The number of atoms in 100gm of `CaCO_3` is:

Options

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

Explanation

To find the number of atoms in 100 grams of \( \text{CaCO}_3 \), we can follow these steps:

### Step 1: Calculate the Molar Mass of \( \text{CaCO}_3 \)
The molar mass is calculated by adding the atomic masses of all the atoms in the compound:

- Calcium (Ca): 40 g/mol
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (and there are 3 oxygen atoms)

So, the molar mass of \( \text{CaCO}_3 \) is:
\[ \text{Molar Mass} = 40 + 12 + (16 \times 3) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 2: Calculate the Number of Moles of \( \text{CaCO}_3 \)
Using the formula:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molar mass}} \]
Given weight = 100 g, Molar mass = 100 g/mol, we have:
\[ \text{Number of moles} = \frac{100 \text{ g}}{100 \text{ g/mol}} = 1 \text{ mole} \]

### Step 3: Calculate the Number of Molecules of \( \text{CaCO}_3 \)
Using Avogadro's number \( N_A \) (approximately \( 6.022 \times 10^{23} \) molecules/mole):
\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 1 \times 6.022 \times 10^{23} \approx 6.022 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the Number of Atoms in \( \text{CaCO}_3 \)
Each molecule of \( \text{CaCO}_3 \) contains 5 atoms (1 Calcium + 1 Carbon + 3 Oxygen):
\[ \text{Number of atoms} = \text{Number of molecules} \times \text{Atoms per molecule} = 6.022 \times 10^{23} \times 5 \]
\[ \text{Number of atoms} = 30.11 \times 10^{23} \text{ atoms} = 3.011 \times 10^{24} \text{ atoms} \]

### Final Answer
The number of atoms in 100 grams of \( \text{CaCO}_3 \) is approximately \( 3.011 \times 10^{24} \) atoms.

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