The total number of protons in 10 g of calcium carbonate is `(N_(0) = 6.023 xx 10^(23))` :-

Options

A. `1.5057 xx 10^(24)`
B. `2.0478 xx 10^(24)`
C. `3.0115 xx 10^(24)`
D. `4.0956 xx 10^(24)`

Answer

To find the total number of protons in 10 g of calcium carbonate (CaCO₃), we can follow these steps:

### Step 1: Determine the molar mass of calcium carbonate (CaCO₃).
- The molar mass is calculated by adding the atomic masses of its constituent elements:
- Calcium (Ca): Atomic mass = 40 g/mol
- Carbon (C): Atomic mass = 12 g/mol
- Oxygen (O): Atomic mass = 16 g/mol (and there are 3 oxygen atoms in CaCO₃)

Molar mass of CaCO₃ = Atomic mass of Ca + Atomic mass of C + (3 × Atomic mass of O)

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

### Step 2: Calculate the number of moles of CaCO₃ in 10 g.
- Use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

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

### Step 3: Determine the total number of protons in one mole of CaCO₃.
- The total number of protons is calculated by summing the atomic numbers of the constituent elements:
- Calcium (Ca): Atomic number = 20
- Carbon (C): Atomic number = 6
- Oxygen (O): Atomic number = 8 (and there are 3 oxygen atoms)

Total protons in one mole of CaCO₃:

\[ \text{Total protons} = \text{Atomic number of Ca} + \text{Atomic number of C} + (3 \times \text{Atomic number of O}) \]

\[ \text{Total protons} = 20 + 6 + (3 \times 8) = 20 + 6 + 24 = 50 \]

### Step 4: Calculate the total number of protons in 0.1 moles of CaCO₃.
- Use Avogadro's number (N₀ = 6.023 × 10²³) to find the total number of protons:

\[ \text{Total protons in 0.1 moles} = \text{Number of moles} \times \text{Total protons in one mole} \times N₀ \]

\[ \text{Total protons} = 0.1 \text{ moles} \times 50 \text{ protons/mole} \times 6.023 \times 10^{23} \]

\[ \text{Total protons} = 0.1 \times 50 \times 6.023 \times 10^{23} = 3.0115 \times 10^{24} \]

### Final Answer:
The total number of protons in 10 g of calcium carbonate is approximately \(3.0115 \times 10^{24}\).

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