A quantity of aluminium has a mass of 54 g. What is the mass of same number of magnesium atoms?

Options

A. `12.1g`
B. `24.3g`
C. `48.6g`
D. `97.2g`

Explanation

To find the mass of magnesium that has the same number of atoms as 54 g of aluminum, we can follow these steps:

### Step 1: Determine the number of moles of aluminum
To find the number of moles of aluminum, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of aluminum (Al) is approximately 27 g/mol. Therefore, for 54 g of aluminum:
\[ \text{Number of moles of Al} = \frac{54 \text{ g}}{27 \text{ g/mol}} = 2 \text{ moles} \]

### Step 2: Calculate the number of atoms of aluminum
Using Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mol, we can find the number of aluminum atoms:
\[ \text{Number of atoms of Al} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of atoms of Al} = 2 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} = 1.2044 \times 10^{24} \text{ atoms} \]

### Step 3: Determine the number of moles of magnesium
Since we want the same number of magnesium atoms, we will also have \(1.2044 \times 10^{24}\) magnesium atoms. We can find the number of moles of magnesium (Mg) using Avogadro's number:
\[ \text{Number of moles of Mg} = \frac{\text{Number of atoms of Mg}}{\text{Avogadro's number}} = \frac{1.2044 \times 10^{24} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} = 2 \text{ moles} \]

### Step 4: Calculate the mass of magnesium
Now, we can find the mass of magnesium using its molar mass, which is approximately 24.3 g/mol:
\[ \text{Mass of Mg} = \text{Number of moles} \times \text{molar mass} \]
\[ \text{Mass of Mg} = 2 \text{ moles} \times 24.3 \text{ g/mol} = 48.6 \text{ g} \]

### Final Answer
The mass of magnesium that has the same number of atoms as 54 g of aluminum is **48.6 g**.

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