The `H-O-H` bond angle in the water molecule is `105^@` , the`H -O` bond distance being `0.94 Å`, The dipole moment for the moelcule is `1.85D`. Calculate the charge on the oxygen atom .

Options

A. `2 xx 10^(-10)` esu
B. `3.28 xx 10^(-10)` esu
C. `3.21 xx 10^(-10)` esu
D. `1.602 xx 10^(-19)` esu

Answer

To calculate the charge on the oxygen atom in a water molecule (H₂O), we can follow these steps:

### Step 1: Understand the relationship between dipole moment, charge, and distance
The dipole moment (μ) is given by the formula:
\[ \mu = q \times d \]
where \( q \) is the charge and \( d \) is the distance between the charges.

### Step 2: Convert the given values to appropriate units
- The dipole moment is given as 1.85 D (Debye). To convert this to ESU cm:
\[ 1 \text{ D} = 3.3356 \times 10^{-30} \text{ C m} = 3.3356 \times 10^{-18} \text{ ESU cm} \]
Thus,
\[ \mu = 1.85 \text{ D} = 1.85 \times 3.3356 \times 10^{-18} \text{ ESU cm} \]
\[ \mu \approx 6.17 \times 10^{-18} \text{ ESU cm} \]

- The bond distance (H-O) is given as 0.94 Å. Convert this to cm:
\[ 0.94 \text{ Å} = 0.94 \times 10^{-8} \text{ cm} \]

### Step 3: Calculate the charge using the dipole moment formula
Using the dipole moment formula:
\[ \mu = q \times d \]
We can rearrange this to find the charge \( q \):
\[ q = \frac{\mu}{d} \]
Substituting the values we have:
\[ q = \frac{6.17 \times 10^{-18} \text{ ESU cm}}{0.94 \times 10^{-8} \text{ cm}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ q \approx \frac{6.17 \times 10^{-18}}{0.94 \times 10^{-8}} \]
\[ q \approx 6.57 \times 10^{-10} \text{ ESU} \]

### Step 5: Considering the two O-H bonds in H₂O
Since there are two O-H bonds in a water molecule, the total charge on the oxygen atom would be:
\[ \text{Total charge on O} = 2 \times q \]
Thus:
\[ \text{Total charge on O} = 2 \times 6.57 \times 10^{-10} \text{ ESU} \]
\[ \text{Total charge on O} \approx 1.314 \times 10^{-9} \text{ ESU} \]

### Final Answer
The charge on the oxygen atom in the water molecule is approximately \( 1.314 \times 10^{-9} \text{ ESU} \).

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