Exercises: Cells, potentials and spontaneity

You have a Daniell galvanic cell made up of a zinc electrode immersed in a $1.0\text{ M}$ solution of $\mathrm{ZnSO_4}$ and a copper electrode immersed in a $1.0\text{ M}$ solution of $\mathrm{CuSO_4}$, at $25\text{ }^\circ\mathrm{C}$. The standard reduction potentials are $E^\circ(\mathrm{Zn}^{2+}/\mathrm{Zn}) = -0.76\text{ V}$ and $E^\circ(\mathrm{Cu}^{2+}/\mathrm{Cu}) = +0.34\text{ V}$.

1. a) Write the conventional cell notation or diagram, indicating the anode and the cathode.
2. b) State the sign or polarity assigned to each electrode and briefly justify which half-reaction takes place at each.

Consider a galvanic cell under standard conditions ($25\text{ }^\circ\mathrm{C}$, concentrations $1.0\text{ M}$) based on the overall reaction: $\mathrm{Cu(s)} + 2\,\mathrm{Ag^+}(\text{aq}) \rightarrow \mathrm{Cu}^{2+}(\text{aq}) + 2\,\mathrm{Ag(s)}$. Data: $E^\circ(\mathrm{Ag}^+/\mathrm{Ag}) = +0.80\text{ V}$ and $E^\circ(\mathrm{Cu}^{2+}/\mathrm{Cu}) = +0.34\text{ V}$.

1. a) Calculate the standard electromotive force of the cell, $E^\circ_{\text{pila}}$.
2. b) Justify in detail why the standard reduction potential of the $\mathrm{Ag}^+/\mathrm{Ag}$ couple must not be multiplied by the stoichiometric coefficient 2 when calculating the emf of the cell.

For a cell made up of the couples $\mathrm{Ni}^{2+}/\mathrm{Ni}$ and $\mathrm{Cd}^{2+}/\mathrm{Cd}$ at $25\text{ }^\circ\mathrm{C}$, the overall spontaneous reaction under standard conditions is $\mathrm{Cd(s)} + \mathrm{Ni}^{2+}(\text{aq}) \rightarrow \mathrm{Cd}^{2+}(\text{aq}) + \mathrm{Ni(s)}$, the standard electromotive force being $E^\circ_{\text{pila}} = +0.15\text{ V}$. Data: Faraday constant $F = 96485\text{ C}\times\text{mol}^{-1}$.

1. a) Determine the value of the standard Gibbs energy change, $\Delta G^\circ$, in $\text{kJ}\times\text{mol}^{-1}$.
2. b) Deduce the criterion for spontaneity from the sign of $\Delta G^\circ$ and $E^\circ_{\text{pila}}$.

In the laboratory, a Daniell galvanic cell is set up at $25\text{ }^\circ\mathrm{C}$ with metallic zinc and copper electrodes immersed in $1.0\text{ M}$ aqueous solutions of their respective cations, connected by a salt bridge of $\mathrm{KNO_3}$. The diagram of the experimental set-up is shown below:

Data: $E^\circ(\mathrm{Zn}^{2+}/\mathrm{Zn}) = -0.76\text{ V}$; $E^\circ(\mathrm{Cu}^{2+}/\mathrm{Cu}) = +0.34\text{ V}$.

1. a) Determine the standard electromotive force of the cell and state the correct direction of electron flow through the external metallic conductor.
2. b) Explain which species carries the charge through the salt bridge and towards which beaker the $\mathrm{K^+}$ and $\mathrm{NO_3^-}$ ions migrate respectively, stating why electrons do not flow through the solution.

A galvanic cell is built by connecting a half-cell with a chromium rod immersed in $\mathrm{Cr(NO_3)_3}\text{ }1.0\text{ M}$ and another with a lead rod in $\mathrm{Pb(NO_3)_2}\text{ }1.0\text{ M}$, at $25\text{ }^\circ\mathrm{C}$, using a salt bridge saturated with $\mathrm{NH_4NO_3}$. Data: $E^\circ(\mathrm{Cr}^{3+}/\mathrm{Cr}) = -0.74\text{ V}$, $E^\circ(\mathrm{Pb}^{2+}/\mathrm{Pb}) = -0.13\text{ V}$, $F = 96485\text{ C}\times\text{mol}^{-1}$.

1. a) Write the anode and cathode half-equations and the balanced overall ionic equation, and calculate the standard potential of the cell.
2. b) Explain how electroneutrality is maintained in each half-cell, specifying the movement of the salt bridge ions, and calculate the value of $\Delta G^\circ$ for the overall reaction.

The feasibility of a cell based on the standard couples $\mathrm{Fe}^{3+}/\mathrm{Fe}^{2+}$ and $\mathrm{I_2}/\mathrm{I^-}$ at $25\text{ }^\circ\mathrm{C}$ is analysed, with reactants under standard conditions. Data: $E^\circ(\mathrm{Fe}^{3+}/\mathrm{Fe}^{2+}) = +0.77\text{ V}$; $E^\circ(\mathrm{I_2}/\mathrm{I^-}) = +0.54\text{ V}$; $F = 96485\text{ C}\times\text{mol}^{-1}$.

1. a) Write the balanced equation of the spontaneous redox reaction under standard conditions, identify the oxidising and reducing species, and calculate $E^\circ_{\text{pila}}$ and $\Delta G^\circ$.
2. b) A student claims that, because $\Delta G^\circ < 0$, the reaction will always be spontaneous at any concentration and in any experimental context. Justify, with reasoning, why this claim is false, analysing the difference between $\Delta G^\circ$ and $\Delta G$.

