Suppose that gold is being plated on to another metal in an electrolytic cell. The half - cell reaction producing the `Au(s)` is `AuCl_(4)^(-)+3e^(-)+Au(s)+4Cl^(-)`. If a 0.30 A current runs for 15.00 minute, what mass of `Au(s)` will be plated, assume all the electrons are used in the reduction of `AuCl_(4)^(-)` ? the Faraday constant is 96485 C/mol and molar mass of Au is 197.

Options

A. 0.184 g
B. 0.551 g
C. 1.84 g
D. 0.613 g

Answer

To solve the problem of calculating the mass of gold (Au) plated in an electrolytic cell, we will follow these steps:

### Step 1: Convert the time from minutes to seconds
Given:
- Time = 15.00 minutes

To convert minutes to seconds:
\[ \text{Time in seconds} = 15 \, \text{minutes} \times 60 \, \text{seconds/minute} = 900 \, \text{seconds} \]

### Step 2: Calculate the total charge (Q) passed through the cell
Using the formula:
\[ Q = I \times t \]
Where:
- \(I = 0.30 \, \text{A}\)
- \(t = 900 \, \text{s}\)

Calculating the total charge:
\[ Q = 0.30 \, \text{A} \times 900 \, \text{s} = 270 \, \text{C} \]

### Step 3: Calculate the number of moles of electrons transferred
Using Faraday's constant:
\[ \text{Number of moles of electrons} = \frac{Q}{F} \]
Where:
- \(F = 96485 \, \text{C/mol}\)

Calculating the moles of electrons:
\[ \text{Number of moles of electrons} = \frac{270 \, \text{C}}{96485 \, \text{C/mol}} \approx 0.00280 \, \text{mol} \]

### Step 4: Relate moles of electrons to moles of gold plated
From the half-cell reaction:
\[ \text{AuCl}_4^{-} + 3e^{-} \rightarrow \text{Au(s)} + 4\text{Cl}^{-} \]
This indicates that 3 moles of electrons are needed to plate 1 mole of gold.

Calculating moles of gold plated:
\[ \text{Moles of Au} = \frac{\text{Moles of electrons}}{3} = \frac{0.00280 \, \text{mol}}{3} \approx 0.000933 \, \text{mol} \]

### Step 5: Calculate the mass of gold plated
Using the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
Where the molar mass of gold (Au) is given as 197 g/mol.

Calculating the mass of gold:
\[ \text{Mass of Au} = 0.000933 \, \text{mol} \times 197 \, \text{g/mol} \approx 0.184 \, \text{g} \]

### Final Answer
The mass of gold plated is approximately **0.184 g**.

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