The chlorine end of the chlorine monoxide radical carries a charge of `+0.167e`. The bond length is 154.6 pm. Calculate the dipole moment of the radical in Debye units.

Options

A. 2.35 D
B. 1.24 D
C. 1.59 D
D. 2.05 D

Answer

To calculate the dipole moment of the chlorine monoxide radical, we will follow these steps:

### Step 1: Convert the charge from electrons to ESU
The charge on the chlorine end of the chlorine monoxide radical is given as \( +0.167e \). We know that the charge of one electron is approximately \( 4.80 \times 10^{-10} \) ESU. Therefore, we can calculate the charge in ESU as follows:

\[ \text{Charge in ESU} = 0.167 \times 4.80 \times 10^{-10} \, \text{ESU} \]

### Step 2: Calculate the bond length in centimeters
The bond length is given as \( 154.6 \, \text{pm} \) (picometers). We need to convert this to centimeters. Since \( 1 \, \text{pm} = 10^{-12} \, \text{m} \) and \( 1 \, \text{m} = 100 \, \text{cm} \), we can convert picometers to centimeters:

\[ \text{Bond length in cm} = 154.6 \times 10^{-12} \, \text{m} \times \frac{100 \, \text{cm}}{1 \, \text{m}} = 154.6 \times 10^{-10} \, \text{cm} \]

### Step 3: Calculate the dipole moment in ESU cm
The dipole moment (\( \mu \)) is calculated using the formula:

\[ \mu = \text{Charge} \times \text{Distance} \]

Substituting the values we have:

\[ \mu = (0.167 \times 4.80 \times 10^{-10} \, \text{ESU}) \times (154.6 \times 10^{-10} \, \text{cm}) \]

### Step 4: Simplify the calculation
Now we perform the multiplication:

\[ \mu = 0.167 \times 4.80 \times 154.6 \times 10^{-20} \, \text{ESU cm} \]

Calculating this gives:

\[ \mu \approx 123.92 \times 10^{-20} \, \text{ESU cm} \]

### Step 5: Convert the dipole moment to Debye
To convert the dipole moment from ESU cm to Debye, we use the conversion factor \( 1 \, \text{Debye} = 10^{-18} \, \text{ESU cm} \):

\[ \text{Dipole moment in Debye} = \frac{123.92 \times 10^{-20} \, \text{ESU cm}}{10^{-18} \, \text{ESU cm/Debye}} = 123.92 \times 10^{-2} \, \text{Debye} \]

This simplifies to:

\[ \text{Dipole moment in Debye} \approx 1.2392 \, \text{Debye} \]

### Step 6: Round to appropriate significant figures
Rounding to three significant figures gives us:

\[ \text{Dipole moment} \approx 1.24 \, \text{Debye} \]

### Final Answer
Thus, the dipole moment of the chlorine monoxide radical is approximately **1.24 Debye**.

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