The number of atoms in 50gm of `CaCO_3` is:

Options

A. 5Na
B. 0.5Na
C. 2.5Na
D. 2Na

Explanation

To find the number of atoms in 50 grams of calcium carbonate (CaCO₃), we can follow these steps:

### Step 1: Calculate the Molar Mass of CaCO₃
The molar mass of a compound is calculated by adding the atomic masses of all the atoms in the formula.

- Calcium (Ca) has an atomic mass of approximately 40 g/mol.
- Carbon (C) has an atomic mass of approximately 12 g/mol.
- Oxygen (O) has an atomic mass of approximately 16 g/mol. Since there are three oxygen atoms in CaCO₃, we multiply by 3.

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

### Step 2: Calculate the Number of Moles in 50 grams of CaCO₃
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{50 \text{ g}}{100 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 3: Calculate the Number of Molecules
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol), we can find the number of molecules:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ = 0.5 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} = 3.011 \times 10^{23} \text{ molecules} \]

### Step 4: Calculate the Number of Atoms
Each molecule of CaCO₃ contains 5 atoms (1 Calcium, 1 Carbon, and 3 Oxygen). Therefore, the total number of atoms is:
\[ \text{Number of atoms} = \text{Number of molecules} \times \text{Number of atoms per molecule} \]
\[ = 3.011 \times 10^{23} \text{ molecules} \times 5 \text{ atoms/molecule} = 1.5055 \times 10^{24} \text{ atoms} \]

### Final Answer
The number of atoms in 50 grams of CaCO₃ is approximately \(1.5055 \times 10^{24}\) atoms.

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