A copper plate of 20 cm x 10 cm is to be plated with silver of 1 mm thickness on both the sides. Number of moles of silver required for plating is (density of silver =10.8 g m /cc)____________

Answer

To solve the problem of determining the number of moles of silver required to plate a copper plate of dimensions 20 cm x 10 cm with a thickness of 1 mm on both sides, we can follow these steps:

### Step 1: Calculate the Surface Area of the Copper Plate
The surface area (A) of the copper plate can be calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]
Given:
- Length = 20 cm
- Breadth = 10 cm

Calculating the area:
\[ A = 20 \, \text{cm} \times 10 \, \text{cm} = 200 \, \text{cm}^2 \]

### Step 2: Calculate the Total Volume of Silver Required
Since the silver is plated on both sides of the copper plate, we need to consider the thickness on both sides. The total thickness of silver will be:
\[ \text{Total Thickness} = 1 \, \text{mm} + 1 \, \text{mm} = 2 \, \text{mm} = 0.2 \, \text{cm} \]

Now, we can calculate the volume (V) of silver required using the formula:
\[ V = A \times \text{Total Thickness} \]
Calculating the volume:
\[ V = 200 \, \text{cm}^2 \times 0.2 \, \text{cm} = 40 \, \text{cm}^3 \]

### Step 3: Calculate the Mass of Silver Required
To find the mass (m) of silver, we use the density (d) of silver:
\[ \text{Density of silver} = 10.8 \, \text{g/cm}^3 \]
Using the formula:
\[ m = d \times V \]
Calculating the mass:
\[ m = 10.8 \, \text{g/cm}^3 \times 40 \, \text{cm}^3 = 432 \, \text{g} \]

### Step 4: Calculate the Number of Moles of Silver Required
To find the number of moles (n) of silver, we use the formula:
\[ n = \frac{\text{mass}}{\text{molar mass}} \]
The molar mass of silver (Ag) is approximately 108 g/mol. Therefore:
\[ n = \frac{432 \, \text{g}}{108 \, \text{g/mol}} = 4 \, \text{moles} \]

### Final Answer
The number of moles of silver required for plating is **4 moles**.

---