Passage of a current for 548 seconds through a siver coulometer results in the deposition of 0.746g of silver.What is the current (in A)?

Options

A. 1.22
B. 1.16
C. 1.07
D. 1

Answer

To calculate the current (I) in amperes when a current passes through a silver coulometer for a specific time, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of silver deposited (m) = 0.746 g
- Time (t) = 548 seconds

2. **Determine the Molar Mass of Silver:**
- The molar mass of silver (Ag) = 108 g/mol

3. **Use Faraday's Law of Electrolysis:**
- According to Faraday's law, 1 Faraday (F) of charge (96500 C) deposits the molar mass of the element in grams. For silver, this means:
\[ 1 \text{ F} = 96500 \text{ C} \text{ deposits } 108 \text{ g of Ag} \]

4. **Calculate the Charge Required for 1 g of Silver:**
- To find the charge required for 1 g of silver:
\[ \text{Charge for 1 g of Ag} = \frac{96500 \text{ C}}{108 \text{ g}} \approx 893.52 \text{ C/g} \]

5. **Calculate the Charge Required for 0.746 g of Silver:**
- Now, calculate the charge (Q) required for 0.746 g of silver:
\[ Q = \frac{96500 \text{ C}}{108 \text{ g}} \times 0.746 \text{ g} \approx 666.56 \text{ C} \]

6. **Use the Formula Relating Charge, Current, and Time:**
- The relationship between charge (Q), current (I), and time (t) is given by:
\[ Q = I \times t \]
- Rearranging for current (I):
\[ I = \frac{Q}{t} \]

7. **Substitute the Values:**
- Substitute the calculated charge and the given time into the formula:
\[ I = \frac{666.56 \text{ C}}{548 \text{ s}} \approx 1.22 \text{ A} \]

8. **Final Answer:**
- The current (I) is approximately **1.22 A**.