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 determine the number of unit cells in 10 g of NaCl, we will follow these steps:

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

**Calculation:**
\[ \text{Molar mass of NaCl} = 23 + 35.5 = 58.5 \, \text{g/mol} \]

### Step 2: Calculate the number of moles of NaCl in 10 g
Using the molar mass, we can find the number of moles of NaCl in 10 g.

**Calculation:**
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{10 \, \text{g}}{58.5 \, \text{g/mol}} \]

\[ \text{Number of moles} = 0.171 \, \text{mol} \]

### Step 3: Calculate the number of formula units in NaCl
Since each mole of NaCl contains Avogadro's number of formula units (approximately \(6.022 \times 10^{23}\)), we can calculate the total number of formula units in 0.171 moles.

**Calculation:**
\[ \text{Number of formula units} = \text{Number of moles} \times \text{Avogadro's number} \]

\[ \text{Number of formula units} = 0.171 \, \text{mol} \times 6.022 \times 10^{23} \, \text{units/mol} \]

\[ \text{Number of formula units} \approx 1.03 \times 10^{23} \]

### Step 4: Determine the number of unit cells
In NaCl, the number of formula units corresponds to the number of unit cells, since each unit cell contains one formula unit of NaCl.

Thus, the number of unit cells in 10 g of NaCl is approximately \(1.03 \times 10^{23}\).

### Final Answer:
The number of unit cells in 10 g of NaCl is approximately \(1.03 \times 10^{23}\).

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