Question

How many tetrahedral voids are present in 0.4 mole of a compound that forms hcp structure?

• A. $4.8 \times 10^{23}$
• B. $3.011 \times 10^{23}$
• C. $1.2 \times 10^{23}$
• D. $2.4 \times 10^{23}$

Hint:

To solve this instantly without full calculation, remember that the total number of tetrahedral voids per mole is exactly $2 \times N_A \approx 12 \times 10^{23}$. Multiplying this straight by the given moles gives: $0.4 \times 12 \times 10^{23} = 4.8 \times 10^{23}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We are given the number of moles of a compound crystallizing in a hexagonal close-packed (hcp) structural lattice. We need to calculate the total number of tetrahedral voids contained within this sample size.

Step 2: Key Formula or Approach:
In any close-packed crystalline structure (hcp or ccp), if the total number of constituent atoms or lattice particles is $N$, then: $$\text{Number of octahedral voids} = N$$ $$\text{Number of tetrahedral voids} = 2N$$ The total number of particles can be found by multiplying the number of moles by Avogadro's constant ($N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}$).

Step 3: Detailed Explanation:
First, calculate the total number of constituent particles ($N$) present in $0.4\ \text{moles}$ of the compound: $$N = \text{Moles} \times N_A$$ $$N = 0.4 \times 6.022 \times 10^{23} = 2.4088 \times 10^{23}\ \text{particles}$$ Now, apply the structural relationship to find the total number of tetrahedral voids: $$\text{Number of tetrahedral voids} = 2N$$ $$\text{Number of tetrahedral voids} = 2 \times 2.4088 \times 10^{23} = 4.8176 \times 10^{23}$$ Rounding this to match the precision of the given choices yields $4.8 \times 10^{23}$.

Step 4: Final Answer:
The total number of tetrahedral voids is $4.8 \times 10^{23}$, which corresponds to option (A).