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).
- 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, and there are three oxygen atoms in CaCO₃.

Calculating the molar mass:
\[ \text{Molar mass of CaCO}_3 = \text{mass of Ca} + \text{mass of C} + 3 \times \text{mass of O} \]
\[ = 40 + 12 + 3 \times 16 = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 2: Calculate the number of moles of CaCO₃ in 10 g.
Using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
\[ = \frac{10 \text{ g}}{100 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 3: Determine the number of protons in one formula unit of CaCO₃.
- Calcium (Ca) has 20 protons.
- Carbon (C) has 6 protons.
- Oxygen (O) has 8 protons, and there are three oxygen atoms.

Calculating the total number of protons in one formula unit:
\[ \text{Total protons} = \text{protons from Ca} + \text{protons from C} + 3 \times \text{protons from O} \]
\[ = 20 + 6 + 3 \times 8 = 20 + 6 + 24 = 50 \text{ protons} \]

### Step 4: Calculate the total number of protons in 0.1 moles of CaCO₃.
The total number of protons in 0.1 moles of CaCO₃ can be calculated by multiplying the number of moles by the number of protons per formula unit and Avogadro's number (N₀):
\[ \text{Total protons} = \text{Number of moles} \times \text{Protons per formula unit} \times N_0 \]
\[ = 0.1 \times 50 \times 6.022 \times 10^{23} \]
\[ = 5 \times 6.022 \times 10^{23} = 3.011 \times 10^{24} \text{ protons} \]

### Final Answer:
The total number of protons in 10 g of calcium carbonate is approximately \(3.011 \times 10^{24}\).

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