An empirical model suggests that the dipole moment (in Debye) of a diatomic molecule…

CHEMISTRY · Multi-part · A Level · Chemistry · Bonding · Bonding

Problem

An empirical model suggests that the dipole moment

\mu

(in Debye) of a diatomic molecule can be approximated by

\mu = k\,(\Delta EN)\,r

, where

\Delta EN

is the electronegativity difference between the two atoms and

r

is the bond length in ångströms. The constant

k

is assumed to be the same for a set of chemically similar bonds. Measured data for two diatomic molecules are given below: 1. HF:

\mu = 1.82\,\text{D}

r = 0.92\,\text{Å}

\Delta EN = 1.8

2. HCl:

\mu = 1.08\,\text{D}

r = 1.27\,\text{Å}

\Delta EN = 0.9

Three additional bonds of interest share the same constant

k

but lack measured dipole moments: – HBr (

r = 1.41\,\text{Å}

\Delta EN = 0.7

) – HI (

r = 1.61\,\text{Å}

\Delta EN = 0.4

) – HF

^{\ast}

(an excited-state species with

r = 1.10\,\text{Å}

\Delta EN = 1.8

) (a) Using the data for HF and HCl, determine the numerical value of the proportionality constant

k

to two significant figures. Show your work. (b) Using the

k

found in part (a), predict

\mu

for HBr, HI, and excited-state HF

^{\ast}

. Record each predicted dipole moment to two significant figures. (c) Rank the five H–halogen bonds (including both forms of HF) from smallest to largest predicted dipole moment. (d) Discuss how simultaneous changes in bond length and electronegativity difference can either reinforce or oppose each other when determining overall bond polarity, citing two specific comparisons from your ranking.

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