The number of atoms in 10gm of `CaCO_3` is:

Options

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

Explanation

To find the number of atoms in 10 grams of calcium carbonate (CaCO₃), we can follow these steps:

### Step 1: Calculate the molar mass of CaCO₃
- The molar mass of CaCO₃ is 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 CaCO₃)

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

### Step 2: Calculate the number of moles of CaCO₃ in 10 grams
- Using the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

Substituting the values:
\[ \text{Number of moles of CaCO₃} = \frac{10 \text{ g}}{100 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 3: Calculate the number of molecules of CaCO₃
- To find the number of molecules, we use Avogadro's number (Nₐ), which is approximately \(6.022 \times 10^{23}\) molecules/mol:
\[ \text{Number of molecules} = \text{Number of moles} \times Nₐ \]
\[ \text{Number of molecules of CaCO₃} = 0.1 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
\[ = 6.022 \times 10^{22} \text{ molecules} \]

### Step 4: Calculate the total number of atoms in CaCO₃
- Each molecule of CaCO₃ contains 5 atoms (1 Ca + 1 C + 3 O). Therefore, the total number of atoms is:
\[ \text{Total number of atoms} = \text{Number of molecules} \times \text{Number of atoms per molecule} \]
\[ \text{Total number of atoms} = 6.022 \times 10^{22} \text{ molecules} \times 5 \text{ atoms/molecule} \]
\[ = 3.011 \times 10^{23} \text{ atoms} \]

### Final Answer:
The number of atoms in 10 grams of CaCO₃ is approximately \(3.011 \times 10^{23}\) atoms.

---