Co-ordination number (CN) of barium ion `(Ba^(2+))` in `BaF_(2)` is 8. What is the CN of `F^(-)` ion ?

Explanation

To determine the coordination number (CN) of the fluoride ion (F⁻) in barium fluoride (BaF₂), we can follow these steps:

### Step 1: Understand Coordination Number
The coordination number of an ion in a compound refers to the number of nearest neighboring ions that surround it. In this case, we know that the coordination number of the barium ion (Ba²⁺) is 8. This means that each barium ion is surrounded by 8 fluoride ions.

### Step 2: Analyze the Charge Balance
Since each fluoride ion has a charge of -1, the total negative charge contributed by the 8 fluoride ions surrounding the barium ion is:
\[ \text{Total negative charge} = 8 \times (-1) = -8 \]

### Step 3: Determine the Required Positive Charge
To maintain charge neutrality in the compound, the total positive charge from the barium ions must balance the total negative charge from the fluoride ions. Given that each barium ion has a charge of +2, we can calculate how many barium ions are needed to balance the -8 charge:
\[ \text{Let } n \text{ be the number of barium ions.} \]
The total positive charge from the barium ions is:
\[ \text{Total positive charge} = n \times (+2) = +2n \]
Setting the total positive charge equal to the total negative charge for charge balance:
\[ 2n = 8 \]
Solving for \( n \):
\[ n = \frac{8}{2} = 4 \]
This means we need 4 barium ions to balance the charge contributed by the 8 fluoride ions.

### Step 4: Determine the Coordination Number of Fluoride Ion
Now, since each barium ion is surrounded by 8 fluoride ions, and we have established that there are 4 barium ions, we can determine the coordination number of the fluoride ion. Each fluoride ion is shared among the barium ions.

Given that there are 8 fluoride ions surrounding 4 barium ions, the coordination number of the fluoride ion can be calculated as:
\[ \text{Coordination number of F}^- = \frac{\text{Total number of F}^- \text{ ions}}{\text{Number of Ba}^{2+} \text{ ions}} = \frac{8}{4} = 2 \]

However, since each F⁻ ion is coordinated to multiple Ba²⁺ ions, we need to consider the arrangement. In the structure of BaF₂, each F⁻ ion is typically surrounded by 4 Ba²⁺ ions.

Thus, the coordination number of the fluoride ion (F⁻) is:
\[ \text{Coordination number of F}^- = 4 \]

### Final Answer
The coordination number of the fluoride ion (F⁻) in BaF₂ is **4**.

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