Textbook Question
Silver can be electroplated at the cathode of an electrolysis cell by the half-reaction: Ag+(aq) + e– → Ag(s) What mass of silver would plate onto the cathode if a current of 6.8 A flowed through the cell for 72 min?
Ch.20 - Electrochemistry
Chapter 20, Problem 106
What mass of aluminum metal can be produced per hour in the electrolysis of a molten aluminum salt using a current of 25 A?
Verified step by step guidance1
Identify the relevant electrochemical reaction: The reduction of aluminum ions to aluminum metal is represented by the half-reaction: \( \text{Al}^{3+} + 3e^- \rightarrow \text{Al} \).
Determine the number of moles of electrons required: From the half-reaction, 3 moles of electrons are needed to produce 1 mole of aluminum.
Use Faraday's Law of Electrolysis: The amount of substance produced at an electrode is directly proportional to the quantity of electricity passed through the electrolyte. The formula is \( n = \frac{I \cdot t}{n_e \cdot F} \), where \( n \) is the number of moles of aluminum, \( I \) is the current in amperes, \( t \) is the time in seconds, \( n_e \) is the number of moles of electrons, and \( F \) is Faraday's constant (approximately 96485 C/mol).
Calculate the time in seconds for one hour: Since the problem asks for the mass produced per hour, convert 1 hour into seconds (1 hour = 3600 seconds).
Calculate the mass of aluminum produced: Use the molar mass of aluminum (approximately 26.98 g/mol) to convert the moles of aluminum to grams.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electrolysis
Electrolysis is a chemical process that uses electrical energy to drive a non-spontaneous reaction. In the context of aluminum production, it involves passing an electric current through molten aluminum salts, causing the aluminum ions to migrate to the cathode where they are reduced to form aluminum metal. This process is essential for extracting metals from their ores.
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01:21
The Electrolytic Cell
Faraday's Laws of Electrolysis
Faraday's Laws of Electrolysis quantify the relationship between the amount of substance produced at an electrode and the electric charge passed through the electrolyte. The first law states that the mass of a substance altered at an electrode is directly proportional to the quantity of electricity that passes through the electrolyte. This principle is crucial for calculating the mass of aluminum produced based on the current and time.
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01:40Faraday's Constant in Electrochemistry
Current and Charge
Electric current, measured in amperes (A), is the flow of electric charge. In electrolysis, the total charge (in coulombs) can be calculated by multiplying the current by the time (in seconds). Understanding this relationship is vital for determining how much aluminum can be produced in a given time frame, as it directly influences the electrolysis process.
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01:53Formal Charge
Related Practice
Textbook Question
A major source of sodium metal is the electrolysis of molten sodium chloride. What magnitude of current produces 1.0 kg of sodium metal in 1 hour?
Textbook Question
Consider the reaction shown here occurring at 25°C. Cr(s) + Cd2+(aq) → Cr2+(aq) + Cd(s) Determine E°cell, K, and ∆G°rxn for the reaction and complete the table.
[Cd2+] [Cr2+] Q Ecell 𝚫Grxn
1.00 1.00
1.00 1.00 × 10-5
1.00 × 10-5 1.00
4.18 × 10-4 1.00