Find number of oxygen atoms present in 100 mg of CaCO_3. (Atomic mass of Ca = 40 u, C = 12 u, O = 16 u)

Options

A. `6.02 xx 10^(23)`
B. `6.02 xx 10^(20)`
C. `1.806 xx 10^(21)`
D. `1.204 xx 10^(20)`

Answer

To find the number of oxygen atoms present in 100 mg of CaCO₃ (calcium carbonate), we can follow these steps:

### Step 1: Calculate the Molar Mass of CaCO₃
The molar mass of calcium carbonate (CaCO₃) can be calculated by adding the atomic masses of its constituent elements:
- Atomic mass of Calcium (Ca) = 40 u
- Atomic mass of Carbon (C) = 12 u
- Atomic mass of Oxygen (O) = 16 u (and there are 3 oxygen atoms in CaCO₃)

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

### Step 2: Convert the Mass from mg to g
We need to convert the mass of CaCO₃ from milligrams to grams:
\[ 100 \text{ mg} = 100 \times 10^{-3} \text{ g} = 0.1 \text{ g} \]

### Step 3: Calculate the Number of Moles of CaCO₃
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
\[ = \frac{0.1 \text{ g}}{100 \text{ g/mol}} = 0.001 \text{ moles} \]

### Step 4: Calculate the Number of Oxygen Atoms
In one mole of CaCO₃, there are 3 moles of oxygen atoms. Therefore, the number of moles of oxygen in 0.001 moles of CaCO₃ is:
\[ \text{Number of moles of O} = 3 \times 0.001 = 0.003 \text{ moles} \]

Now, we can find the number of oxygen atoms using Avogadro's number (\(6.022 \times 10^{23}\) atoms/mole):
\[ \text{Number of oxygen atoms} = \text{Number of moles of O} \times \text{Avogadro's number} \]
\[ = 0.003 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \]
\[ = 1.8066 \times 10^{21} \text{ oxygen atoms} \]

### Final Answer
Thus, the number of oxygen atoms present in 100 mg of CaCO₃ is approximately \(1.81 \times 10^{21}\) oxygen atoms.

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