Problem 101
The simplest way to write the reaction for discharge in a lithium-ion battery is Li(on carbon)(s) \(+\mathrm{CoO}_{2}(\mathrm{s}) \rightarrow 6 \mathrm{C}(\mathrm{s})+\mathrm{LiCoO}_{2}(\mathrm{s})\) (a) What are the oxidation numbers for cobalt in the two substances in the battery? (b) In such a battery, what reaction occurs at the cathode? At the anode? (c) An electrolyte is needed for ion conduction within the battery. From what you know about lithium chemistry, can the electrolyte in the battery be dissolved in water?
Problem 104
Consider an electrochemical cell based on the halfreactions \(\mathrm{Ni}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-} \rightarrow \mathrm{Ni}(\mathrm{s})\) and \(\mathrm{Cd}^{2+}(\mathrm{aq})+\) \(2 e^{-} \rightarrow C d(s)\) (a) Diagram the cell, and label each of the com. ponents (including the anode, cathode, and salt bridge). (b) Use the equations for the half-reactions to write a balanced, net ionic equation for the overall cell reaction. (c) What is the polarity of each electrode? (d) What is the value of \(E^{\circ}\) cell? (e) In which direction do electrons flow in the external circuit? (f) Assume that a salt bridge containing \(\mathrm{NaNO}_{3}\) connects the two half-cells. In which direction do the \(\mathrm{Na}^{+}(\text {aq })\) ions move? In which direction do the \(\mathrm{NO}_{3}^{-}\) (aq) ions move? (g) Calculate the equilibrium constant for the reaction. (h) If the concentration of \(\mathrm{Cd}^{2+}\) is reduced to \(0.010 \mathrm{M}\) and \(\left[\mathrm{Ni}^{2+}\right]=1.0 \mathrm{M},\) what is the value of \(E_{\text {cell }}\) ? Is the net reaction still the reaction given in part (b)? (i) If 0.050 A is drawn from the battery, how long can it last if you begin with 1.0 L of each of the solutions and each was initially \(1.0 \mathrm{M}\) in dissolved species? Each electrode weighs \(50.0 \mathrm{g}\) in the beginning.
Problem 106
An old method of measuring the current flowing in a circuit was to use a "silver coulometer." The current passed first through a solution of \(\mathrm{Ag}^{+}(\mathrm{aq})\) and then into another solution containing an electroactive species. The amount of silver metal deposited at the cathode was weighed. From the mass of silver, the number of atoms of silver was calculated. Since the reduction of a silver ion requires one electron, this value equaled the number of electrons passing through the circuit. If the time was noted, the average current could be calculated. If, in such an experiment, 0.052 g of Ag is deposited during \(450 \mathrm{s},\) what was the current flowing in the circuit?
Problem 108
A Four metals, \(A, B, C,\) and \(D\), exhibit the following properties: (a) Only A and C react with L.O M hydrochloric acid to give \(\mathrm{H}_{2}(\mathrm{g})\) (b) When \(C\) is added to solutions of the ions of the other metals, metallic \(\mathrm{B}, \mathrm{D},\) and \(\mathrm{A}\) are formed. (c) Metal D reduces \(\mathrm{B}^{n+}\) to give metallic \(\mathrm{B}\) and \(\mathbf{D}^{n+1}\) Based on this information, arrange the four metals in order of increasing ability to act as reducing agents.
Problem 110
A The amount of oxygen, \(\mathrm{O}_{2}\), dissolved in a water sample at \(25^{\circ} \mathrm{C}\) can be determined by titration. The first step is to add solutions of \(\mathrm{MnSO}_{4}\) and NaOH to the water to convert the dissolved oxygen to \(\mathrm{MnO}_{2}\). A solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \(\mathrm{KI}\) is then added to convert the \(\mathrm{MnO}_{2}\) to \(\mathrm{Mn}^{2+},\) and the iodide ion is converted to \(\mathrm{I}_{2}\). The \(\mathrm{I}_{2}\) is then titrated with standardized \(\mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3-}\) (a) Balance the equation for the reaction of \(\mathrm{Mn}^{2+}\) ions with \(\mathrm{O}_{2}\) in basic solution. (b) Balance the equation for the reaction of \(\mathrm{MnO}_{2}\) with \(\mathbf{I}^{-}\) in acid solution. (c) Balance the equation for the reaction of \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\) with \(\mathrm{I}_{2}\) (d) Calculate the amount of \(\mathbf{O}_{2}\) in \(25.0 \mathrm{mL}\) of water if the titration requires \(2.45 \mathrm{mL}\) of \(0.0112 \mathrm{M} \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) solution.
Problem 111
Fluorinated organic compounds are used as herbicides, flame retardants, and fire-extinguishing agents, among other things. A reaction such as $$ \mathrm{CH}_{3} \mathrm{SO}_{2} \mathrm{F}+3 \mathrm{HF} \rightarrow \mathrm{CF}_{3} \mathrm{SO}_{2} \mathrm{F}+3 \mathrm{H}_{2} $$ is carried out electrochemically in liquid HF as the solvent. (a) If you electrolyze \(150 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{SO}_{2} \mathrm{F}\), what mass of HF is required, and what mass of each product can be isolated? (b) Is \(\mathrm{H}_{2}\) produced at the anode or the cathode of the electrolysis cell? (c) A typical electrolysis cell operates at \(8.0 \mathrm{V}\) and 250 A. How many kilowatt-hours of energy does one such cell consume in 24 hours?
Problem 113
A hydrogen-oxygen fuel cell operates on the simple reaction $$ \mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\ell) $$ If the cell is designed to produce 1.5 A of current and if the hydrogen is contained in a 1.0 -L. tank at 200 atm pressure at \(25^{\circ} \mathrm{C},\) how long can the fuel cell operate before the hydrogen runs out? (Assume there is an unlimited supply of \(\mathbf{O}_{2}\).)
Problem 114
A (a) Is it easier to reduce water in acid or base? To evaluate this, consider the half-reaction \(2 \mathrm{H}_{2} \mathrm{O}(\ell)+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{OH}^{-}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g})\) \(E^{*}=-0.83 \mathrm{V}\) (b) What is the reduction potential for water for solutions at \(\mathrm{pH}=7\) (neutral) and \(\mathrm{pH}=1\) (acid)? Comment on the value of \(E^{\circ}\) at \(\mathrm{pH}=1\)
Problem 115
A Living organisms derive energy from the oxidation of food, typified by glucose. $$ \mathrm{C}_{0} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq})+6 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 6 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) $$ Electrons in this redox process are transferred from glucose to oxygen in a series of at least 25 steps. It is instructive to calculate the total daily current flow in a typical organism and the rate of energy expenditure (power). (See T. P. Chirpich: Journal of Chemical Education, Vol. \(52,\) p. 99 1975.) (a) The molar enthalpy of combustion of glucose is \(-2800 \mathrm{kJ} / \mathrm{mol}\) -nan. If you are on a typical daily diet of 2400 Cal (kilocalories), what amount of glucose (in moles) must be consumed in a day if glucose is the only source of energy? What amount of \(\mathrm{O}_{2}\) must be consumed in the oxidation process? (b) How many moles of electrons must be supplied to reduce the amount of \(\mathrm{O}_{2}\) calculated in part (a)? (c) Based on the answer in part (b), calculate the current flowing, per second, in your body from the combustion of glucose. (d) If the average standard potential in the electron transport chain is \(1.0 \mathrm{V},\) what is the rate of energy expenditure in watts?
