If the dipole moment of HCl is 1.08 D and the bond distance is `1.27Å`, the partial charge on hydrogen and chlorine , respectively are

Options

A. `+1.0 and -1.0`
B. `+.85 and -.85`
C. `+0.356 and -0.356`
D. `+0.177 and -0.177`

Answer

To find the partial charges on hydrogen and chlorine in HCl, we can use the dipole moment formula and the given values. Here’s a step-by-step solution:

### Step 1: Understand the Dipole Moment
The dipole moment (μ) is given by the formula:
\[ \mu = Q \times D \]
where:
- \( \mu \) is the dipole moment,
- \( Q \) is the partial charge,
- \( D \) is the bond distance.

### Step 2: Convert Units
We need to convert the bond distance from angstroms to meters:
\[ 1 \text{ Å} = 10^{-10} \text{ m} \]
Thus,
\[ D = 1.27 \text{ Å} = 1.27 \times 10^{-10} \text{ m} \]

### Step 3: Convert Dipole Moment to SI Units
The dipole moment is given as 1.08 D. We need to convert this to coulomb-meters:
Using the conversion:
\[ 1 \text{ D} = 3.34 \times 10^{-29} \text{ C m} \]
So,
\[ \mu = 1.08 \text{ D} = 1.08 \times 3.34 \times 10^{-29} \text{ C m} \]
Calculating this gives:
\[ \mu = 3.6072 \times 10^{-29} \text{ C m} \]

### Step 4: Rearrange the Dipole Moment Formula
Now, we can rearrange the dipole moment formula to solve for the partial charge \( Q \):
\[ Q = \frac{\mu}{D} \]

### Step 5: Substitute the Values
Substituting the values we have:
\[ Q = \frac{3.6072 \times 10^{-29} \text{ C m}}{1.27 \times 10^{-10} \text{ m}} \]

### Step 6: Calculate the Partial Charge
Calculating this gives:
\[ Q = 2.838 \times 10^{-19} \text{ C} \]

### Step 7: Find the Fractional Charge
To find the fractional charge, we can compare it to the charge of an electron, which is:
\[ e = 1.6 \times 10^{-19} \text{ C} \]
Thus, the fractional charge is:
\[ \text{Fractional Charge} = \frac{Q}{e} = \frac{2.838 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 0.177 \]

### Final Result
The partial charges on hydrogen and chlorine are:
- Partial charge on Hydrogen (H): \( +0.177e \)
- Partial charge on Chlorine (Cl): \( -0.177e \)