Polar covalent molecules exhibit dipole moment. Dipole moment is equal to the product of charge separation , q and the bond length d for the bond. Unit of dipole moment is debye. One debye is equal to `10^(-18)` esu cm.
Dipole moments is a vector quantity. It has both magnitude and direction. Hence, dipole moment of a molecule depends upon the relative orientation of the bond dipoles, but not on the polarity of bonds alone. A symmetrical structure shows zero dipole moment. Thus, dipole moment helps to predict the geometry of a molecules. Dipole moment values can be distinguish between cis- and trans- isomers, ortho, meta and pare-forms of a substance, etc.
Q. A diatomic molecule has a dipole moment of 1.2D. If the bond length is `1.0times10^(-8)` cm, what fraction of charge does exist each atom?

Options

A. `0.1`
B. `0.2`
C. `0.25`
D. `0.3`

Explanation

To solve the problem, we need to find the fraction of charge that exists on each atom of a diatomic molecule with a given dipole moment and bond length. Here’s a step-by-step solution:

### Step 1: Understand the relationship between dipole moment, charge, and bond length
The dipole moment (\( \mu \)) is given by the formula:
\[ \mu = q \cdot d \]
where:
- \( \mu \) is the dipole moment,
- \( q \) is the charge separation,
- \( d \) is the bond length.

### Step 2: Convert the dipole moment from Debye to esu cm
Given that the dipole moment is \( 1.2 \, D \) and \( 1 \, D = 10^{-18} \, \text{esu cm} \), we convert it:
\[ \mu = 1.2 \, D = 1.2 \times 10^{-18} \, \text{esu cm} \]

### Step 3: Use the bond length
The bond length is given as:
\[ d = 1.0 \times 10^{-8} \, \text{cm} \]

### Step 4: Rearrange the dipole moment formula to find charge \( q \)
We can rearrange the formula to solve for \( q \):
\[ q = \frac{\mu}{d} \]

### Step 5: Substitute the values into the formula
Substituting the known values into the equation:
\[ q = \frac{1.2 \times 10^{-18} \, \text{esu cm}}{1.0 \times 10^{-8} \, \text{cm}} = 1.2 \times 10^{-10} \, \text{esu} \]

### Step 6: Calculate the fraction of charge on each atom
The charge of a single electron is approximately \( 4.8 \times 10^{-10} \, \text{esu} \). To find the fraction of charge on each atom, we divide the charge \( q \) by the charge of an electron:
\[ \text{Fraction of charge on each atom} = \frac{q}{\text{Charge of electron}} = \frac{1.2 \times 10^{-10} \, \text{esu}}{4.8 \times 10^{-10} \, \text{esu}} = 0.25 \]

### Conclusion
Thus, the fraction of charge that exists on each atom is \( 0.25 \) or \( 25\% \).

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