`19.7` kg of gold was recovered from a smuggler . How many atoms of gold were recovered ? (At . Wt. of gold (Au)=197)

Options

A. 100
B. `6.023xx10^(23)`
C. `6.023xx10^(24)`
D. `6.023xx10^(25)`

Answer

To solve the problem of how many atoms of gold were recovered from 19.7 kg of gold, we can follow these steps:

### Step 1: Convert the mass of gold from kilograms to grams
Given that the mass of gold is 19.7 kg, we can convert this to grams by multiplying by 1000 (since 1 kg = 1000 g).

\[ \text{Mass of gold in grams} = 19.7 \, \text{kg} \times 1000 \, \text{g/kg} = 19700 \, \text{g} \]

### Step 2: Calculate the number of moles of gold
We know the atomic weight (molar mass) of gold (Au) is 197 g/mol. To find the number of moles of gold, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Substituting the values we have:

\[ \text{Number of moles of Au} = \frac{19700 \, \text{g}}{197 \, \text{g/mol}} = 100 \, \text{moles} \]

### Step 3: Calculate the number of atoms
Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol, we can find the total number of atoms in the gold recovered:

\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]

Substituting the values:

\[ \text{Number of atoms} = 100 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{25} \, \text{atoms} \]

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

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