Cd amalgam is preapred by electrolysis of a solution `CdCI_(2)` using a mercury cathode. How long should a current of `5A` be passed in order to prepare `12% Cd-Hg` amalgam on a cathode of `2g, Hg`( atomic weight of `Cd = 112.4)`

Explanation

To solve the problem of preparing a 12% Cd-Hg amalgam using electrolysis, we can break it down into several steps:

### Step 1: Determine the amount of cadmium needed
Given that the amalgam is 12% cadmium by weight, we need to find out how much cadmium is required for 2 grams of mercury (Hg).

\[ \text{Weight of Cd in amalgam} = \frac{12}{100} \times \text{Weight of Hg} \]

Substituting the weight of Hg:

\[ \text{Weight of Cd} = \frac{12}{100} \times 2 \, \text{g} = 0.24 \, \text{g} \]

### Step 2: Calculate the moles of cadmium
Next, we need to convert the weight of cadmium into moles using its atomic weight (112.4 g/mol).

\[ \text{Moles of Cd} = \frac{\text{Weight of Cd}}{\text{Atomic weight of Cd}} = \frac{0.24 \, \text{g}}{112.4 \, \text{g/mol}} \approx 0.00213 \, \text{mol} \]

### Step 3: Determine the moles of electrons required
Cadmium ions (Cd²⁺) gain 2 electrons to become cadmium metal (Cd). Therefore, the number of moles of electrons required is:

\[ \text{Moles of electrons} = 2 \times \text{Moles of Cd} = 2 \times 0.00213 \, \text{mol} \approx 0.00426 \, \text{mol} \]

### Step 4: Calculate the total charge required
Using Faraday's constant (approximately 96500 C/mol), we can calculate the total charge (Q) required for the electrolysis:

\[ Q = \text{Moles of electrons} \times \text{Faraday's constant} = 0.00426 \, \text{mol} \times 96500 \, \text{C/mol} \approx 411.39 \, \text{C} \]

### Step 5: Calculate the time required for electrolysis
Using the formula \( Q = I \times t \), where \( I \) is the current (5 A), we can rearrange to find the time (t):

\[ t = \frac{Q}{I} = \frac{411.39 \, \text{C}}{5 \, \text{A}} \approx 82.28 \, \text{s} \]

### Final Answer
The time required to prepare the 12% Cd-Hg amalgam is approximately **82.28 seconds**.

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