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

Explanation

To find the equivalent mass of the metal deposited when passing 3 A of electricity for 50 minutes, we can use Faraday's laws of electrolysis. Here’s a step-by-step solution:

### Step 1: Convert Time from Minutes to Seconds
We need to convert the time from minutes to seconds because the standard unit of time in electrochemical calculations is seconds.

\[ \text{Time in seconds} = 50 \text{ minutes} \times 60 \text{ seconds/minute} = 3000 \text{ seconds} \]

### Step 2: Calculate Total Charge (Q)
Using the formula for charge, \( Q = I \times t \), where \( I \) is the current in amperes and \( t \) is the time in seconds.

\[ Q = 3 \text{ A} \times 3000 \text{ s} = 9000 \text{ C} \]

### Step 3: Use Faraday's Law to Find Equivalent Mass
According to Faraday's law, the equivalent mass of the metal can be calculated using the formula:

\[ \text{Equivalent mass} = \frac{\text{Weight of metal deposited}}{\text{Charge (C)}/96500} \]

Where:
- Weight of metal deposited = 1.8 g
- Charge = 9000 C

### Step 4: Substitute Values into the Formula
Now, we can substitute the values into the formula:

\[ \text{Equivalent mass} = \frac{1.8 \text{ g}}{9000 \text{ C}/96500} \]

### Step 5: Calculate the Equivalent Mass
First, calculate \( \frac{9000}{96500} \):

\[ \frac{9000}{96500} \approx 0.0932 \]

Now, substitute this value back into the equation:

\[ \text{Equivalent mass} = \frac{1.8 \text{ g}}{0.0932} \approx 19.3 \text{ g/equiv} \]

### Final Answer
The equivalent mass of the metal is approximately **19.3 g/equiv**.

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