Number of unit cells in 10 g NaCl

Options

A. `(1.5)/(58.5)xx10^(24)`
B. `(2.5)/(58.5)xx10^(23)`
C. `(5.6)/(58.5)xx10^(20)`
D. `(5.6)/(58.5)xx10^(21)`

Answer

To find the number of unit cells in 10 g of NaCl, we can follow these steps:

### Step 1: Calculate the number of moles of NaCl
The formula to calculate the number of moles is:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molar weight}} \]
Here, the given weight of NaCl is 10 g and the molar weight of NaCl is 58.5 g/mol. Therefore:
\[ \text{Number of moles} = \frac{10 \, \text{g}}{58.5 \, \text{g/mol}} \approx 0.171 \, \text{moles} \]

### Step 2: Calculate the number of formula units (molecules) in 10 g of NaCl
Using Avogadro's number (\(N_A = 6.022 \times 10^{23}\) molecules/mol), we can find the total number of molecules:
\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 0.171 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} \]
Calculating this gives:
\[ \text{Number of molecules} \approx 1.030 \times 10^{23} \, \text{molecules} \]

### Step 3: Determine the number of unit cells
In NaCl, there are 4 formula units (molecules) per unit cell. Therefore, to find the number of unit cells, we divide the total number of molecules by the number of molecules per unit cell:
\[ \text{Number of unit cells} = \frac{\text{Number of molecules}}{\text{Molecules per unit cell}} = \frac{1.030 \times 10^{23} \, \text{molecules}}{4} \]
Calculating this gives:
\[ \text{Number of unit cells} \approx 2.575 \times 10^{22} \, \text{unit cells} \]

### Final Answer
The number of unit cells in 10 g of NaCl is approximately \(2.575 \times 10^{22}\).

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