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Where t is the time in seconds, n the number of moles of electrons, and F is the Faraday constant.
Moles of electrons can be used in stoichiometry problems. The time required to deposit a specified amount of metal might also be requested, as in the second of the following examples.
From the problem, the solution contains AgNO _{3} , so the reaction at the cathode involves 1 mole of electrons for each mole of silver
The atomic mass of silver is 107.9 g/mol, so
Check your answer: From the stoichiometry, 1 mole of electrons would produce 1 mole of silver. Less than one-half a mole of electrons was involved and less than one-half a mole of silver was produced.
${\text{Al}}^{\mathrm{3+}}(aq)+3\phantom{\rule{0.2em}{0ex}}{\text{e}}^{\text{\u2212}}\phantom{\rule{0.2em}{0ex}}\u27f6\phantom{\rule{0.2em}{0ex}}\text{Al}(s);$ 7.77 mol Al = 210.0 g Al.
Solving in steps, and taking care with the units, the volume of Cr required is
Cubic centimeters were used because they match the volume unit used for the density. The amount of Cr is then
Since the solution contains chromium(III) ions, 3 moles of electrons are required per mole of Cr. The total charge is then
The time required is then
Check your answer: In a long problem like this, a single check is probably not enough. Each of the steps gives a reasonable number, so things are probably correct. Pay careful attention to unit conversions and the stoichiometry.
231 g Zn required 446 minutes.
Using electricity to force a nonspontaneous process to occur is electrolysis. Electrolytic cells are electrochemical cells with negative cell potentials (meaning a positive Gibbs free energy), and so are nonspontaneous. Electrolysis can occur in electrolytic cells by introducing a power supply, which supplies the energy to force the electrons to flow in the nonspontaneous direction. Electrolysis is done in solutions, which contain enough ions so current can flow. If the solution contains only one material, like the electrolysis of molten sodium chloride, it is a simple matter to determine what is oxidized and what is reduced. In more complicated systems, like the electrolysis of aqueous sodium chloride, more than one species can be oxidized or reduced and the standard reduction potentials are used to determine the most likely oxidation (the half-reaction with the largest [most positive] standard reduction potential) and reduction (the half-reaction with the smallest [least positive]standard reduction potential). Sometimes unexpected half-reactions occur because of overpotential. Overpotential is the difference between the theoretical half-reaction reduction potential and the actual voltage required. When present, the applied potential must be increased, making it possible for a different reaction to occur in the electrolytic cell. The total charge, Q , that passes through an electrolytic cell can be expressed as the current ( I ) multiplied by time ( Q = It ) or as the moles of electrons ( n ) multiplied by Faraday’s constant ( Q = nF ). These relationships can be used to determine things like the amount of material used or generated during electrolysis, how long the reaction must proceed, or what value of the current is required.
Identify the reaction at the anode, reaction at the cathode, the overall reaction, and the approximate potential required for the electrolysis of the following molten salts. Assume standard states and that the standard reduction potentials in Appendix L are the same as those at each of the melting points. Assume the efficiency is 100%.
(a) CaCl _{2}
(b) LiH
(c) AlCl _{3}
(d) CrBr _{3}
What mass of each product is produced in each of the electrolytic cells of the previous problem if a total charge of 3.33 $\times $ 10 ^{5} C passes through each cell? Assume the voltage is sufficient to perform the reduction.
(a) $\begin{array}{}\\ \text{mass Ca}=\text{69.1 g}\\ {\text{mass Cl}}_{2}=\text{122 g}\end{array};$ (b) $\begin{array}{l}\text{mass Li}=\text{23.9 g}\\ {\text{mass H}}_{2}=\text{3.48 g}\end{array};$ (c) $\begin{array}{l}\text{mass Al}=\text{31.0 g}\\ {\text{mass Cl}}_{2}=\text{122 g}\end{array};$ (d) $\begin{array}{l}\text{mass Cr}=\text{59.8 g}\\ {\text{mass Br}}_{2}=\text{276 g}\end{array}$
How long would it take to reduce 1 mole of each of the following ions using the current indicated? Assume the voltage is sufficient to perform the reduction.
(a) Al ^{3+} , 1.234 A
(b) Ca ^{2+} , 22.2 A
(c) Cr ^{5+} , 37.45 A
(d) Au ^{3+} , 3.57 A
A current of 2.345 A passes through the cell shown in [link] for 45 minutes. What is the volume of the hydrogen collected at room temperature if the pressure is exactly 1 atm? Assume the voltage is sufficient to perform the reduction. (Hint: Is hydrogen the only gas present above the water?)
0.79 L
An irregularly shaped metal part made from a particular alloy was galvanized with zinc using a Zn(NO _{3} ) _{2} solution. When a current of 2.599 A was used, it took exactly 1 hour to deposit a 0.01123-mm layer of zinc on the part. What was the total surface area of the part? The density of zinc is 7.140 g/cm ^{3} . Assume the efficiency is 100%.
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