Question

In a certain electrolysis experiment involving \(\mathrm{Al}^{3+}\) ions, \(60.2 \mathrm{~g}\) of \(\mathrm{Al}\) is recovered when a current of \(0.352 \mathrm{~A}\) is used. How many minutes did the electrolysis last?

Short answer

The electrolysis lasted approximately 30,584 minutes.

Step-by-step solution

Calculate Moles of Aluminum

First, calculate the number of moles of aluminum, which is given by the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of aluminum (\( \mathrm{Al} \)) is approximately \( 26.98 \mathrm{~g/mol} \). Therefore, the moles of aluminum recovered is \( \frac{60.2}{26.98} \approx 2.231 \mathrm{~mol} \).

Find Total Charge Required

Use Faraday's law of electrolysis, which states that the charge (\( Q \)) required is given by \( Q = n \times F \times z \), where \( n \) is the moles of substance, \( F \) is Faraday's constant \( (96485 \mathrm{~C/mol}) \), and \( z \) is the charge number of the ion (which is 3 for \( \mathrm{Al}^{3+} \) ions). Thus, \( Q = 2.231 \times 96485 \times 3 \approx 645882 \mathrm{~C} \).

Determine Time in Seconds

Use the relationship between current (\( I \)), charge (\( Q \)), and time (\( t \)) given by \( Q = I \times t \). Rearrange this to find time: \( t = \frac{Q}{I} \). Substituting the values, \( t = \frac{645882}{0.352} \approx 1835062 \mathrm{~s} \).

Convert Seconds to Minutes

Since there are 60 seconds in a minute, convert the time from seconds to minutes: \( \frac{1835062}{60} \approx 30584 \mathrm{~minutes} \).

Key concepts

Faraday's law

Faraday's law is pivotal in understanding electrolysis calculations. It provides a relationship between the electric charge and the amount of substance transformed during electrolysis. The key equation is:

• \( Q = n \times F \times z \)

Here:

• \( Q \) is the total charge in Coulombs (C)
• \( n \) stands for the moles of the substance involved in the reaction
• \( F \) is Faraday's constant, approximately \( 96485 C/mol \) — it represents the charge of one mole of electrons
• \( z \) is the charge number of the ion (3 for \( \text{Al}^{3+} \) ions)

The law ties together charge, moles, and ion charge to determine the charge needed for a reaction. In our case, we used it to calculate the charge required to recover aluminum in the reaction.

Current and charge

In electrolysis, understanding the relationship between current and charge is crucial. Current (\( I \)) is defined as the rate of flow of charge per unit of time, expressed in amperes (A). The key relationship here is:

• \( Q = I \times t \)

Where:

• \( Q \) is charge in Coulombs (C)
• \( I \) is current in amperes, which in this case is \( 0.352 A \)
• \( t \) is time in seconds

This formula helps us understand how much electric charge passes through the circuit over a period of time. By rearranging the formula, we can solve for time if the charge and current are known. This is how we determined the total time of the electrolysis process.

Moles of aluminum

Calculating moles is essential in chemical reactions to determine how much of a substance is involved. For aluminum in our exercise, the formula used is:

• \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \)

Given:

• The mass of aluminum recovered is \( 60.2 g \)
• The molar mass of aluminum is approximately \( 26.98 g/mol \)

Substituting these values gives us:

• \( \text{moles of Al} \approx \frac{60.2}{26.98} \approx 2.231 \text{ moles} \)

This calculation helps us understand the quantity of aluminum obtained, which is crucial for applying Faraday's law to find the required charge for the process.

Time conversion

After calculating the time in seconds for an electrolysis reaction, it's often necessary to convert this figure into minutes to make it more understandable. The conversion is straightforward since there are 60 seconds in a minute.

• To convert from seconds to minutes, use: \( \frac{\text{seconds}}{60} \)

In our example:

• The calculated time from the electrolysis was \( 1835062 \, s \)
• Converted to minutes: \( \frac{1835062}{60} \approx 30584 \, \text{minutes} \)

Understanding time conversion ensures clear communication and practical comprehension of electrolysis durations. It can help one grasp how long an industrial or laboratory process will take.