Which of the following will contain same number of atoms as 20g of calcium?

Options

A. 24g magnesium
B. 12g carbon
C. 8g oxygen gas
D. 16g oxygen atom

Answer

To determine which of the given options contains the same number of atoms as 20g of calcium, we will follow these steps:

### Step 1: Calculate the number of moles of calcium.
The formula to calculate the number of moles is:
\[ \text{Number of moles} = \frac{\text{Weight (g)}}{\text{Molecular Weight (g/mol)}} \]
For calcium:
- Weight = 20 g
- Molecular Weight of Calcium = 40 g/mol

Substituting the values:
\[ \text{Number of moles of calcium} = \frac{20 \, \text{g}}{40 \, \text{g/mol}} = 0.5 \, \text{moles} \]

### Step 2: Calculate the number of atoms in calcium.
To find the number of atoms, we use Avogadro's number (\(N_a\)), which is approximately \(6.022 \times 10^{23}\) atoms/mol.
\[ \text{Number of atoms} = \text{Number of moles} \times N_a \]
Substituting the values:
\[ \text{Number of atoms in calcium} = 0.5 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 3.011 \times 10^{23} \, \text{atoms} \]

### Step 3: Analyze each option to find the equivalent number of atoms.
We will calculate the number of atoms for each option provided.

#### Option 1: 24g of Magnesium
- Molecular Weight of Magnesium = 24 g/mol
\[ \text{Number of moles of magnesium} = \frac{24 \, \text{g}}{24 \, \text{g/mol}} = 1 \, \text{mole} \]
\[ \text{Number of atoms} = 1 \, \text{mole} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms} \]

#### Option 2: 12g of Carbon
- Molecular Weight of Carbon = 12 g/mol
\[ \text{Number of moles of carbon} = \frac{12 \, \text{g}}{12 \, \text{g/mol}} = 1 \, \text{mole} \]
\[ \text{Number of atoms} = 1 \, \text{mole} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 6.022 \times 10^{23} \, \text{atoms} \]

#### Option 3: 8g of Oxygen Gas (O2)
- Molecular Weight of Oxygen (O2) = 32 g/mol
\[ \text{Number of moles of O2} = \frac{8 \, \text{g}}{32 \, \text{g/mol}} = 0.25 \, \text{moles} \]
Since O2 contains 2 oxygen atoms:
\[ \text{Number of moles of oxygen atoms} = 0.25 \, \text{moles} \times 2 = 0.5 \, \text{moles} \]
\[ \text{Number of atoms} = 0.5 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 3.011 \times 10^{23} \, \text{atoms} \]

#### Option 4: 16g of Sulfur
- Molecular Weight of Sulfur = 32 g/mol
\[ \text{Number of moles of sulfur} = \frac{16 \, \text{g}}{32 \, \text{g/mol}} = 0.5 \, \text{moles} \]
\[ \text{Number of atoms} = 0.5 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} = 3.011 \times 10^{23} \, \text{atoms} \]

### Conclusion:
From our calculations, we find that 8g of oxygen gas (O2) and 16g of sulfur both contain the same number of atoms as 20g of calcium, which is \(3.011 \times 10^{23}\) atoms.