Write a mathematical formula for mole ratio. How long will it take to produce 2.415g of Ag metal from its salt solution by passing a current of 3A? Molar mass of Ag= 107.9 g`mol^-1`

Answer

To solve the problem of how long it will take to produce 2.415 g of Ag metal from its salt solution by passing a current of 3A, we will follow these steps:

### Step 1: Determine the number of moles of Ag produced
We start by calculating the number of moles of silver (Ag) produced using the formula:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]

Given:
- Mass of Ag (w) = 2.415 g
- Molar mass of Ag = 107.9 g/mol

Calculating the number of moles of Ag:

\[ \text{Number of moles of Ag} = \frac{2.415 \, \text{g}}{107.9 \, \text{g/mol}} \approx 0.0224 \, \text{mol} \]

### Step 2: Determine the number of moles of electrons required
From the half-reaction for the reduction of silver ions to silver metal, we see that:

\[ \text{Ag}^+ + e^- \rightarrow \text{Ag} \]

This indicates that 1 mole of Ag requires 1 mole of electrons. Therefore, the number of moles of electrons required is equal to the number of moles of Ag produced:

\[ \text{Moles of electrons} = 0.0224 \, \text{mol} \]

### Step 3: Calculate the total charge (Q) required
Using Faraday's law, the total charge (Q) can be calculated using the formula:

\[ Q = n \times F \]

Where:
- \( n \) = number of moles of electrons
- \( F \) = Faraday's constant = 96500 C/mol

Calculating the total charge:

\[ Q = 0.0224 \, \text{mol} \times 96500 \, \text{C/mol} \approx 2166.88 \, \text{C} \]

### Step 4: Calculate the time (t) required to pass this charge
Using the formula:

\[ Q = I \times t \]

Where:
- \( I \) = current in amperes (A)
- \( t \) = time in seconds (s)

Rearranging the formula to solve for time:

\[ t = \frac{Q}{I} \]

Substituting the values:

\[ t = \frac{2166.88 \, \text{C}}{3 \, \text{A}} \approx 722.29 \, \text{s} \]

### Step 5: Convert time from seconds to minutes
To convert seconds to minutes, divide by 60:

\[ t \approx \frac{722.29 \, \text{s}}{60} \approx 12.04 \, \text{minutes} \]

### Final Answer
It will take approximately **12.04 minutes** to produce 2.415 g of Ag metal from its salt solution by passing a current of 3A.

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