To solve the problem of determining the time required to coat aluminum metal on the surface of a square plate using molten AlCl₃ solution and a current of 10 A, we can follow these steps:
### Step 1: Calculate the Volume of Aluminum Required
The plate is square with a length of 20 cm and a thickness of 5 mm on both sides.
1. Convert the dimensions to the same unit:
- Length = 20 cm = 200 mm
- Thickness = 5 mm (for both sides, total thickness = 5 mm + 5 mm = 10 mm)
2. Calculate the volume (V) of aluminum required:
\[
V = \text{Length} \times \text{Width} \times \text{Thickness} = 200 \, \text{mm} \times 200 \, \text{mm} \times 10 \, \text{mm} = 400000 \, \text{mm}^3
\]
Convert this volume to mL (1 mL = 1000 mm³):
\[
V = \frac{400000 \, \text{mm}^3}{1000} = 400 \, \text{mL}
\]
### Step 2: Calculate the Mass of Aluminum
Using the specific gravity of aluminum (1.8 g/mL), we can find the mass (m) of aluminum:
\[
m = \text{Density} \times \text{Volume} = 1.8 \, \text{g/mL} \times 400 \, \text{mL} = 720 \, \text{g}
\]
### Step 3: Calculate the Number of Moles of Aluminum
The molar mass of aluminum (Al) is approximately 27 g/mol. Therefore, the number of moles (n) of aluminum is:
\[
n = \frac{m}{\text{Molar Mass}} = \frac{720 \, \text{g}}{27 \, \text{g/mol}} \approx 26.67 \, \text{mol}
\]
### Step 4: Determine the Total Charge Required
Using Faraday's law, the total charge (Q) required can be calculated using the formula:
\[
Q = n \times F \times z
\]
Where:
- \( F \) (Faraday's constant) = 96500 C/mol
- \( z \) (number of electrons transferred per atom of aluminum) = 3 (for Al³⁺)
Thus,
\[
Q = 26.67 \, \text{mol} \times 96500 \, \text{C/mol} \times 3 \approx 7725000 \, \text{C}
\]
### Step 5: Calculate the Time Required
Using the relationship \( Q = I \times T \), where \( I \) is the current (10 A):
\[
T = \frac{Q}{I} = \frac{7725000 \, \text{C}}{10 \, \text{A}} = 772500 \, \text{s}
\]
### Step 6: Convert Time to Hours
Convert seconds to hours:
\[
T \approx \frac{772500 \, \text{s}}{3600 \, \text{s/hour}} \approx 214.58 \, \text{hours}
\]
### Final Answer
The time required to coat aluminum metal on the surface of the square plate is approximately **214.58 hours**.
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