Chapter 18

A galvanic cell is based on the following half-reactions: $$\begin{array}{ll}{\mathrm{Fe}}^{2+}+2{\mathrm{e}}^{-}⟶\mathrm{Fe}(s)& {\mathcal{E}}^{\circ }=-0.440\mathrm{V}\\ 2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}⟶{\mathrm{H}}_2(g)& {\mathcal{E}}^{\circ }=0.000\mathrm{V}\end{array}$$ where the iron compartment contains an iron electrode and $\left[{\mathrm{Fe}}^{2+}\right]=1.00\times {10}^{-3}M$ and the hydrogen compartment contains a platinum electrode, $P_{{\mathrm{H}}_2}=1.00\mathrm{atm},$ and a weak acid, HA, at an initial concentration of 1.00 $\mathrm{M}$ . If the observed cell potential is 0.333 $\mathrm{V}$ at ${25}^{\circ }\mathrm{C},$ calculate the $K_{\mathrm{a}}$ value for the weak acid HA.

The measurement of $\mathrm{pH}$ using a glass electrode obeys the Nernst equation. The typical response of a pH meter at ${25.00}^{\circ }\mathrm{C}$ is given by the equation $${\mathcal{E}}_{\text{ meas }}={\mathcal{E}}_{\text{ ref }}+0.05916\mathrm{pH}$$ where ${\mathcal{E}}_{\text{ ref }}$ contains the potential of the reference electrode and all other potentials that arise in the cell that are not related to the hydrogen ion concentration. Assume that ${\mathcal{E}}_{\mathrm{ref}}=0.250\mathrm{V}$ and that ${\mathcal{E}}_{\text{ meas }}=0.480\mathrm{V}$ a. What is the uncertainty in the values of $\mathrm{pH}$ and $\left[{\mathrm{H}}^{+}\right]$ if the nncertainty in the measured potential is $+1\mathrm{mV}$ $(\pm 0.001\mathrm{V})?$ b. To what precision must the potential be measured for the uncertainty in $\mathrm{pH}$ to be $\pm 0.02\mathrm{pH}$ unit?

You have a concentration cell with Cu electrodes and $\left[{\mathrm{Cu}}^{2+}\right]=1.00M(\text{ right side })$ and $1.0\times {10}^{-4}M(\text{ left side })$ a. Calculate the potential for this cell at ${25}^{\circ }\mathrm{C}$ b. The ${\mathrm{Cu}}^{2+}$ ion reacts with ${\mathrm{NH}}_3$ to form $\mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4^{2+}$ by the following equation: $$\begin{array}{rl}{\mathrm{Cu}}^{2+}(aq)+4{\mathrm{NH}}_3(aq)\rightleftharpoons \mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4^{2+}(aq)& \\ & K=1.0\times {10}^{13}\end{array}$$ Calculate the new cell potential after enough ${\mathrm{NH}}_3$ is added to the left cell compartment such that at equilibrium $\left[{\mathrm{NH}}_3\right]=2.0\mathrm{M}.$

A galvanic cell is based on the following half-reactions: $$\begin{array}{rl}{\mathrm{Ag}}^{+}+{\mathrm{e}}^{-}⟶\mathrm{Ag}(s)& {\mathcal{E}}^{\circ }=0.80\mathrm{V}\\ {\mathrm{Cu}}^{2+}+2{\mathrm{e}}^{-}⟶\mathrm{Cu}(s)& {\mathcal{E}}^{\circ }=0.34\mathrm{V}\end{array}$$ In this cell, the silver compartment contains a silver electrode and excess AgCl(s) $(K_{\mathrm{sp}}=1.6\times {10}^{-10}),$ and the copper compartment contains a copper electrode and $\left[{\mathrm{Cu}}^{2+}\right]=2.0\mathrm{M}$ . a. Calculate the potential for this cell at ${25}^{\circ }\mathrm{C}$ . b. Assuming 1.0 $\mathrm{L}$ of 2.0$M{\mathrm{Cu}}^{2+}$ in the copper compartment, calculate the moles of ${\mathrm{NH}}_3$ that would have to be added to give a cell potential of 0.52 $\mathrm{V}$ at ${25}^{\circ }\mathrm{C}$ (assume no volume change on addition of ${\mathrm{NH}}_3)$ . $${\mathrm{Cu}}^{2+}(aq)+4{\mathrm{NH}}_3(aq)\rightleftharpoons \mathrm{Cu}{\left({\mathrm{NH}}_3\right)}_4^{2+}(aq)K=1.0\times {10}^{13}$$

Given the following two standard reduction potentials, $$\begin{array}{ll}{\mathrm{M}}^{3+}+3{\mathrm{e}}^{-}⟶\mathrm{M}& {\mathcal{E}}^{\circ }=-0.10\mathrm{V}\\ {\mathrm{M}}^{2+}+2{\mathrm{e}}^{-}⟶\mathrm{M}& {\mathcal{E}}^{\circ }=-0.50\mathrm{V}\end{array}$$ solve for the standard reduction potential of the half-reaction $${\mathrm{M}}^{3+}+{\mathrm{e}}^{-}⟶{\mathrm{M}}^{2+}$$ (Hint: You must use the extensive property $\mathrm{\Delta }{G}^{\circ }$ to determine the standard reduction potential.)

