(a) A Cr³⁺(aq) solution is electrolyzed, using a current of 7.60 A. What mass of Cr(s) is plated out after 2.00 days?

Verified step by step guidance

1. Identify the relevant electrochemical reaction: \( \text{Cr}^{3+} + 3e^- \rightarrow \text{Cr(s)} \).
2. Calculate the total charge passed through the solution using the formula \( Q = I \times t \), where \( I \) is the current (7.60 A) and \( t \) is the time in seconds (2.00 days converted to seconds).
3. Determine the number of moles of electrons transferred using Faraday's constant (\( F = 96485 \text{ C/mol} \)) with the formula \( \text{moles of } e^- = \frac{Q}{F} \).
4. Use the stoichiometry of the reaction to find the moles of chromium plated out. Since 3 moles of electrons are required to plate out 1 mole of Cr, divide the moles of electrons by 3.
5. Calculate the mass of chromium using the molar mass of chromium (\( \text{Cr} = 51.9961 \text{ g/mol} \)) and the moles of chromium obtained in the previous step.

Key Concepts

Electrolysis

Electrolysis is a chemical process that uses electrical energy to drive a non-spontaneous reaction. In this process, an electric current is passed through an electrolyte solution, causing the ions to migrate towards the electrodes, where they undergo reduction or oxidation. For the Cr3+ ions in the solution, electrolysis will result in the deposition of chromium metal at the cathode.

Faraday's Laws of Electrolysis

Faraday's Laws of Electrolysis quantify the relationship between the amount of substance transformed at an electrode and the quantity of electric charge passed through the electrolyte. The first law states that the mass of a substance deposited or liberated at an electrode is directly proportional to the total electric charge passed. This relationship is crucial for calculating the mass of chromium plated out in the given electrolysis scenario.

Current and Time Relationship

The relationship between current, time, and charge is fundamental in electrolysis calculations. The total charge (Q) can be calculated using the formula Q = I × t, where I is the current in amperes and t is the time in seconds. This charge is then used in conjunction with Faraday's laws to determine the mass of the substance deposited, making it essential for solving the problem of how much chromium is plated out.