A metal plate weighting 750g is to be electroplated with 0.05% of its weight of silver. If a current of 0.8A is used. Find the time needed for depositing the required weight of silver. `E.C.E.` of silver is `11.18xx10^(-7)kgC^(-1)`.

Options

A. 5 min 32 s
B. 6 min 37 s
C. 4 min 16 s
D. 6 min 10 s

Answer

To solve the problem of electroplating a metal plate with silver, we will follow these steps:

### Step 1: Calculate the weight of silver to be deposited
The weight of silver to be deposited (W) is given as 0.05% of the weight of the metal plate.

\[ W = \frac{0.05}{100} \times \text{Weight of the plate} \]
Given that the weight of the plate is 750 grams, we convert it to kilograms:

\[ W = \frac{0.05}{100} \times 0.75 \text{ kg} = 0.000375 \text{ kg} \]

### Step 2: Use Faraday's Law to find the time required
According to Faraday's law, the weight of the material deposited is given by the formula:

\[ W = Z \times I \times t \]

Where:
- \(W\) = weight of silver deposited (in kg)
- \(Z\) = electrochemical equivalent of silver \(= 11.18 \times 10^{-7} \text{ kg/C}\)
- \(I\) = current (in A)
- \(t\) = time (in seconds)

We need to rearrange this formula to find time \(t\):

\[ t = \frac{W}{Z \times I} \]

### Step 3: Substitute the known values into the equation
Now we can substitute the values we have:

\[ t = \frac{0.000375 \text{ kg}}{(11.18 \times 10^{-7} \text{ kg/C}) \times (0.8 \text{ A})} \]

### Step 4: Calculate the denominator
First, calculate the denominator:

\[ Z \times I = 11.18 \times 10^{-7} \times 0.8 = 8.944 \times 10^{-7} \text{ kg/C} \]

### Step 5: Calculate the time
Now substitute this back into the equation for \(t\):

\[ t = \frac{0.000375}{8.944 \times 10^{-7}} \approx 419.3 \text{ seconds} \]

### Step 6: Convert seconds to minutes
To convert seconds into minutes, we divide by 60:

\[ t \approx \frac{419.3}{60} \approx 6.99 \text{ minutes} \approx 6 \text{ minutes and } 59 \text{ seconds} \]

### Final Answer
Thus, the time needed for depositing the required weight of silver is approximately **6 minutes and 59 seconds**.

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