The total number of protons in 10g of calcium carbonate is `(N_(0) = 6.023xx10^(23))`

Options

A. `1.5057xx10^(24)`
B. `2.0478xx10^(24)`
C. `3.0115xx10^(24)`
D. `4.0956xx10^(24)`

Explanation

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

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

So, the molecular weight of CaCO₃ is:
\[ \text{Molar mass of CaCO}_3 = 40 + 12 + (3 \times 16) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 2: Calculate the number of moles of CaCO₃ in 10 grams
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molar mass}} \]
Substituting the values:
\[ \text{Number of moles of CaCO}_3 = \frac{10 \text{ g}}{100 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 3: Calculate the total number of protons in one mole of CaCO₃
To find the total number of protons in one mole of CaCO₃, we need to sum the atomic numbers of each atom in the compound:
- Calcium (Ca): Atomic number = 20
- Carbon (C): Atomic number = 6
- Oxygen (O): Atomic number = 8 (and there are 3 oxygen atoms)

So, the total number of protons in one mole of CaCO₃ is:
\[ \text{Total protons} = 20 + 6 + (3 \times 8) = 20 + 6 + 24 = 50 \]

### Step 4: Calculate the total number of protons in 0.1 moles of CaCO₃
Now, we can calculate the total number of protons in 0.1 moles of CaCO₃:
\[ \text{Total protons in 0.1 moles} = 0.1 \text{ moles} \times 50 \text{ protons/mole} = 5 \text{ protons} \]

### Step 5: Convert the number of protons to the total number using Avogadro's number
To find the total number of protons, we multiply by Avogadro's number (N₀ = \(6.023 \times 10^{23}\)):
\[ \text{Total protons} = 0.1 \text{ moles} \times 50 \text{ protons/mole} \times 6.023 \times 10^{23} \]
Calculating this gives:
\[ \text{Total protons} = 5 \times 6.023 \times 10^{23} = 3.0115 \times 10^{24} \]

### Final Answer
The total number of protons in 10 grams of calcium carbonate is approximately:
\[ 3.0115 \times 10^{24} \]