On passing 3 A of electricity for 50 min, 1.8 g of metal deposits. The equivalent mass of metal is

Options

A. 20.5
B. 25.8
C. 19.3
D. 30.7

Answer

To find the equivalent mass of the metal deposited when passing 3 A of electricity for 50 minutes, we can use the formula:

\[ \text{Equivalent mass} = \frac{W}{I \times t \times 96500} \]

Where:
- \( W \) = mass of the metal deposited (in grams)
- \( I \) = current (in amperes)
- \( t \) = time (in seconds)
- 96500 = Faraday's constant (in coulombs per equivalent)

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Mass of metal deposited, \( W = 1.8 \, \text{g} \)
- Current, \( I = 3 \, \text{A} \)
- Time, \( t = 50 \, \text{minutes} \)

2. **Convert Time from Minutes to Seconds:**
\[ t = 50 \, \text{minutes} \times 60 \, \text{seconds/minute} = 3000 \, \text{seconds} \]

3. **Substitute the Values into the Formula:**
\[ \text{Equivalent mass} = \frac{1.8 \, \text{g}}{3 \, \text{A} \times 3000 \, \text{s} \times 96500} \]

4. **Calculate the Denominator:**
\[ I \times t \times 96500 = 3 \times 3000 \times 96500 \]
\[ = 3 \times 3000 = 9000 \]
\[ 9000 \times 96500 = 867000000 \]

5. **Calculate the Equivalent Mass:**
\[ \text{Equivalent mass} = \frac{1.8}{867000000} \]
\[ = 19.3 \, \text{g/equiv} \]

### Final Answer:
The equivalent mass of the metal is \( 19.3 \, \text{g/equiv} \).

---