The approximate time duration in hours to electroplate 30 g of calcium from molten calcium chloride using a current of 5 amp is [At. Mass of Ca=40]

Options

A. 8
B. 80
C. 10
D. 16

Answer

To find the approximate time duration in hours to electroplate 30 g of calcium from molten calcium chloride using a current of 5 amperes, we can follow these steps:

### Step 1: Calculate the Equivalent Weight of Calcium
The equivalent weight (EW) of calcium can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{n} \]
where \( n \) is the number of electrons exchanged per atom in the reaction. For calcium, which has an oxidation state of +2 in calcium chloride (CaCl₂), \( n = 2 \).

Given:
- Atomic mass of calcium (Ca) = 40 g/mol

Thus, the equivalent weight of calcium is:
\[ \text{EW} = \frac{40 \, \text{g/mol}}{2} = 20 \, \text{g/equiv} \]

### Step 2: Use the Electrolysis Equation
The relationship between the mass deposited, equivalent weight, current, and time is given by Faraday's law of electrolysis:
\[ \frac{W}{EW} = \frac{I \cdot T}{96500} \]
where:
- \( W \) = mass of the substance deposited (30 g)
- \( EW \) = equivalent weight (20 g/equiv)
- \( I \) = current (5 A)
- \( T \) = time in seconds
- 96500 = Faraday's constant (C/equiv)

### Step 3: Rearranging the Equation
We can rearrange the equation to solve for \( T \):
\[ T = \frac{W \cdot 96500}{EW \cdot I} \]

### Step 4: Plugging in the Values
Substituting the known values into the equation:
\[ T = \frac{30 \, \text{g} \cdot 96500 \, \text{C/equiv}}{20 \, \text{g/equiv} \cdot 5 \, \text{A}} \]

Calculating the numerator:
\[ 30 \cdot 96500 = 2895000 \, \text{C} \]

Calculating the denominator:
\[ 20 \cdot 5 = 100 \, \text{g/equiv \cdot A} \]

Thus, we have:
\[ T = \frac{2895000}{100} = 28950 \, \text{s} \]

### Step 5: Convert Time from Seconds to Hours
To convert seconds to hours, we divide by 3600 (the number of seconds in an hour):
\[ T_{\text{hours}} = \frac{28950}{3600} \approx 8.04 \, \text{hours} \]

### Final Answer
The approximate time duration to electroplate 30 g of calcium from molten calcium chloride using a current of 5 amperes is approximately **8.04 hours**.

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