Problem 45 - Chemistry and Chemical Reactivity

Question

Electrolysis of a solution of \(\mathrm{CuSO}_{4}(\mathrm{aq})\) to give copper metal is carried out using a current of 0.66 A. How long should electrolysis continue to produce 0.50 g of copper?

Step-by-Step Solution

Answer

Electrolysis should continue for approximately 38.36 minutes to produce 0.50 g of copper.

Step 1: Determine the number of moles of copper

First, find the number of moles of copper in 0.50 g. Use the molar mass of copper, which is approximately 63.55 g/mol. Calculate the number of moles using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). So, for copper, it is \( \frac{0.50 \text{ g}}{63.55 \text{ g/mol}} = 0.00787 \text{ moles} \).

Step 2: Use Faraday's Law of Electrolysis

Apply Faraday's Law, which states that the number of moles of electrons \( n \) transferred is equal to the product of current \( I \) (in amperes) and time \( t \) (in seconds) divided by the Faraday constant \( F \) (approximately 96485 C/mol). Accordingly, \( n = \frac{I \cdot t}{F} \). For copper, which requires 2 moles of electrons per mole of copper deposited, we calculate \( n = 2 \times 0.00787 = 0.01574 \text{ moles of electrons} \).

Step 3: Calculate the time required for electrolysis

Rearrange the formula from Step 2 to solve for time \( t \): \( t = \frac{n \cdot F}{I} \). Substitute the values: \( t = \frac{0.01574 \text{ moles} \times 96485 \text{ C/mol}}{0.66 \text{ A}} \). Compute this to find the time in seconds.\( t \approx 2301.6 \text{ seconds} \).

Step 4: Convert time to appropriate unit

Convert the time from seconds to minutes by dividing by 60: \( \frac{2301.6}{60} \approx 38.36 \text{ minutes} \).

Key Concepts

Faraday's Law

Faraday's Law of Electrolysis is a fundamental principle that connects the quantity of electric charge passed through an electrolyte to the amount of substance that undergoes a chemical change at the electrode. The key here is understanding how electrons moving through the solution correspond to the deposition or dissolution of material.
Faraday's Law states that the mass of substance transformed during electrolysis is proportional to the electrical charge passed through the electrolyte. The direct relationship can be expressed as:

• The number of moles of electrons, \( n \), transferred is equal to the current \( I \) (in amperes) multiplied by the time \( t \) (in seconds), divided by the Faraday constant \( F \), which is approximately 96485 C/mol.
• This equation is represented by \( n = \frac{I \cdot t}{F} \).

By using the law, and knowing the stoichiometry of the reaction involved, we can accurately determine how much material is deposited or dissolved during electrolysis.

Copper Deposition

Copper deposition is an example of an electrochemical process that can be described by Faraday's Law of Electrolysis. It involves the transformation of copper ions in a solution into solid copper metal.
Here's how the process works:

• Copper ions (\mathrm{Cu}^{2+}) in the solution gain electrons and are deposited as solid copper (Cu) on the cathode during electrolysis.
• Each copper ion requires two electrons to be reduced from \( \mathrm{Cu}^{2+} \) to \( \mathrm{Cu} \).
• This means that for every mole of copper metal deposited, two moles of electrons are needed.

Understanding this chemical change is crucial for calculating the amount of copper that will be deposited given a certain amount of electric charge, which is directly dependent on the amount of time the current is applied during the electrolysis.

Electrochemical Calculations

When conducting electrolysis and expecting a specific amount of a substance to be produced, electrochemical calculations become vital. These calculations enable precise prediction based on known physical constants and measurements.
For copper deposition, follow these steps:

• Calculate the moles of copper to be deposited using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \).
• Recognize that copper requires two moles of electrons for each mole to be deposited due to its 2+ charge.
• Use Faraday's Law to find the total charge needed: multiply the required moles of electrons by the Faraday constant.
• Solve for the time of electrolysis using the rearranged formula \( t = \frac{n \cdot F}{I} \), where \( n \) is the moles of electrons, \( F \) is the Faraday constant, and \( I \) is the current.

By following these calculations, you can determine not only how long electrolysis needs to continue to achieve your desired deposition of copper but also ensure your process is efficient and accurate.