To write a letter with a graphite pencil, 0.001 g of carbon is required. Number of moles of carbon atoms and the total number of carbon atoms used in writing the letter are respectively.

Options

A. `3.02 xx 10^(23) and 6.023 xx 10^(23)`
B. `1 and 3.02 xx 10^(24)`
C. `8.33 xx 10^(-5) and 5.02 xx 10^(19)`
D. `5.02 xx 10^(19) and 3.02 xx 10^(24)`

Answer

To solve the problem, we need to calculate the number of moles of carbon atoms and the total number of carbon atoms in 0.001 g of carbon.

### Step-by-Step Solution:

1. **Identify the mass of carbon**:
The mass of carbon used to write the letter is given as 0.001 g.

2. **Determine the molar mass of carbon**:
The molar mass of carbon (C) is approximately 12 g/mol.

3. **Calculate the number of moles of carbon**:
The number of moles (n) can be calculated using the formula:
\[ n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ n = \frac{0.001 \text{ g}}{12 \text{ g/mol}} = 8.33 \times 10^{-5} \text{ moles} \]

4. **Calculate the total number of carbon atoms**:
To find the total number of atoms, we use Avogadro's number, which is approximately \(6.022 \times 10^{23} \text{ atoms/mol}\). The total number of atoms can be calculated as:
\[ \text{Total atoms} = n \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Total atoms} = 8.33 \times 10^{-5} \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \]
Performing the multiplication:
\[ \text{Total atoms} \approx 5.01 \times 10^{19} \text{ atoms} \]

### Final Answer:
The number of moles of carbon atoms is approximately \(8.33 \times 10^{-5}\) moles, and the total number of carbon atoms used in writing the letter is approximately \(5.01 \times 10^{19}\) atoms.

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