Find the number of atoms of each type in 0.5 mole of aluminium sulphate.

Options

A. `{:("Al","S","O"),(3.01 xx 10^(23),12.046 xx 10^(23) ,1.8069 xx 10^(24)):}`
B. `{:("Al","S","O"),(6.023 xx 10^(23),9.033 xx10^(23), 3.6138 xx 10^(24)):}`
C. `{:("Al","S","O"),(3.01 xx 10^(23),9.033 xx 10^(23), 12.046 xx 10^(23)):}`
D. `{:("Al","S","O"),(6.023 xx 10^(23),9.033 xx 10^(23),3.6138 xx10^(23)):}`

Answer

To find the number of atoms of each type in 0.5 moles of aluminum sulfate (Al₂(SO₄)₃), we can follow these steps:

### Step 1: Identify the formula of aluminum sulfate
The chemical formula for aluminum sulfate is Al₂(SO₄)₃. This indicates that there are:
- 2 aluminum (Al) atoms
- 3 sulfate (SO₄) groups

### Step 2: Determine the number of atoms in one formula unit
From the formula Al₂(SO₄)₃, we can derive the total number of atoms:
- Each sulfate group (SO₄) contains 1 sulfur (S) atom and 4 oxygen (O) atoms. Therefore, for 3 sulfate groups:
- Sulfur: 3 S atoms
- Oxygen: 3 × 4 = 12 O atoms

So, in one formula unit of aluminum sulfate, we have:
- 2 Al atoms
- 3 S atoms
- 12 O atoms

### Step 3: Calculate the number of atoms in 0.5 moles
Using Avogadro's number (6.022 × 10²³), we can calculate the number of atoms for each type in 0.5 moles.

1. **Aluminum (Al)**:
\[ \text{Number of Al atoms} = 2 \, \text{(atoms per formula unit)} \times 0.5 \, \text{(moles)} \times 6.022 \times 10^{23} \, \text{(atoms/mole)} \]
\[ = 2 \times 0.5 \times 6.022 \times 10^{23} = 6.022 \times 10^{23} \, \text{Al atoms} \]

2. **Sulfur (S)**:
\[ \text{Number of S atoms} = 3 \, \text{(atoms per formula unit)} \times 0.5 \, \text{(moles)} \times 6.022 \times 10^{23} \, \text{(atoms/mole)} \]
\[ = 3 \times 0.5 \times 6.022 \times 10^{23} = 9.033 \times 10^{23} \, \text{S atoms} \]

3. **Oxygen (O)**:
\[ \text{Number of O atoms} = 12 \, \text{(atoms per formula unit)} \times 0.5 \, \text{(moles)} \times 6.022 \times 10^{23} \, \text{(atoms/mole)} \]
\[ = 12 \times 0.5 \times 6.022 \times 10^{23} = 3.633 \times 10^{24} \, \text{O atoms} \]

### Summary of Results
- Number of Al atoms: \( 6.022 \times 10^{23} \)
- Number of S atoms: \( 9.033 \times 10^{23} \)
- Number of O atoms: \( 3.633 \times 10^{24} \)