Answer :
Explanation:
To calculate the time required for the deposition of 2.50 grams of iron (Fe) from an iron (III) nitrate solution, we need to use Faraday's law of electrolysis and some stoichiometric calculations.
### Step 1: Calculate the moles of iron (Fe)
1. Calculate the molar mass of iron (Fe):
- Atomic mass of Fe = 55.845 g/mol
2. Calculate the moles of Fe:
\[
\text{Moles of Fe} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{2.50 \text{ g}}{55.845 \text{ g/mol}} = 0.0448 \text{ mol}
\]
### Step 2: Use Faraday's Law of Electrolysis
Faraday's law relates the amount of substance deposited during electrolysis to the charge passed through the solution. The equation is:
\[ \text{Mass (g)} = \frac{\text{Charge (C)}}{\text{Faraday constant (C/mol)}} \times \text{Molar mass (g/mol)} \]
Where:
- Charge (C) = Current (A) × Time (s)
- Faraday constant (F) = 96485 C/mol (charge per mole of electrons)
### Step 3: Calculate the charge required
1. Determine the charge required using the given current and time:
- Current (I) = 7.5 A
- Time (t) = ? (in seconds)
2. Calculate the charge (Q):
\[
Q = I \times t
\]
### Step 4: Calculate the time (t)
3. Rearrange Faraday's law to solve for time (t):
\[
t = \frac{\text{Mass (g)} \times \text{Faraday constant (C/mol)}}{\text{Current (A)} \times \text{Molar mass (g/mol)}}
\]
4. Substitute the known values:
\[
t = \frac{2.50 \text{ g} \times 96485 \text{ C/mol}}{7.5 \text{ A} \times 55.845 \text{ g/mol}}
\]
5. Calculate the time (t):
\[
t = \frac{241,212.5}{415.8375} \approx 580 \text{ seconds}
\]
### Step 5: Convert seconds to minutes
6. Convert seconds to minutes:
\[
t \approx \frac{580 \text{ seconds}}{60 \text{ s/min}} \approx 9.67 \text{ minutes}
\]
### Conclusion
Approximately **9.67 minutes** will be needed if 7.5 amps are run through a solution of iron (III) nitrate to deposit 2.50 grams of iron (Fe).
