A current of `5.00` A flowing for `30.00 ` min deposits `3.048` g of zinc at the cathode. Hence, equilvalent mass of zinc is:

Options

A. `65.4` g
B. `130.8` g
C. `32.7` g
D. `16.85` g

Answer

To find the equivalent mass of zinc deposited at the cathode, we can use Faraday's first law of electrolysis. The formula we will use is:

\[ E = \frac{m \cdot F}{I \cdot t} \]

Where:
- \(E\) = equivalent mass of the substance
- \(m\) = mass of the substance deposited (in grams)
- \(F\) = Faraday's constant (approximately \(96500 \, C/mol\))
- \(I\) = current (in Amperes)
- \(t\) = time (in seconds)

### Step 1: Convert time from minutes to seconds
Given that the time is \(30.00\) minutes, we need to convert this to seconds:
\[ t = 30.00 \, \text{min} \times 60 \, \text{s/min} = 1800 \, \text{s} \]

### Step 2: Identify the values
Now we have:
- Current, \(I = 5.00 \, A\)
- Time, \(t = 1800 \, s\)
- Mass deposited, \(m = 3.048 \, g\)
- Faraday's constant, \(F = 96500 \, C/mol\)

### Step 3: Substitute values into the formula
Now we can substitute these values into the formula for equivalent mass:
\[ E = \frac{3.048 \, g \cdot 96500 \, C/mol}{5.00 \, A \cdot 1800 \, s} \]

### Step 4: Calculate the equivalent mass
Calculating the numerator:
\[ 3.048 \, g \cdot 96500 \, C/mol = 294,144.00 \, g \cdot C/mol \]

Calculating the denominator:
\[ 5.00 \, A \cdot 1800 \, s = 9000 \, C \]

Now substituting these into the equation:
\[ E = \frac{294144.00 \, g \cdot C/mol}{9000 \, C} = 32.7 \, g/mol \]

### Final Answer
The equivalent mass of zinc is approximately \(32.7 \, g/mol\).

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