How many grams of silver could be plated out on a serving tray by the electrolysis of a solution containing silver in `+1` oxidation state of a period of `8.0h` at a current of `8.46A` ? What is the area of the ray, if the thickness of the silver plating is `0.0254 cm` ? The density of silver is 10.5 g cm^(-3)`.

Explanation

To solve the problem step by step, we will first calculate the mass of silver that can be plated out using electrolysis, and then we will determine the area of the tray based on the thickness of the silver plating and the density of silver.

### Step 1: Calculate the total charge (Q) passed during electrolysis
The total charge can be calculated using the formula:
\[ Q = I \times t \]
where:
- \( I \) = current in amperes (A) = 8.46 A
- \( t \) = time in seconds (s) = 8 hours = \( 8 \times 3600 \) s

Calculating \( t \):
\[ t = 8 \times 3600 = 28800 \, \text{s} \]

Now, substituting the values:
\[ Q = 8.46 \, \text{A} \times 28800 \, \text{s} = 243648 \, \text{C} \]

### Step 2: Calculate the number of moles of silver plated
Using Faraday's law, the number of moles of silver (Ag) plated can be calculated using:
\[ n = \frac{Q}{F} \]
where:
- \( F \) (Faraday's constant) = 96500 C/mol

Substituting the values:
\[ n = \frac{243648 \, \text{C}}{96500 \, \text{C/mol}} \approx 2.52 \, \text{mol} \]

### Step 3: Calculate the mass of silver plated
The mass of silver can be calculated using:
\[ \text{mass} = n \times M \]
where:
- \( M \) (molar mass of silver) = 107.87 g/mol

Substituting the values:
\[ \text{mass} = 2.52 \, \text{mol} \times 107.87 \, \text{g/mol} \approx 272.18 \, \text{g} \]

### Step 4: Calculate the volume of silver plated
Using the density formula:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]
We can rearrange this to find volume:
\[ \text{volume} = \frac{\text{mass}}{\text{density}} \]

Given that the density of silver is \( 10.5 \, \text{g/cm}^3 \):
\[ \text{volume} = \frac{272.18 \, \text{g}}{10.5 \, \text{g/cm}^3} \approx 25.92 \, \text{cm}^3 \]

### Step 5: Calculate the area of the tray
Using the formula for area:
\[ \text{Area} = \frac{\text{volume}}{\text{thickness}} \]

Given that the thickness is \( 0.0254 \, \text{cm} \):
\[ \text{Area} = \frac{25.92 \, \text{cm}^3}{0.0254 \, \text{cm}} \approx 1022.83 \, \text{cm}^2 \]

### Final Answers:
- Mass of silver plated: **272.18 grams**
- Area of the tray: **1022.83 cm²**