The number of carbon atoms in 1 g of `CaCO_3` is,

Options

A. `6.022 xx 10^(23)`
B. `6.022 xx 10^(21)`
C. `3.0125 xx 10^(22)`
D. `1.204 xx 10^(23)`

Explanation

To find the number of carbon atoms in 1 g of calcium carbonate (CaCO₃), we can follow these steps:

### Step 1: Calculate the Molar Mass of Calcium Carbonate (CaCO₃)
- The molar mass of calcium (Ca) = 40 g/mol
- The molar mass of carbon (C) = 12 g/mol
- The molar mass of oxygen (O) = 16 g/mol
- In CaCO₃, there is 1 calcium atom, 1 carbon atom, and 3 oxygen atoms.

Calculating the total molar mass:
\[ \text{Molar mass of CaCO₃} = (1 \times 40) + (1 \times 12) + (3 \times 16) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of CaCO₃ in 1 g
Using the formula for moles:
\[ \text{Moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Substituting the values:
\[ \text{Moles of CaCO₃} = \frac{1 \text{ g}}{100 \text{ g/mol}} = 0.01 \text{ moles} \]

### Step 3: Determine the Number of Moles of Carbon Atoms
In 1 mole of CaCO₃, there is 1 mole of carbon atoms. Therefore, in 0.01 moles of CaCO₃, the number of moles of carbon atoms is:
\[ \text{Moles of Carbon} = 0.01 \text{ moles of CaCO₃} \times 1 \text{ mole of C} = 0.01 \text{ moles of C} \]

### Step 4: Convert Moles of Carbon Atoms to Number of Atoms
To find the number of atoms, we use Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms/mol):
\[ \text{Number of Carbon Atoms} = 0.01 \text{ moles of C} \times 6.022 \times 10^{23} \text{ atoms/mol} \]
Calculating this gives:
\[ \text{Number of Carbon Atoms} = 0.01 \times 6.022 \times 10^{23} = 6.022 \times 10^{21} \text{ atoms} \]

### Final Answer
The number of carbon atoms in 1 g of CaCO₃ is \(6.022 \times 10^{21}\) atoms.

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