L5 - Quantitative Aspects of Electrolysis

objectives

Understandings

Current, duration of electrolysis and charge on the ion affect the amount of product formed at the electrodes during electrolysis.

Applications and Skills

Determination of the relative amounts of products formed during electrolytic processes.

Q = It

The amount of current that is allowed to flow in an electrolytic cell is related to the number of moles of electrons.
The number of moles of electrons can be related to the reactants and products using stoichiometry.
Recall that the SI unit for current (I) is the ampere (A), which is the equivalent of 1 coulomb per second (1 A = 1 CsCs).
The total charge (Q, in coulombs) is given by

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.

Example 1: Converting Current to Moles of Electrons

In one process used for electroplating silver, a current of 10.23 A was passed through an electrolytic cell for exactly 1 hour. How many moles of electrons passed through the cell? What mass of silver was deposited at the cathode from the silver nitrate solution?

Solution

Faraday’s constant can be used to convert the charge (Q) into moles of electrons (n). The charge is the current (I) multiplied by the time

From the problem, the solution contains AgNO3, 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 learning

Aluminum metal can be made from aluminum ions by electrolysis. What is the half-reaction at the cathode? What mass of aluminum metal would be recovered if a current of 2.50 × 103 A passed through the solution for 15.0 minutes? Assume the yield is 100%.

Al³⁺(aq)+3e⁻⟶Al(s)Al3+(aq)+3e−⟶Al(s); 7.77 mol Al = 210.0 g Al.

Example 2: Time Required for Deposition

In one application, a 0.010-mm layer of chromium must be deposited on a part with a total surface area of 3.3 m2 from a solution of containing chromium(III) ions. How long would it take to deposit the layer of chromium if the current was 33.46 A? The density of chromium (metal) is 7.19 g/cm3.

Solution

This problem brings in a number of topics covered earlier. An outline of what needs to be done is:

If the total charge can be determined, the time required is just the charge divided by the current
The total charge can be obtained from the amount of Cr needed and the stoichiometry
The amount of Cr can be obtained using the density and the volume Cr required
The volume Cr required is the thickness times the area

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 Learning

What mass of zinc is required to galvanize the top of a 3.00 m × 5.50 m sheet of iron to a thickness of 0.100 mm of zinc? If the zinc comes from a solution of Zn(NO3)2 and the current is 25.5 A, how long will it take to galvanize the top of the iron? The density of zinc is 7.140 g/cm3.

231 g Zn required 446 minutes.

Additional Practice

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) CaCl2

(b) LiH

(d) CrBr3

2. What mass of each product is produced in each of the electrolytic cells of the previous problem if a total charge of 3.33 × 105 C passes through each cell? Assume the voltage is sufficient to perform the reduction.

3. 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) Al3+, 1.234 A

(b) Ca2+, 22.2 A

(d) Au3+, 3.57 A

4. A current of 2.345 A passes through the cell shown in Figure 2 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?)

5. An irregularly shaped metal part made from a particular alloy was galvanized with zinc using a Zn(NO3)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/cm3. Assume the efficiency is 100%.

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