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Problem: Use the dipole moments of HF and HCl (HCl µ = 1.08 D;{ m{D}}, HF µ = 1.82 D;{ m{D}}) together with the percent ionic character of each bond (HCl 20% ionic, HF 45% ionic) to estimate the bond length in each molecule.

FREE Expert Solution

Recall that dipole moment (μ) can be calculated using the following equation:

μ=Q·r

where:
Q = charge of a bond with 100% ionic character = 1.6 x 10-19 C
r = distance between the atoms or bond length


On the other hand, the percent ionic character is given by:

%ionic character=μobservedμ100% ionic char.x100

where:
μobserved = observed or actual dipole moment
μ100% ionic char. = dipole moment of a bond with 100% ionic character


For HF:

Step 1: Calculate the dipole moment of a bond with 100% ionic character.

Given:

μ = 1.82 D
% ionic character = 45%.

%ionic character=μobservedμ100% ionic char.×10045%100=1.82 Dμ100% ionic char.0.45 (μ100% ionic char.)=1.82 Dμ100% ionic char.(μ100% ionic char.)0.45 (μ100% ionic char.)0.45=1.82 D0.45

μ100% ionic char. = 5.4 D



Step 2: Calculate the bond length of HF.

Given:

1 D = 3.34 x 10-30 C•m
μ = 5.4 D
Q = 1.6 x 10-19 C


μ=Q·rr=μQr=5.4 D× (3.34×10-30 C·m1 D)1.6×10-19 Cr=1.8036×10-29 C·m1.6×10-19 C

r = 8.44x10-11 m

converto picometer (pm):     1 pm = 10-12 m

r=8.44×10-11 m×1 pm10-12 m

r = 84.4 pm



The bond length of the H-F bond is 84.4 pm.



For HCl:

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Problem Details

Use the dipole moments of HF and HCl (HCl µ = 1.08 D, HF µ = 1.82 D) together with the percent ionic character of each bond (HCl 20% ionic, HF 45% ionic) to estimate the bond length in each molecule.

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