Calculate the number of aluminium ions present in 0.051 g of aluminium oxide.
(Hint: The mass of an ion is the same as that of an atom of the same element. Atomic mass of Al = 27 u)

Explanation

To calculate the number of aluminium ions present in 0.051 g of aluminium oxide (Al₂O₃), we can follow these steps:

### Step 1: Determine the molecular mass of aluminium oxide (Al₂O₃)
- The molecular mass of Al₂O₃ can be calculated using the atomic masses of aluminium (Al) and oxygen (O).
- Atomic mass of Al = 27 g/mol
- Atomic mass of O = 16 g/mol
- Since there are 2 Al atoms and 3 O atoms in Al₂O₃, the molecular mass is calculated as:

\[ \text{Molecular mass of Al₂O₃} = (2 \times 27) + (3 \times 16) = 54 + 48 = 102 \text{ g/mol} \]

### Step 2: Use the mole concept to find the number of moles of Al₂O₃ in 0.051 g
- The number of moles of a substance is given by the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

- For Al₂O₃:

\[ \text{Number of moles of Al₂O₃} = \frac{0.051 \text{ g}}{102 \text{ g/mol}} \approx 0.0005 \text{ moles} \]

### Step 3: Calculate the number of molecules of Al₂O₃
- Using Avogadro's number (6.022 × 10²³ molecules/mol), we can find the number of molecules:

\[ \text{Number of molecules of Al₂O₃} = 0.0005 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 3.011 \times 10^{20} \text{ molecules} \]

### Step 4: Determine the number of aluminium ions in Al₂O₃
- Each molecule of Al₂O₃ contains 2 aluminium ions (Al³⁺). Therefore, the total number of aluminium ions is:

\[ \text{Number of Al³⁺ ions} = 2 \times \text{Number of molecules of Al₂O₃} = 2 \times 3.011 \times 10^{20} \approx 6.022 \times 10^{20} \text{ ions} \]

### Final Answer
The number of aluminium ions present in 0.051 g of aluminium oxide is approximately \(6.022 \times 10^{20}\) ions.

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