The mass of unit cell of `CaF_(2)` (fluorite structure) corresponds to

Options

A. mass of `8Ca^(+2)` ions & `4 F^(-)` ions
B. mass of `4 Ca^( +2)` ions & `8 F^(-)` ions
C. mass of `4Ca^(+2)` ions & `4 F^(-)` ions
D. mass of `1Ca^(+2)` ions & `2 F^(-)` ions

Answer

To determine the mass of the unit cell of \( \text{CaF}_2 \) (fluorite structure), we can follow these steps:

### Step 1: Identify the Composition of the Unit Cell
In the fluorite structure of \( \text{CaF}_2 \), there are:
- 1 Calcium ion (\( \text{Ca}^{2+} \)) for every 2 Fluoride ions (\( \text{F}^- \)).
- Therefore, in one unit cell, there are 4 Calcium ions and 8 Fluoride ions.

### Step 2: Calculate the Molar Mass of Each Ion
- The molar mass of Calcium (\( \text{Ca} \)) is approximately \( 40.08 \, \text{g/mol} \).
- The molar mass of Fluoride (\( \text{F} \)) is approximately \( 19.00 \, \text{g/mol} \).

### Step 3: Calculate the Total Mass of the Ions in the Unit Cell
- For Calcium:
\[ \text{Mass of 4 Ca}^{2+} = 4 \times 40.08 \, \text{g/mol} = 160.32 \, \text{g/mol} \]

- For Fluoride:
\[ \text{Mass of 8 F}^{-} = 8 \times 19.00 \, \text{g/mol} = 152.00 \, \text{g/mol} \]

### Step 4: Add the Masses Together
Now, we can find the total mass of the unit cell:
\[ \text{Total mass of unit cell} = \text{Mass of 4 Ca}^{2+} + \text{Mass of 8 F}^{-} \]
\[ \text{Total mass of unit cell} = 160.32 \, \text{g/mol} + 152.00 \, \text{g/mol} = 312.32 \, \text{g/mol} \]

### Conclusion
The mass of the unit cell of \( \text{CaF}_2 \) corresponds to \( 312.32 \, \text{g/mol} \).

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