How many unit cell are present in a cubic-shaped ideal crystal of `NaCl` of mass `1.0 g`?

Options

A. `2.57xx10^(21)`
B. `5.14xx10^(21)`
C. `1.28xx10^(21)`
D. `1.71xx10^(21)`

Explanation

To determine how many unit cells are present in a cubic-shaped ideal crystal of NaCl with a mass of 1.0 g, we can follow these steps:

### Step 1: Calculate the number of moles of NaCl
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]
The molar mass of NaCl (sodium chloride) is approximately 58.5 g/mol. Given that the mass of NaCl is 1.0 g, we can calculate the number of moles:
\[ \text{Number of moles} = \frac{1.0 \, \text{g}}{58.5 \, \text{g/mol}} \approx 0.0171 \, \text{mol} \]

### Step 2: Calculate the number of NaCl formula units
Using Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol, we can find the total number of NaCl formula units:
\[ \text{Number of NaCl units} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of NaCl units} = 0.0171 \, \text{mol} \times 6.022 \times 10^{23} \, \text{units/mol} \approx 1.03 \times 10^{22} \, \text{units} \]

### Step 3: Determine the number of unit cells
In each unit cell of NaCl, there are 4 NaCl formula units. Therefore, to find the number of unit cells, we divide the total number of NaCl units by the number of units per cell:
\[ \text{Number of unit cells} = \frac{\text{Number of NaCl units}}{\text{Number of units per cell}} \]
\[ \text{Number of unit cells} = \frac{1.03 \times 10^{22} \, \text{units}}{4} \approx 2.57 \times 10^{21} \, \text{unit cells} \]

### Final Answer
The number of unit cells present in a cubic-shaped ideal crystal of NaCl of mass 1.0 g is approximately \(2.57 \times 10^{21}\).

---