Problem 66
A sample of iron ore weighing \(0.2792 \mathrm{~g}\) was dissolved in an excess of a dilute acid solution. All the iron was first converted to Fe(II) ions. The solution then required \(23.30 \mathrm{~mL}\) of \(0.0194 \mathrm{M} \mathrm{KMnO}_{4}\) for oxidation to Fe(III) ions. Calculate the percent by mass of iron in the ore.
Problem 67
The concentration of a hydrogen peroxide solution can be conveniently determined by titration against a standardized potassium permanganate solution in an acidic medium according to the following unbalanced equation: $$\mathrm{MnO}_{4}^{-}+\mathrm{H}_{2} \mathrm{O}_{2} \longrightarrow \mathrm{O}_{2}+\mathrm{Mn}^{2+}$$ (a) Balance this equation. (b) If \(36.44 \mathrm{~mL}\) of a 0.01652 \(M \mathrm{KMnO}_{4}\) solution is required to completely oxidize \(25.00 \mathrm{~mL}\) of an \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution, calculate the molarity of the \(\mathrm{H}_{2} \mathrm{O}_{2}\) solution.
Problem 69
Based on the following standard reduction potentials: $$\begin{aligned}\mathrm{Fe}^{2+}(a q)+2 e^{-} & \longrightarrow \mathrm{Fe}(s) & & E_{1}^{\circ}=-0.44 \mathrm{~V} \\ \mathrm{Fe}^{3+}(a q)+e^{-} \longrightarrow \mathrm{Fe}^{2+}(a q) & E_{2}^{\circ} &=0.77 \mathrm{~V} \end{aligned}$$ calculate the standard reduction potential for the halfreaction:$$\mathrm{Fe}^{3+}(a q)+3 e^{-} \longrightarrow \mathrm{Fe}(s) \quad E_{3}^{\circ}=?$$
Problem 71
From the following information, calculate the solubility product of \(\mathrm{AgBr}\) : $$ \begin{array}{ll} \mathrm{Ag}^{+}(a q)+e^{-} \longrightarrow \mathrm{Ag}(s) & E^{\circ}=0.80 \mathrm{~V} \\ \mathrm{AgBr}(s)+e^{-} \longrightarrow \mathrm{Ag}(s)+\mathrm{Br}^{-}(a q) & E^{\circ}=0.07 \mathrm{~V} \end{array} $$
Problem 72
Consider a galvanic cell composed of the SHE and a half-cell using the reaction \(\mathrm{Ag}^{+}(a q)+e^{-} \longrightarrow \mathrm{Ag}(s)\). (a) Calculate the standard cell potential. (b) What is the spontaneous cell reaction under standard-state conditions? (c) Calculate the cell potential when \(\left[\mathrm{H}^{+}\right]\) in the hydrogen electrode is changed to (i) \(1.0 \times 10^{-2} M\) and (ii) \(1.0 \times 10^{-5} M\), all other reagents being held at standard- state conditions. (d) Based on this cell arrangement, suggest a design for a pH meter.
Problem 73
A galvanic cell consists of a silver electrode in contact with \(346 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) solution and a magnesium electrode in contact with \(288 \mathrm{~mL}\) of \(0.100 \mathrm{M}\) \(\mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) solution. (a) Calculate \(E\) for the cell at \(25^{\circ} \mathrm{C}\). (b) A current is drawn from the cell until \(1.20 \mathrm{~g}\) of silver has been deposited at the silver electrode. Calculate \(E\) for the cell at this stage of operation.
Problem 75
Calculate the emf of the following concentration cell at $$ \begin{array}{l} 25^{\circ} \mathrm{C}: \\ \quad \mathrm{Cu}(s)\left|\mathrm{C} \mathrm{u}^{2+}(0.080 \mathrm{M}) \| \mathrm{Cu}^{2+}(1.2 M)\right| \mathrm{Cu}(s) \end{array} $$
Problem 76
The cathode reaction in the Leclanché cell is given by: $$ 2 \mathrm{MnO}_{2}(s)+\mathrm{Zn}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{ZnMn}_{2} \mathrm{O}_{4}(s) $$ If a Leclanché cell produces a current of \(0.0050 \mathrm{~A}\), calculate how many hours this current supply will last if there is initially \(4.0 \mathrm{~g}\) of \(\mathrm{MnO}_{2}\) present in the cell. Assume that there is an excess of \(\mathrm{Zn}^{2+}\) ions.The cathode reaction in the Leclanché cell is given by: $$2 \mathrm{MnO}_{2}(s)+\mathrm{Zn}^{2+}(a q)+2 e^{-} \longrightarrow \mathrm{ZnMn}_{2} \mathrm{O}_{4}(s)$$ If a Leclanché cell produces a current of \(0.0050 \mathrm{~A}\), calculate how many hours this current supply will last if there is initially \(4.0 \mathrm{~g}\) of \(\mathrm{MnO}_{2}\) present in the cell. Assume that there is an excess of \(\mathrm{Zn}^{2+}\) ions.
Problem 77
For a number of years, it was not clear whether mercury(I) ions existed in solution as \(\mathrm{Hg}^{+}\) or as \(\mathrm{Hg}_{2}^{2+}\). To distinguish between these two possibilities, we could set up the following system: $$ \operatorname{Hg}(l) \mid \text { soln } \mathrm{A} \| \operatorname{soln} \mathrm{B} \mid \operatorname{Hg}(l)$$ where soln A contained 0.263 g mercury(I) nitrate per liter and soln B contained \(2.63 \mathrm{~g}\) mercury(I) nitrate per liter. If the measured emf of such a cell is \(0.0289 \mathrm{~V}\) at \(18^{\circ} \mathrm{C},\) what can you deduce about the nature of the mercury(I) ions?
Problem 80
Describe an experiment that would enable you to determine which is the cathode and which is the anode in a galvanic cell using copper and zinc electrodes.
