Calculate the dipole moment of HCl given that the bond length is 1.27 Å and the

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Question: Calculate the dipole moment of HCl given that the bond length is 1.27 Å and the charge separation is 0.33 e.

Options:

Correct Answer: 1.1 D

Solution:

Dipole moment (μ) = charge (q) × distance (d). μ = 0.33 e × 1.27 × 10^-10 m = 4.2 × 10^-29 C·m = 1.1 D.

Calculate the dipole moment of HCl given that the bond length is 1.27 Å and the charge separation is 0.33 e.

Calculate the dipole moment of HCl given that the bond length is 1.27 Å and the charge separation is 0.33 e.

Step 1: Understand the formula for dipole moment, which is μ = q × d, where μ is the dipole moment, q is the charge, and d is the distance.
Step 2: Identify the values given in the question. The charge separation (q) is 0.33 e and the bond length (d) is 1.27 Å.
Step 3: Convert the bond length from Ångströms to meters. 1 Å = 1 × 10^-10 m, so 1.27 Å = 1.27 × 10^-10 m.
Step 4: Convert the charge from elementary charge (e) to coulombs. The elementary charge e is approximately 1.6 × 10^-19 C, so 0.33 e = 0.33 × 1.6 × 10^-19 C.
Step 5: Calculate the charge in coulombs: 0.33 × 1.6 = 0.528, so 0.33 e = 0.528 × 10^-19 C.
Step 6: Now, use the dipole moment formula: μ = q × d = (0.528 × 10^-19 C) × (1.27 × 10^-10 m).
Step 7: Perform the multiplication: μ = 0.528 × 1.27 × 10^-29 C·m.
Step 8: Calculate the result: μ ≈ 4.2 × 10^-29 C·m.
Step 9: Convert the dipole moment from C·m to Debye (D). 1 D = 3.336 × 10^-29 C·m, so μ in D = (4.2 × 10^-29 C·m) / (3.336 × 10^-29 C·m/D).
Step 10: Calculate the final result: μ ≈ 1.1 D.

Dipole Moment Calculation – The dipole moment is calculated using the formula μ = q × d, where q is the charge separation and d is the bond length.
Unit Conversion – Understanding the conversion of charge from elementary charge (e) to coulombs and the bond length from angstroms to meters.