reduction occur at the same time. In a redox reaction, one of the reactant is oxidized and the other is reduced simultaneously.

${\text{E}}^{\text{o}}{}_{\text{cell}}$-the cell potential measured at specified temperature conditions which is used to compare the potentials of different cells since, the ${\text{E}}_{\text{cell}}$ is affected by concentration changes as reaction proceeds and due to energy loss from heating of the cell and external circuit.

The Standard Gibb’s free energy change and the standard cell potential are related as followed:

$\text{Δ}°\text{G}\text{=}\text{-nFE}{°}_{\text{cell}}$

n - Number of electrons involved per equivalent of the net redox reaction in the cell

F - Faraday’s Constant (96500 C)

$\text{E}{°}_{\text{cell}}$ - Standard cell potential.

Explanation of Solution

The given information says that two voltaic cells are combined. The half reactions are depicted as follows,

  $\begin{array}{l}A{u}^{3+}\left(aq\right)+3e^{-}\rightleftharpoons Au\left(s\right)E^{\circ }=1.50V\\ \\ C{r}^{3+}\left(aq\right)+3e^{-}\rightleftharpoons Cr\left(s\right)E^{\circ }=-0.74V\\ \\ C{o}^{2+}\left(aq\right)+2e^{-}\rightleftharpoons Co\left(s\right)E^{\circ }=-0.28V\\ \\ Z{n}^{2+}\left(aq\right)+2e^{-}\rightleftharpoons Zn\left(s\right)E^{\circ }=-0.76V\end{array}$

Applying, the formula $E^{\circ }{}_{cell}=E^{\circ }{}_{cathode}-E^{\circ }{}_{anode}$, cell potential is determined as follows,

  $\begin{array}{l}{E}^{\circ }{}_{cell}=E^{\circ }{}_{cathode}-E^{\circ }{}_{anode}\\ \\ For\text{ cell Au/Cr}\Rightarrow E^{\circ }{}_{cell}=1.50V-\left(-0.74V\right)\\ =2.24\text{ V}\\ \\ For\text{ cell Co/Zn}\Rightarrow E^{\circ }{}_{cell}=-0.28V-\left(-0.76V\right)\\ =0.48\text{ V}\end{array}$

When two cells are connected in series the total cell potential is obtained by adding the potentials of individual cells present.

    $\begin{array}{c}{E}^{\circ }{}_{series}=E^{\circ }{}_{\text{Au/Cr}}+E^{\circ }{}_{\text{Co/Zn}}\\ \\ =\text{ 2}\text{.24 V + 0}\text{.48V}\\ \\ \text{= 2}\text{.72 V}\text{.}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The cell that acts as voltaic cell and the one that act as electrolytic cell present in the given cell has to be identified when the given condition is applied.

Concept Introduction:

An electrochemical cell is a device in which a redox reaction is used to convert chemical energy into electrical energy. Such device is also known as the galvanic or voltaic cell.

Redox reaction: Redox reaction is a type of chemical reaction, where both the oxidation and reduction occur at the same time. In a redox reaction, one of the reactant is oxidized and the other is reduced simultaneously.

${\text{E}}^{\text{o}}{}_{\text{cell}}$-the cell potential measured at specified temperature conditions which is used to compare the potentials of different cells since, the ${\text{E}}_{\text{cell}}$ is affected by concentration changes as reaction proceeds and due to energy loss from heating of the cell and external circuit.

The Standard Gibb’s free energy change and the standard cell potential are related as followed:

$\text{Δ}°\text{G}\text{=}\text{-nFE}{°}_{\text{cell}}$

n - Number of electrons involved per equivalent of the net redox reaction in the cell

F - Faraday’s Constant (96500 C)

$\text{E}{°}_{\text{cell}}$ - Standard cell potential.

