To solve the problem, we need to find the percentage of covalent character in a diatomic molecule given its dipole moment and bond distance. Let's break it down step by step:
### Step 1: Understand the Dipole Moment
The dipole moment (μ) is a measure of the polarity of a chemical bond and is given by the formula:
\[
\mu = q \times r
\]
where:
- \(q\) is the charge (in ESU),
- \(r\) is the bond distance (in cm).
### Step 2: Convert Given Values
We are given:
- Observed dipole moment (\(μ_{observed}\)) = 1.2 D
- Bond distance = 1 Å = \(1 \times 10^{-8}\) cm
We also know that:
1 Debye = \(10^{-18}\) ESU cm.
### Step 3: Calculate the Charge
We need to calculate the charge (\(q\)) using the observed dipole moment. First, we convert the observed dipole moment from Debye to ESU cm:
\[
μ_{observed} = 1.2 \, \text{D} = 1.2 \times 10^{-18} \, \text{ESU cm}
\]
### Step 4: Calculate the Charge Using the Dipole Moment Formula
Using the dipole moment formula, we can rearrange it to find \(q\):
\[
q = \frac{μ_{observed}}{r}
\]
Substituting the known values:
\[
q = \frac{1.2 \times 10^{-18} \, \text{ESU cm}}{1 \times 10^{-8} \, \text{cm}} = 1.2 \times 10^{-10} \, \text{ESU}
\]
### Step 5: Calculate the Theoretical Dipole Moment
Next, we calculate the theoretical (calculated) dipole moment (\(μ_{calculated}\)) using the charge of an electron (\(q_e = 4.8 \times 10^{-10} \, \text{ESU}\)):
\[
μ_{calculated} = q_e \times r = 4.8 \times 10^{-10} \, \text{ESU} \times 1 \times 10^{-8} \, \text{cm} = 4.8 \times 10^{-18} \, \text{ESU cm} = 4.8 \, \text{D}
\]
### Step 6: Calculate the Percentage of Covalent Character
Now, we can find the percentage of covalent character using the formula:
\[
\text{Percentage of Covalent Character} = \left( \frac{μ_{observed}}{μ_{calculated}} \right) \times 100
\]
Substituting the values:
\[
\text{Percentage of Covalent Character} = \left( \frac{1.2 \, \text{D}}{4.8 \, \text{D}} \right) \times 100 = 25\%
\]
### Step 7: Conclusion
Thus, the percentage of covalent character in the diatomic molecule is **25%**.
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