You have aqueous solutions containing chloride ($\mathrm{Cl^-}$), bromide ($\mathrm{Br^-}$) and iodide ($\mathrm{I^-}$) ions, all at concentration $1.0\text{ M}$ and at $25\text{ }^\circ\mathrm{C}$. You want to select an oxidising agent in its standard state that is able to spontaneously oxidise the iodide ion to molecular iodine ($\mathrm{I_2}$), and the bromide ion to liquid bromine ($\mathrm{Br_2}$), but that does not oxidise the chloride ion to chlorine gas ($\mathrm{Cl_2}$).

Standard reduction potential data at $25\text{ }^\circ\mathrm{C}$:

$E^\circ(\mathrm{I_2}/\mathrm{I^-}) = +0.54\text{ V}$; $E^\circ(\mathrm{Br_2}/\mathrm{Br^-}) = +1.07\text{ V}$; $E^\circ(\mathrm{Cl_2}/\mathrm{Cl^-}) = +1.36\text{ V}$.

Oxidising agent candidates: $\mathrm{Fe}^{3+}(\text{aq})$ with $E^\circ(\mathrm{Fe}^{3+}/\mathrm{Fe}^{2+}) = +0.77\text{ V}$; $\mathrm{IO_3^-}(\text{aq})/\mathrm{I_2(s)}$ in acidic medium with $E^\circ = +1.20\text{ V}$; $\mathrm{MnO_4^-}(\text{aq})/\mathrm{Mn}^{2+}(\text{aq})$ in acidic medium with $E^\circ = +1.51\text{ V}$.

1. a) Select the most suitable oxidising agent, justifying your answer by comparing the potentials of the candidates and calculating $E^\circ$ and $\Delta G^\circ$ for the reaction of the chosen oxidising agent with each halide, using the lowest whole-number coefficients.
2. b) Write the balanced overall reaction that takes place between the selected oxidising agent and the bromide ion in acidic medium. Data: $F = 96485\text{ C}\times\text{mol}^{-1}$.

A metal sheet containing a mixture of cadmium, silver and iron is placed in solutions of acids and salts at $25\text{ }^\circ\mathrm{C}$ to evaluate displacement reactions.

Data: $E^\circ(\mathrm{Ag}^+/\mathrm{Ag}) = +0.80\text{ V}$; $E^\circ(\mathrm{H}^+/\mathrm{H_2}) = 0.00\text{ V}$; $E^\circ(\mathrm{Pb}^{2+}/\mathrm{Pb}) = -0.13\text{ V}$; $E^\circ(\mathrm{Cd}^{2+}/\mathrm{Cd}) = -0.40\text{ V}$; $E^\circ(\mathrm{Fe}^{2+}/\mathrm{Fe}) = -0.44\text{ V}$. Constant $F = 96485\text{ C}\times\text{mol}^{-1}$.

1. a) Determine which metals in the sheet will dissolve spontaneously in an aqueous $1.0\text{ M}$ solution of hydrochloric acid ($\mathrm{HCl}$), releasing hydrogen gas under standard conditions, and write the corresponding reactions.
2. b) If a piece of pure iron metal is immersed in a solution containing $\mathrm{Pb}^{2+}$ and $\mathrm{Cd}^{2+}$ ions, both at standard concentration $1.0\text{ M}$, reason quantitatively whether the iron will displace one, both or neither of these cations from the solution, calculating the standard emf and $\Delta G^\circ$ of the processes that are spontaneous. Use the thermodynamic model of standard potentials, without dissolved oxygen, complexation or passivation; the prediction does not give information about the actual rate.

The stability of the peroxide and the oxidation of the $\mathrm{Sn}^{2+}$ cation in acidic medium are studied at $25\text{ }^\circ\mathrm{C}$. Two reagents are available: potassium permanganate ($\mathrm{KMnO_4}$) and hydrogen peroxide ($\mathrm{H_2O_2}$). The standard reduction potentials are known:

$E^\circ(\mathrm{Sn}^{4+}/\mathrm{Sn}^{2+}) = +0.15\text{ V}$; $E^\circ(\mathrm{MnO_4^-}/\mathrm{Mn}^{2+}) = +1.51\text{ V}$; $E^\circ(\mathrm{O_2}/\mathrm{H_2O_2}) = +0.68\text{ V}$; $E^\circ(\mathrm{H_2O_2}/\mathrm{H_2O}) = +1.78\text{ V}$. Data: $F = 96485\text{ C}\times\text{mol}^{-1}$.

1. a) Show, with reasoning, using the values of $E^\circ$ and $\Delta G^\circ$, whether $\mathrm{H_2O_2}$ is thermodynamically stable with respect to disproportionation into water and oxygen under standard conditions at $25\text{ }^\circ\mathrm{C}$.
2. b) Justify whether the $\mathrm{Sn}^{2+}$ ion can be oxidised to $\mathrm{Sn}^{4+}$ by $\mathrm{MnO_4^-}$ in acidic medium, and determine the minimum volume, in $\text{mL}$, of $\mathrm{KMnO_4}\text{ }0.020\text{ M}$ solution needed to completely oxidise $25.0\text{ mL}$ of $\mathrm{Sn}^{2+}\text{ }0.050\text{ M}$. For the titration in b), assume quantitative reduction of permanganate to manganese(II), excess sulfuric acid and no side reactions.