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

Options

A. `6xx10^(20)`
B. `1.5xx10^(23)`
C. `6xx106(23)`
D. `0.5xx10^(23)`

Answer

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

### Step 1: Calculate the molar mass of NaCl
The molar mass of NaCl can be calculated by adding the atomic masses of sodium (Na) and chlorine (Cl):
- Atomic mass of Na = 23 g/mol
- Atomic mass of Cl = 35.5 g/mol
- Molar mass of NaCl = 23 + 35.5 = 58.5 g/mol

**Hint:** Remember that the molar mass is the mass of one mole of a substance, which is the sum of the atomic masses of its constituent elements.

### Step 2: Calculate the number of moles of NaCl in 58.5 g
Using the molar mass calculated in Step 1:
- Number of moles = mass (g) / molar mass (g/mol)
- Number of moles of NaCl = 58.5 g / 58.5 g/mol = 1 mole

**Hint:** The number of moles tells us how many times the molar mass fits into the given mass.

### Step 3: Use Avogadro's number to find the number of formula units
Avogadro's number (N_A) is approximately \(6.022 \times 10^{23}\) units/mol. Therefore, the number of formula units in 1 mole of NaCl is:
- Number of formula units = 1 mole × \(6.022 \times 10^{23}\) units/mole = \(6.022 \times 10^{23}\) formula units

**Hint:** Avogadro's number is a constant that relates the number of particles to the amount of substance in moles.

### Step 4: Determine the number of unit cells
In a face-centered cubic (FCC) structure 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:
- Number of unit cells = Total formula units / Formula units per unit cell
- Number of unit cells = \(6.022 \times 10^{23}\) formula units / 4 = \(1.5055 \times 10^{23}\) unit cells

**Hint:** The structure of the crystal lattice determines how many formula units are present in each unit cell.

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