A chemist wishes to determine the concentration of ${\mathrm{CrO}}_4^{2-}$ electrochemically. A cell is constructed consisting of a saturated calomel electrode (SCE; see Exercise 111$)$ and a silver wire coated with ${\mathrm{Ag}}_2{\mathrm{CrO}}_4$ . The ${\mathcal{E}}^{\circ }$ value for the following half-reaction is 0.446 $\mathrm{V}$ relative to the standard hydrogen electrode: $${\mathrm{Ag}}_2{\mathrm{CrO}}_4+2{\mathrm{e}}^{-}⟶2\mathrm{Ag}+{\mathrm{CrO}}_4^{2-}$$ a. Calculate ${\mathcal{E}}_{\text{ cell }\text{ and }}\mathrm{\Delta }G$ at ${25}^{\circ }\mathrm{C}$ for the cell reaction when $\left[{\mathrm{CrO}}_4^{2-}\right]=1.00\mathrm{mol}/\mathrm{L}$ . b. Write the Nernst equation for the cell. Assume that the SCE concentrations are constant. c. If the coated silver wire is placed in a solution (at ${25}^{\circ }\mathrm{C})$ in which $\left[{\mathrm{CrO}}_4^{2-}\right]=1.00\times {10}^{-5}M,$ what is the expected cell potential? d. The measured cell potential at ${25}^{\circ }\mathrm{C}$ is 0.504 $\mathrm{V}$ when the coated wire is dipped into a solution of unknown $\left[{\mathrm{CrO}}_4^{2-}\right].$ What is $\left[{\mathrm{CrO}}_4^{2-}\right]$ for this solution? e. Using data from this problem and from Table $18.1,$ calculate the solubility product $\left(K_{\mathrm{sp}}\right)$ for ${\mathrm{Ag}}_2{\mathrm{CrO}}_4$.

When copper reacts with nitric acid, a mixture of $\mathrm{NO}(g)$ and ${\mathrm{NO}}_2(g)$ is evolved. The volume ratio of the two product gases depends on the concentration of the nitric acid according to the equilibrium $$2{\mathrm{H}}^{+}(aq)+2{\mathrm{NO}}_3^{-}(aq)+\mathrm{NO}(g)\rightleftharpoons 3{\mathrm{NO}}_2(g)+{\mathrm{H}}_2\mathrm{O}(l)$$ Consider the following standard reduction potentials at ${25}^{\circ }\mathrm{C}:$ $$3{\mathrm{e}}^{-}+4{\mathrm{H}}^{+}(aq)+{\mathrm{NO}}_3^{-}(aq)⟶\mathrm{NO}(g)+2{\mathrm{H}}_2\mathrm{O}(l)$$ $${\mathcal{E}}^{\circ }=0.957\mathrm{V}$$ $${\mathrm{e}}^{-}+2{\mathrm{H}}^{+}(aq)+{\mathrm{NO}}_3^{-}(aq)⟶{\mathrm{NO}}_2(g)+2{\mathrm{H}}_2\mathrm{O}(l)$$ $${\mathcal{E}}^{\circ }=0.775\mathrm{V}$$ a. Calculate the equilibrium constant for the above reaction. b. What concentration of nitric acid will produce a NO and NO ${}_2$ mixture with only 0.20$\mathrm{\%}{\mathrm{NO}}_2$ (by moles) at ${25}^{\circ }\mathrm{C}$ and 1.00 atm? Assume that no other gases are present and that the change in acid concentration can be neglected.

The following standard reduction potentials have been determined for the aqueous chemistry of indium: $${\mathrm{In}}^{3+}(aq)+2{\mathrm{e}}^{-}⟶{\mathrm{In}}^{+}(aq){\mathcal{E}}^{\circ }=-0.444\mathrm{V}$$ $${\mathrm{In}}^{+}(aq)+{\mathrm{e}}^{-}⟶\mathrm{In}(s){\mathcal{E}}^{\circ }=-0.126\mathrm{V}$$ a. What is the equilibrium constant for the disproportionation reaction, where a species is both oxidized and reduced, shown below? $$3{\ln }^{+}(aq)⟶2\mathrm{In}(s)+{\mathrm{In}}^{3+}(aq)$$ b. What is $\mathrm{\Delta }{G}_i^{\circ }$ for ${\mathrm{In}}^{+}(aq)$ if $\mathrm{\Delta }{G}_f^{\circ }=-97.9\mathrm{kJ}/\mathrm{mol}$ for ${\mathrm{In}}^{3+}(aq)?$

An electrochemical cell is set up using the following unbalanced reaction: $${\mathrm{M}}^{a+}(aq)+\mathrm{N}(s)⟶{\mathrm{N}}^{2+}(aq)+\mathrm{M}(s)$$ The standard reduction potentials are: $${\mathrm{M}}^{a+}+a{\mathrm{e}}^{-}⟶\mathrm{M}{\mathcal{E}}^{\circ }=0.400\mathrm{V}$$ $${\mathrm{N}}^{2+}+2{\mathrm{e}}^{-}⟶\mathrm{N}{\mathcal{E}}^{\circ }=0.240\mathrm{V}$$ The cell contains 0.10$M{\mathrm{N}}^{2+}$ 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 $w_{\text{ max }}$ for this electrochemical cell.

Three electrochemical cells were connected in series so that the same quantity of electrical current passes through all three cells. In the first cell, 1.15 g chromium metal was deposited from a chromium (III) nitrate solution. In the second cell, 3.15 $\mathrm{g}$ osmium was deposited from a solution made of ${\mathrm{Os}}^{n+}$ and nitrate ions. What is the name of the salt? In the third cell, the electrical charge passed through a solution containing ${\mathrm{X}}^{2+}$ ions caused deposition of 2.11 $\mathrm{g}$ metallic $\mathrm{X}$ . What is the electron configuration of $\mathrm{X}?$