If the density of crystalline CsCI is 3.988 `g cm^-3` , calculate the volume effectively occupied by a single CsCl ion pair in the crystal ( CsCl = 168.4 )`

Options

A. `7.01 * 10^(-23) cm^3`
B. `6.02 * 10^(-24) cm^3`
C. `1 cm^3`
D. `3.5 * 10^(-23) cm^3`

Answer

To calculate the volume effectively occupied by a single CsCl ion pair in the crystal, we will follow these steps:

### Step 1: Identify the given data
- Density of CsCl (ρ) = 3.988 g/cm³
- Molar mass of CsCl (M) = 168.4 g/mol
- Avogadro's number (Nₐ) = 6.022 × 10²³ mol⁻¹

### Step 2: Calculate the volume of 1 mole of CsCl
Using the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
Rearranging the formula to find volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]
Substituting the values:
\[ \text{Volume of 1 mole of CsCl} = \frac{168.4 \, \text{g}}{3.988 \, \text{g/cm}^3} \]

### Step 3: Perform the calculation
Calculating the volume:
\[ \text{Volume} = \frac{168.4}{3.988} \approx 42.24 \, \text{cm}^3 \]

### Step 4: Calculate the volume occupied by a single CsCl ion pair
To find the volume occupied by a single ion pair, we divide the volume of 1 mole by Avogadro's number:
\[ \text{Volume per ion pair} = \frac{\text{Volume of 1 mole}}{Nₐ} = \frac{42.24 \, \text{cm}^3}{6.022 \times 10^{23}} \]

### Step 5: Perform the final calculation
Calculating the volume per ion pair:
\[ \text{Volume per ion pair} \approx \frac{42.24}{6.022 \times 10^{23}} \approx 7.01 \times 10^{-23} \, \text{cm}^3 \]

### Final Answer
The volume effectively occupied by a single CsCl ion pair in the crystal is approximately \( 7.01 \times 10^{-23} \, \text{cm}^3 \).

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