The number of unit cells in `58.5 g` of `NaCl` is nearly

Options

A. `6 xx 10^(20)`
B. `3 xx 10^(22)`
C. `1.5 xx 10^(23)`
D. `0.5 xx 10^(24)`

Explanation

To find the number of unit cells in 58.5 g of NaCl, we can follow these steps:

### Step 1: Calculate the number of moles of NaCl
The molar mass of NaCl (sodium chloride) is calculated as follows:
- Molar mass of Na (sodium) = 23 g/mol
- Molar mass of Cl (chlorine) = 35.5 g/mol
- Therefore, molar mass of NaCl = 23 g/mol + 35.5 g/mol = 58.5 g/mol

Now, we can calculate the number of moles in 58.5 g of NaCl:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{58.5 \text{ g}}{58.5 \text{ g/mol}} = 1 \text{ mole} \]

### Step 2: Use Avogadro's number to find the number of formula units
Avogadro's number (Na) is approximately \(6.022 \times 10^{23}\) entities (atoms, molecules, or formula units) per mole. Since we have 1 mole of NaCl:
\[ \text{Number of formula units} = 1 \text{ mole} \times 6.022 \times 10^{23} \text{ units/mole} = 6.022 \times 10^{23} \text{ units} \]

### Step 3: Determine the number of unit cells
In the case of NaCl, each unit cell contains 4 formula units of NaCl. Therefore, to find the number of unit cells, we divide the total number of formula units by the number of formula units per unit cell:
\[ \text{Number of unit cells} = \frac{\text{Number of formula units}}{\text{Number of formula units per unit cell}} = \frac{6.022 \times 10^{23}}{4} = 1.5055 \times 10^{23} \]

### Conclusion
Rounding this to two significant figures, we find that the number of unit cells in 58.5 g of NaCl is approximately:
\[ \text{Number of unit cells} \approx 1.5 \times 10^{23} \]

### Final Answer
The number of unit cells in 58.5 g of NaCl is nearly \(1.5 \times 10^{23}\).

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