The number of units cells in 17.0 grams of NaCl is approximately

Options

A. `12 xx 10^(20)`
B. `3 xx 10^(23)`
C. `6 xx 10^(23)`
D. `1 xx 10^(24)`

Answer

To find the number of unit cells in 17.0 grams of NaCl, we can follow these steps:

### Step 1: Calculate the number of moles of NaCl
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Given:
- Mass of NaCl = 17.0 grams
- Molar mass of NaCl = Molar mass of Na (23 g/mol) + Molar mass of Cl (35.5 g/mol) = 58.5 g/mol

Now, substituting the values:
\[ \text{Number of moles} = \frac{17.0 \text{ g}}{58.5 \text{ g/mol}} \approx 0.2905 \text{ moles} \]

### Step 2: Calculate the number of molecules
Using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol), we can find the total number of molecules:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of molecules} = 0.2905 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.747 \times 10^{23} \text{ molecules} \]

### Step 3: Determine the number of unit cells
In NaCl, the structure is face-centered cubic (FCC), which contains 4 formula units per unit cell. Therefore, to find the number of unit cells, we can use the formula:
\[ \text{Number of unit cells} = \frac{\text{Number of molecules}}{\text{Number of formula units per unit cell}} \]
Substituting the values:
\[ \text{Number of unit cells} = \frac{1.747 \times 10^{23} \text{ molecules}}{4} \approx 4.3675 \times 10^{22} \text{ unit cells} \]

### Step 4: Approximate the result
To express this in a more manageable form, we can round it:
\[ \text{Number of unit cells} \approx 0.43675 \times 10^{23} \approx 4.37 \times 10^{22} \text{ unit cells} \]

### Conclusion
The approximate number of unit cells in 17.0 grams of NaCl is \(4.37 \times 10^{22}\).