A very thin copper plate is electro`-` plated with gold using gold chloride in `HCl`. The current was passed for `20 mi n`. And the increase in the weight of the plate was found to be `2g.[Au=197]`. The current passed was `-`

Options

A. `0.816 amp`
B. `1.632 amp`
C. `2.448 amp`
D. `3.164amp`

Explanation

To solve the problem of calculating the current passed during the electroplating of a thin copper plate with gold, we can follow these steps:

### Step 1: Understand the electroplating process
The electroplating process involves depositing a layer of metal (in this case, gold) onto a substrate (the copper plate) using an electrolytic solution (gold chloride in HCl). The relevant reaction can be represented as:
\[ \text{AuCl}_3 + 3e^- \rightarrow \text{Au} + 3\text{Cl}^- \]
This indicates that 3 moles of electrons are needed to deposit 1 mole of gold.

### Step 2: Calculate the equivalent weight of gold
The atomic weight of gold (Au) is given as 197 g/mol. Since 3 electrons are required to deposit 1 mole of gold, the equivalent weight of gold can be calculated as:
\[ \text{Equivalent weight of Au} = \frac{\text{Atomic weight}}{n} = \frac{197}{3} \approx 65.67 \text{ g/equiv} \]

### Step 3: Use the formula for electroplating
The weight of the deposited metal can be related to the current, time, and equivalent weight using the formula:
\[ W = \frac{I \cdot t \cdot E}{96500} \]
Where:
- \( W \) = weight of gold deposited (2 g)
- \( I \) = current in amperes (what we need to find)
- \( t \) = time in seconds (20 minutes = 20 × 60 = 1200 seconds)
- \( E \) = equivalent weight of gold (approximately 65.67 g/equiv)
- 96500 = Faraday's constant (the charge of one mole of electrons in coulombs)

### Step 4: Rearrange the formula to solve for current
Rearranging the formula to solve for current \( I \):
\[ I = \frac{W \cdot 96500}{t \cdot E} \]

### Step 5: Substitute the known values into the equation
Substituting the known values:
- \( W = 2 \) g
- \( t = 1200 \) s
- \( E \approx 65.67 \) g/equiv

\[ I = \frac{2 \cdot 96500}{1200 \cdot 65.67} \]

### Step 6: Calculate the current
Now, performing the calculations:
1. Calculate the numerator:
\[ 2 \cdot 96500 = 193000 \]
2. Calculate the denominator:
\[ 1200 \cdot 65.67 \approx 78796 \]
3. Now divide:
\[ I = \frac{193000}{78796} \approx 2.448 \text{ A} \]

### Conclusion
The current passed during the electroplating process is approximately **2.448 A**.

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