Solve step by step: If 49.0 g of palladium is plated at the cathode from palladium II ions in solution, determine the amount of time (in minutes) that this electrochemical cell will run for if 20.0 A flows through the cell.

To solve this problem, we need to use Faraday's laws of electrolysis. Here are the steps involved:

1. **Determine the molar mass of palladium (Pd):**
   The molar mass of palladium (Pd) is approximately 106.42 g/mol.

2. **Calculate the number of moles of palladium plated:**
   \[
   \text{Moles of Pd} = \frac{\text{Mass of Pd}}{\text{Molar mass of Pd}} = \frac{49.0 \text{ g}}{106.42 \text{ g/mol}} \approx 0.4604 \text{ mol}
   \]

3. **Determine the number of moles of electrons needed:**
   Since palladium II ions (Pd²⁺) are being reduced, each ion requires 2 electrons to be plated.
   \[
   \text{Moles of electrons} = 2 \times \text{Moles of Pd} = 2 \times 0.4604 \text{ mol} = 0.9208 \text{ mol}
   \]

4. **Convert moles of electrons to charge (in coulombs):**
   The Faraday constant (F) is \( 96485 \text{ C/mol} \), which is the charge of one mole of electrons.
   \[
   \text{Charge} = \text{Moles of electrons} \times F = 0.9208 \text{ mol} \times 96485 \text{ C/mol} \approx 88806 \text{ C}
   \]

5. **Calculate the time required (in seconds) using the current:**
   The current (I) is given as 20.0 A, and we know that \( I = \frac{Q}{t} \).
   \[
   t = \frac{Q}{I} = \frac{88806 \text{ C}}{20.0 \text{ A}} = 4440.3 \text{ s}
   \]

6. **Convert the time from seconds to minutes:**
   \[
   t \text{ (minutes)} = \frac{t \text{ (seconds)}}{60} = \frac{4440.3 \text{ s}}{60} \approx 74.01 \text{ minutes}
   \]

Therefore, the electrochemical cell will run for approximately 74.01 minutes.

Would you like further details on any step or have any other questions?

Here are 5 related questions you might find interesting:
1. How do you determine the equivalent weight of a metal in electroplating?
2. What are Faraday's laws of electrolysis?
3. How is the Faraday constant derived?
4. How can you calculate the efficiency of an electroplating process?
5. What are the applications of electroplating in industry?

**Tip:** Always ensure that you balance the electrochemical equation correctly when dealing with electrolysis problems, as it directly impacts the stoichiometry of the reaction and the subsequent calculations.

Learn how to calculate the time required for an electrochemical cell to plate 49.0 g of palladium using 20.0 A of current. Detailed step-by-step solution using Faraday's laws of electrolysis and current electricity. Suitable for advanced high school and college students.

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