Aluminium having atomic mass 27 g/mol crystallizes in face centered packed cubic crystal. Find the number of Al atoms in 10g aluminium. How many unit cells will be present in it?
Understand the Problem
The question asks us to find the number of aluminum (Al) atoms in 10 grams of aluminum and how many unit cells will be present, given that aluminum has an atomic mass of 27 g/mol and it crystallizes in a face-centered cubic structure.
Answer
The number of aluminum atoms in 10 grams is approximately $2.23 \times 10^{23}$, and the number of unit cells is approximately $5.57 \times 10^{22}$.
Answer for screen readers
The number of aluminum atoms in 10 grams of aluminum is approximately $2.23 \times 10^{23}$ atoms, and the number of unit cells is approximately $5.57 \times 10^{22}$ unit cells.
Steps to Solve
- Calculate Moles of Aluminum To find the number of moles of aluminum in 10 grams, use the formula: $$ \text{Moles} = \frac{\text{mass (grams)}}{\text{molar mass (g/mol)}} $$ Here, the molar mass of aluminum is 27 g/mol.
Calculating: $$ \text{Moles} = \frac{10 , \text{g}}{27 , \text{g/mol}} \approx 0.3704 , \text{mol} $$
- Determine Number of Atoms To find the number of atoms, apply Avogadro's number, which is approximately $6.022 \times 10^{23} , \text{atoms/mol}$. The formula is: $$ \text{Number of atoms} = \text{Moles} \times \text{Avogadro's Number} $$
Calculating: $$ \text{Number of atoms} = 0.3704 , \text{mol} \times 6.022 \times 10^{23} , \text{atoms/mol} \approx 2.23 \times 10^{23} \text{ atoms} $$
- Calculate Number of Unit Cells In a face-centered cubic (FCC) structure, there are 4 atoms per unit cell. To find the number of unit cells: $$ \text{Number of unit cells} = \frac{\text{Number of atoms}}{4} $$
Calculating: $$ \text{Number of unit cells} = \frac{2.23 \times 10^{23}}{4} \approx 5.57 \times 10^{22} \text{ unit cells} $$
The number of aluminum atoms in 10 grams of aluminum is approximately $2.23 \times 10^{23}$ atoms, and the number of unit cells is approximately $5.57 \times 10^{22}$ unit cells.
More Information
Aluminum is commonly used in various applications due to its lightweight and corrosion-resistant properties. The face-centered cubic structure allows for a high packing efficiency.
Tips
- Forgetting to convert grams to moles correctly using the molar mass.
- Misapplying Avogadro's number; it should always be used with the amount in moles.
- Not considering the number of atoms per unit cell in an FCC structure, which is 4.
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