19.7 kg of gold was recovered from a smuggler. How many atoms of gold were recovered?

Options

A. 100
B. `6.023 xx 10^(23)`
C. `6.02 xx 10^(24)`
D. `6.02 xx 10^(25)`

Explanation

To find the number of atoms of gold recovered from a smuggler, we can follow these steps:

### Step 1: Convert the mass of gold from kilograms to grams.
Given:
- Mass of gold = 19.7 kg

To convert kilograms to grams:
\[ \text{Mass in grams} = \text{Mass in kg} \times 1000 \]
\[ \text{Mass in grams} = 19.7 \, \text{kg} \times 1000 = 19700 \, \text{g} \]

### Step 2: Calculate the number of moles of gold.
The formula to calculate the number of moles is:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of gold (Au) is approximately 197 g/mol.
\[ \text{Number of moles} = \frac{19700 \, \text{g}}{197 \, \text{g/mol}} = 100 \, \text{moles} \]

### Step 3: Calculate the number of atoms in the moles of gold.
Using Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) atoms/mole:
\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of atoms} = 100 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \]
\[ \text{Number of atoms} = 6.022 \times 10^{25} \, \text{atoms} \]

### Final Answer:
The number of atoms of gold recovered is approximately \( 6.022 \times 10^{25} \) atoms.

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