The gaseous potassium chloride molecule has a measured dipole moment of `10.0D`, which indicates that it is a very polar molecule. The separation between the nuclei in this molecule is `2.67xx10^(-8)`cm. Calculate the percentage ionic character in KCl molecule.

Explanation

To calculate the percentage ionic character in the potassium chloride (KCl) molecule, we can follow these steps:

### Step 1: Identify the given data
- Measured dipole moment (μ_observed) = 10.0 D (Debye)
- Separation between the nuclei (l) = 2.67 x 10^(-8) cm

### Step 2: Convert the separation from cm to esu (electrostatic units)
We need to convert the length from cm to meters for calculations. Since 1 D = 3.336 x 10^(-29) C·m, we will use the conversion factor for dipole moments.

### Step 3: Calculate the calculated dipole moment (μ_calculated)
The formula for the calculated dipole moment is:
\[ \mu_{\text{calculated}} = q \cdot l \]
where:
- \( q \) = charge in esu (for KCl, we can use the charge of an electron, which is approximately \( 4.8 \times 10^{-10} \) esu)
- \( l \) = separation between the nuclei in cm

Substituting the values:
\[ \mu_{\text{calculated}} = 4.8 \times 10^{-10} \, \text{esu} \times 2.67 \times 10^{-8} \, \text{cm} \]
Now, we convert this to Debye:
\[ 1 \, \text{D} = 3.336 \times 10^{-29} \, \text{C·m} \]
Thus, we will convert the result from esu·cm to Debye.

### Step 4: Calculate the percentage ionic character
The formula for percentage ionic character is:
\[ \text{Percentage Ionic Character} = \left( \frac{\mu_{\text{observed}}}{\mu_{\text{calculated}}} \right) \times 100 \]

### Step 5: Perform the calculations
1. Calculate \( \mu_{\text{calculated}} \):
\[ \mu_{\text{calculated}} = 4.8 \times 10^{-10} \times 2.67 \times 10^{-8} = 1.28 \times 10^{-17} \, \text{esu·cm} \]
Convert to Debye:
\[ \mu_{\text{calculated}} = \frac{1.28 \times 10^{-17}}{3.336 \times 10^{-29}} \approx 12.2821 \, \text{D} \]

2. Now calculate the percentage ionic character:
\[ \text{Percentage Ionic Character} = \left( \frac{10.0}{12.2821} \right) \times 100 \approx 81.5\% \]

### Final Answer
The percentage ionic character in KCl is approximately **81.5%**.

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