Explanation of Solution

The difference in voltages occurs when the given cells are connected in series that is connecting $\left(\text{Au/Cr}\right)$ as voltaic and $\left(\text{Co/Zn}\right)$ as electrolytic cell. The difference in voltages that is as follows,

    $\begin{array}{c}{E}^{\circ }{}_{series}=E^{\circ }{}_{\text{Au/Cr}}-E^{\circ }{}_{\text{Co/Zn}}\\ \\ =\text{ 2}\text{.24 V - 0}\text{.48V}\\ \\ \text{= 1}\text{.76 V}\text{.}\end{array}$

(d)

Interpretation Introduction

Interpretation:

The metal ion that gets reduced in each cell has to be identified.

Concept Introduction:

An electrochemical cell is a device in which a redox reaction is used to convert chemical energy into electrical energy. Such device is also known as the galvanic or voltaic cell.

Redox reaction: Redox reaction is a type of chemical reaction, where both the oxidation and reduction occur at the same time. In a redox reaction, one of the reactant is oxidized and the other is reduced simultaneously.

Explanation of Solution

The given information says that two voltaic cells are combined. The half reactions are depicted as follows,

  $\begin{array}{l}A{u}^{3+}\left(aq\right)+3e^{-}\rightleftharpoons Au\left(s\right)E^{\circ }=1.50V\\ \\ C{r}^{3+}\left(aq\right)+3e^{-}\rightleftharpoons Cr\left(s\right)E^{\circ }=-0.74V\\ \\ C{o}^{2+}\left(aq\right)+2e^{-}\rightleftharpoons Co\left(s\right)E^{\circ }=-0.28V\\ \\ Z{n}^{2+}\left(aq\right)+2e^{-}\rightleftharpoons Zn\left(s\right)E^{\circ }=-0.76V\end{array}$

Analyzing the reduction potentials of ${\text{Au}}^{\text{3+}}$ and $C{r}^{\text{3+}}$ it is clear that ${\text{Au}}^{\text{3+}}$ gets easily reduced since its reduction potential is higher than $C{r}^{\text{3+}}$.

Similarly, analyzing the reduction potentials of $C{o}^{\text{2+}}$ and $Z{n}^{\text{2+}}$ it is clear that $C{o}^{\text{2+}}$ gets easily reduced since its reduction potential is higher than $Z{n}^{\text{2+}}$.

(e)

Interpretation Introduction

Interpretation:

The amount of metal obtained from electrolytic cell when 2 grams of metal plates out from voltaic cell has to be identified.

Concept Introduction:

An electrochemical cell is a device in which a redox reaction is used to convert chemical energy into electrical energy. Such device is also known as the galvanic or voltaic cell.

Redox reaction: Redox reaction is a type of chemical reaction, where both the oxidation and reduction occur at the same time. In a redox reaction, one of the reactant is oxidized and the other is reduced simultaneously.

Explanation of Solution

The difference in voltages occurs when the given cells are connected in series that is connecting $\left(\text{Au/Cr}\right)$ as voltaic and $\left(\text{Co/Zn}\right)$ as electrolytic cell. The difference in voltages that is as follows,

    $\begin{array}{c}{E}^{\circ }{}_{series}=E^{\circ }{}_{\text{Au/Cr}}-E^{\circ }{}_{\text{Co/Zn}}\\ \\ =\text{ 2}\text{.24 V - 0}\text{.48V}\\ \\ \text{= 1}\text{.76 V}\text{.}\end{array}$

As per above connection, $\text{Co/Zn}$ is forced to operate in reverse direction which results in reduction of ${\text{Zn}}^{\text{2+}}$.

Therefore, the mass of zinc produced is calculated as follows,

    $\begin{array}{c}ZnMass=2\text{ g Au}\left(\frac{1molAu}{197\text{ g Au}}\right)\left(\frac{3mol{e}^{-}}{1molAu}\right)\left(\frac{1molZn}{2mol{e}^{-}}\right)\left(\frac{65.41\text{ g Zn}}{1molZn}\right)\\ =0.996g\text{ Zn}\text{.}\end{array}$