The number of atoms in 20gm of `CaCO_3` is:

Options

A. 5Na
B. 0.5Na
C. 1Na
D. 10Na

Explanation

To find the number of atoms in 20 grams of \( \text{CaCO}_3 \), we will follow these steps:

### Step 1: Calculate the molar mass of \( \text{CaCO}_3 \)
- The molar mass of \( \text{CaCO}_3 \) can be calculated by adding the atomic masses of its constituent elements:
- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (and there are 3 oxygen atoms in \( \text{CaCO}_3 \))

\[ \text{Molar mass of } \text{CaCO}_3 = 40 + 12 + (3 \times 16) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 2: Calculate the number of moles of \( \text{CaCO}_3 \)
- Use the formula for moles:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
- Given mass = 20 g
- Molar mass = 100 g/mol

\[ \text{Number of moles} = \frac{20 \text{ g}}{100 \text{ g/mol}} = 0.2 \text{ moles} \]

### Step 3: Calculate the number of molecules of \( \text{CaCO}_3 \)
- The number of molecules can be calculated using Avogadro's number (\( N_A \)), which is approximately \( 6.022 \times 10^{23} \) molecules/mol.

\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 0.2 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ \text{Number of molecules} \approx 1.2044 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the number of atoms in \( \text{CaCO}_3 \)
- Each molecule of \( \text{CaCO}_3 \) contains 5 atoms (1 Ca, 1 C, and 3 O).

\[ \text{Number of atoms} = \text{Number of molecules} \times \text{Number of atoms per molecule} \]
\[ \text{Number of atoms} = 1.2044 \times 10^{23} \text{ molecules} \times 5 \text{ atoms/molecule} \]
\[ \text{Number of atoms} \approx 6.022 \times 10^{23} \text{ atoms} \]

### Final Answer:
The number of atoms in 20 grams of \( \text{CaCO}_3 \) is approximately \( 6.022 \times 10^{23} \) atoms.

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