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The chlorine end of the chlorine monoxid...

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.

A

2.35 D

B

1.24 D

C

1.59 D

D

2.05 D

Text Solution

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The correct Answer is:
To calculate the dipole moment of the chlorine monoxide radical, we can follow these steps: ### Step 1: Identify the charge The charge on the chlorine end of the chlorine monoxide radical is given as \( +0.167e \), where \( e \) is the elementary charge. ### Step 2: Convert the charge to ESU The value of the elementary charge \( e \) is approximately \( 4.80 \times 10^{-10} \) ESU. Therefore, we can calculate the charge in ESU as follows: \[ \text{Charge} = 0.167 \times 4.80 \times 10^{-10} \text{ ESU} \] ### Step 3: Calculate the charge in ESU Calculating the above expression: \[ \text{Charge} = 0.167 \times 4.80 \times 10^{-10} = 8.016 \times 10^{-11} \text{ ESU} \] ### Step 4: Convert bond length to centimeters The bond length is given as \( 154.6 \) pm (picometers). We need to convert this to centimeters: \[ \text{Bond length} = 154.6 \text{ pm} = 154.6 \times 10^{-12} \text{ m} = 154.6 \times 10^{-10} \text{ cm} \] ### Step 5: Calculate the dipole moment The dipole moment \( \mu \) can be calculated using the formula: \[ \mu = \text{Charge} \times \text{Bond length} \] Substituting the values we have: \[ \mu = (8.016 \times 10^{-11} \text{ ESU}) \times (154.6 \times 10^{-10} \text{ cm}) \] ### Step 6: Perform the multiplication Calculating the dipole moment: \[ \mu = 8.016 \times 10^{-11} \times 154.6 \times 10^{-10} = 1.240 \times 10^{-20} \text{ ESU cm} \] ### Step 7: Convert dipole moment to Debye To convert the dipole moment from ESU cm to Debye, we use the conversion factor \( 1 \text{ Debye} = 10^{-18} \text{ ESU cm} \): \[ \mu = \frac{1.240 \times 10^{-20} \text{ ESU cm}}{10^{-18}} = 1.240 \times 10^{-2} \text{ Debye} \] ### Step 8: Final result Thus, the dipole moment in Debye is approximately: \[ \mu \approx 1.24 \text{ Debye} \]
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