An electroplating unit plates `3.0 g` of silver on a brass plate in `3.0` minutes. Find the current used by the unit. The electrochemical equivalent of silver is `1.12 xx 10^(-6) kg C^(-1)`.

Explanation

To solve the problem, we will use Faraday's law of electrolysis, which relates the mass of a substance deposited during electrolysis to the current, time, and electrochemical equivalent of the substance.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of silver deposited (M) = 3.0 g
- Electrochemical equivalent of silver (Z) = \(1.12 \times 10^{-6} \, \text{kg/C}\)
- Time (T) = 3.0 minutes

2. **Convert the Mass from grams to kilograms:**
\[ M = 3.0 \, \text{g} = 3.0 \times 10^{-3} \, \text{kg} \]

3. **Convert Time from minutes to seconds:**
\[ T = 3.0 \, \text{minutes} = 3.0 \times 60 = 180 \, \text{seconds} \]

4. **Use Faraday's Law:**
According to Faraday's law:
\[ M = Z \cdot I \cdot T \]
Rearranging the formula to find the current (I):
\[ I = \frac{M}{Z \cdot T} \]

5. **Substitute the Values into the Formula:**
\[ I = \frac{3.0 \times 10^{-3} \, \text{kg}}{(1.12 \times 10^{-6} \, \text{kg/C}) \cdot (180 \, \text{s})} \]

6. **Calculate the Current:**
\[ I = \frac{3.0 \times 10^{-3}}{(1.12 \times 10^{-6}) \cdot 180} \]
\[ I = \frac{3.0 \times 10^{-3}}{2.016 \times 10^{-4}} \approx 14.88 \, \text{A} \]

Rounding this, we find:
\[ I \approx 15 \, \text{A} \]

### Final Answer:
The current used by the electroplating unit is approximately **15 A**.

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