Suppose that gold is being plated onto another metal in a electrolytic cell. The half`-` cell reaction producing the `Au(s)` is `AuCl_(4)^(c-) rarr Au(s)+4Cl^(c-)+3e^(-)`
If a `0.30- A` current runs for `1.50 mi n` , what mass of `Au(s)` will be plated, assuming all the electrons are used in the reduction of `AuCl_(4)?`

Options

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

Answer

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

### Step 1: Write down the given data
- Current (I) = 0.30 A
- Time (t) = 1.50 minutes

### Step 2: Convert time from minutes to seconds
Since the time is given in minutes, we need to convert it to seconds for our calculations.
\[ t = 1.50 \, \text{minutes} \times 60 \, \text{seconds/minute} = 90 \, \text{seconds} \]

### Step 3: Calculate the total charge (Q) using the formula \( Q = I \times t \)
\[ Q = 0.30 \, \text{A} \times 90 \, \text{s} = 27 \, \text{C} \]

### Step 4: Calculate the number of Faradays (F) using the formula \( \text{Number of Faradays} = \frac{Q}{96500} \)
\[ \text{Number of Faradays} = \frac{27 \, \text{C}}{96500 \, \text{C/F}} \approx 0.00028 \, \text{F} \]

### Step 5: Analyze the half-cell reaction
The half-cell reaction is:
\[ \text{AuCl}_4^{-} + 3e^{-} \rightarrow \text{Au}(s) + 4\text{Cl}^{-} \]
This indicates that 3 moles of electrons (or 3 Faradays) are required to produce 1 mole of Au.

### Step 6: Calculate the moles of Au produced
From the reaction, we know:
\[ 1 \, \text{F} \rightarrow \frac{1}{3} \, \text{moles of Au} \]
Thus, the moles of Au produced from the Faradays calculated:
\[ \text{Moles of Au} = \frac{0.00028 \, \text{F}}{3} \approx 0.0000933 \, \text{moles of Au} \]

### Step 7: Calculate the mass of Au using the formula \( \text{mass} = \text{moles} \times \text{molar mass} \)
The molar mass of Au is approximately 197 g/mol.
\[ \text{mass of Au} = 0.0000933 \, \text{moles} \times 197 \, \text{g/mol} \approx 0.0184 \, \text{g} \]

### Step 8: Final result
The mass of Au plated is approximately:
\[ \text{mass of Au} \approx 0.184 \, \text{g} \]

### Summary
The mass of gold (Au) that will be plated in the electrolytic cell is approximately **0.184 grams**.