The number of Faradays needed to reduce 4 g equivalents of ` Cu^(2+)` to Cu metal will be

Options

A. 1
B. 2
C. `1//2`
D. 8

Answer

To find the number of Faradays needed to reduce 4 gram equivalents of \( \text{Cu}^{2+} \) to Cu metal, we can follow these steps:

### Step 1: Understand the concept of Faraday's laws of electrolysis
Faraday's first law states that the amount of substance deposited at an electrode is directly proportional to the amount of electric charge passed through the solution. The relationship can be expressed as:
\[ W \propto Q \]
where \( W \) is the weight of the substance deposited and \( Q \) is the charge.

### Step 2: Use the formula for charge
The relationship can be rewritten using the equation:
\[ W = Z \cdot Q \]
where \( Z \) is the electrochemical equivalent. The electrochemical equivalent \( Z \) can be calculated using:
\[ Z = \frac{\text{Molar Mass}}{n \cdot F} \]
where:
- Molar Mass of Cu = 63.5 g/mol
- \( n \) (number of electrons transferred) for \( \text{Cu}^{2+} \) to Cu = 2
- \( F \) (Faraday's constant) = 96500 C/mol

### Step 3: Calculate the electrochemical equivalent for Cu
Substituting the values into the equation for \( Z \):
\[ Z = \frac{63.5 \, \text{g/mol}}{2 \cdot 96500 \, \text{C/mol}} \]

### Step 4: Calculate the total charge required
Given that we have 4 gram equivalents of Cu, we can express the total charge \( Q \) required to deposit this amount:
\[ Q = \text{Gram Equivalent} \cdot n \cdot F \]
Here, the Gram Equivalent for copper is given as 4. Therefore:
\[ Q = 4 \cdot 2 \cdot 96500 \]

### Step 5: Calculate the number of Faradays
Since 1 Faraday corresponds to 96500 C, we can calculate the number of Faradays required:
\[ \text{Number of Faradays} = \frac{Q}{F} = \frac{4 \cdot 2 \cdot 96500}{96500} = 4 \]

Thus, the number of Faradays needed to reduce 4 gram equivalents of \( \text{Cu}^{2+} \) to Cu metal is **4 Faradays**.

### Summary of Steps:
1. Understand Faraday's laws of electrolysis.
2. Use the formula \( W = Z \cdot Q \).
3. Calculate \( Z \) using the molar mass, n-factor, and Faraday's constant.
4. Calculate the total charge \( Q \) required for 4 gram equivalents.
5. Determine the number of Faradays by dividing the total charge by Faraday's constant.