Aluminum, titanium, and several other metals can be col-ored by an electrochemical process called anodizing. Anodizing oxidizes a metal anode to yield a porous metal oxide coating that can incorporate dye molecules to give brilliant colors. In the oxidation of aluminum, for instance, the electrode reactions are The thickness of the aluminum oxide coating that forms on the anode can be controlled by varying the current flow during the electrolysis. How many minutes are required to produce a 0.0100-mm thick coating of Al2O3 (density 3.97 g/cm^3) on a square piece of aluminum metal 10.0 cm on an edge if the current passed through the piece is 0.600 A?

Verified step by step guidance

1. Calculate the volume of the aluminum oxide coating using the formula: Volume = Area \times Thickness. The area of the square piece is 10.0 \text{ cm} \times 10.0 \text{ cm}.
2. Convert the thickness from millimeters to centimeters to match the units of area.
3. Use the density of \( \text{Al}_2\text{O}_3 \) to find the mass of the coating: Mass = Volume \times Density.
4. Determine the number of moles of \( \text{Al}_2\text{O}_3 \) using its molar mass.
5. Use Faraday's laws of electrolysis to calculate the time required. First, find the total charge needed using the moles of \( \text{Al}_2\text{O}_3 \) and the stoichiometry of the reaction, then use the current to find the time in seconds and convert to minutes.

Key Concepts

Anodizing Process

Anodizing is an electrochemical process that enhances the natural oxide layer on metals, particularly aluminum. During anodizing, the metal acts as an anode in an electrolytic cell, where it is oxidized to form a protective and decorative oxide layer. This process not only increases corrosion resistance but also allows for the incorporation of dyes, resulting in vibrant colors.

Electrolysis and Faraday's Laws

Electrolysis is a chemical process that uses electrical energy to drive a non-spontaneous reaction. Faraday's laws of electrolysis relate the amount of substance transformed at an electrode to the quantity of electricity passed through the electrolyte. Specifically, the first law states that the mass of a substance altered at an electrode is proportional to the total electric charge passed, which is crucial for calculating the time required for anodizing.

Calculating Coating Thickness

The thickness of the anodized coating can be calculated using the density of the oxide and the volume produced during electrolysis. The volume is determined by the charge passed through the system, which can be calculated from the current and time. By knowing the desired thickness and the dimensions of the aluminum piece, one can derive the time needed to achieve the specified coating thickness using the relationship between mass, volume, and density.