Question

(a) Although HC1 (1.27 A) is a longer molecule than HF (0.92 A), it has a smaller dipole moment (1.03 D compared to 1.75 D). How do you account for this fact? (b) The dipole moment of \(\mathrm{CH}_{3} \mathrm{~F}\) is \(1.847 \mathrm{D}\), and of \(\mathrm{CD}_{3} \mathrm{~F}, 1.858 \mathrm{D}\). (D is \({ }^{2} \mathrm{H}\), deuterium.) Compared with the \(\mathrm{C}-\mathrm{H}\) bond, what is the direction of the \(C-D\) dipole?

Short answer

The smaller dipole moment in HCl compared to HF is due to the greater difference in electronegativity between H and F (higher value for \(\delta\)) compensating for the smaller bond length in HF. The direction of the C-D dipole in CD3F is the same as the C-H dipole in CH3F, as evidenced by the slightly larger dipole moment in CD3F compared to CH3F.

Step-by-step solution

a) Comparing HCl and HF dipole moments

In order to account for the fact that HCl has a smaller dipole moment than HF even though it has a longer bond length, we need to consider the differences in electronegativity between the atoms forming the bond. The dipole moment of a bond can be calculated using the formula: \[ \mu = \delta \times d \] where: - \(\mu\) is the dipole moment - \(\delta\) is the difference in electronegativity between the two atoms - \(d\) is the bond length Since HCl has a longer bond length (\(1.27\, Å\)) compared to HF (\(0.92\, Å\)), it might seem counterintuitive that it has a smaller dipole moment. However, the difference in electronegativity between H and F is greater than the difference between H and Cl, leading to a higher value for \(\delta\) in the HF bond. As a result, this increased electronegativity difference compensates for the smaller bond length, leading to a higher dipole moment in HF.

b) C-H and C-D dipoles in CH3F and CD3F

We are given the dipole moments of CH3F (\(1.847\, D\)) and CD3F (\(1.858\, D\)). To determine the direction of the C-D dipole in CD3F, we must first understand how isotopes affect dipole moments. When deuterium (\(^2H\), or D) replaces hydrogen in a bond, the bond strength and the vibrational frequency of the bond will change due to the increased mass of deuterium compared to hydrogen. This results in a slight modification of the bond's polarizability, which can affect the overall dipole moment of the molecule. From the given information, we can see that the dipole moment of CD3F is slightly larger than that of CH3F. If the direction of the C-D bond dipole was reversed with respect to the C-H dipole, we would expect to see a significant decrease in the overall dipole moment of the molecule. Since the dipole moment in CD3F is slightly larger than that in CH3F, we can conclude that the direction of the C-D dipole in CD3F is the same as the direction of the C-H dipole in CH3F.

Key concepts

Electronegativity and Dipole Moments

Electronegativity refers to the ability of an atom in a molecule to attract shared electrons in a chemical bond. It plays a critical role in determining the dipole moment, which is a measure of the separation of positive and negative electric charges in a molecule.

For instance, in the comparison between hydrogen chloride (HCl) and hydrogen fluoride (HF), despite HCl having a longer bond length, HF has a greater dipole moment due to the high electronegativity of fluorine compared to chlorine. This increased attraction for electrons in HF leads to a greater electron density around the fluorine atom, creating a stronger polar bond.

Effect of Electronegativity on Dipole Moment

When discussing electronegativity and its influence on dipole moments, it is essential to remember that a larger difference in electronegativity will produce a more substantial dipole moment in a molecule. In homework scenarios, students should consider both the electronegativity difference and bond length to predict the dipole moment accurately.

Bond Lengths Influence on Dipole Moments

Bond length, the distance between the nuclei of two bonded atoms, is another factor that impacts the dipole moment. Generally, a longer bond will have a higher dipole moment, provided the electronegativity difference remains constant, because there's greater separation of charge.

However, as seen in the HC1 vs. HF example, a higher electronegativity difference can override the effect of a shorter bond length, resulting in a larger dipole moment.

Understanding Bond Length and Dipole Interaction

Students need to realize that while bond length is a contributing factor, it does not solely determine the strength of the dipole moment. The underlying principle denotes that both bond length and electronegativity should be considered together to determine the dipole moment. Shorter bond lengths do not automatically equate to smaller dipole moments; the interplay with electronegativity is key.

Molecular Dipoles and Polarity

Molecular dipoles emerge from the polar bonds within a compound. The vector addition of all individual bond dipoles results in the overall dipole moment of a molecule. Molecular geometry plays a significant part in this, as asymmetrical shapes allow for a net dipole, whereas symmetrical shapes may cancel out individual dipoles, leaving a nonpolar molecule.

For example, CH3F has a trigonal pyramidal shape, which means it has a net dipole due to the polar C-F bond and contributes to the overall direction of the molecular dipole.

Geometry's Role in Molecular Dipoles

When addressing homework questions related to molecular dipoles, it is crucial for students to depict the molecule's geometry and take into account the vector direction of each bond dipole to correctly determine the direction and magnitude of the molecular dipole.

Isotope Effects on Dipoles

Isotopes can slightly affect the dipole moments of molecules due to differences in mass. Heavier isotopes like deuterium (D) can influence the vibrational characteristics of a bond, which can alter the distribution of charge and, in turn, the dipole moment.

The comparison of dipole moments between CH3F and CD3F shows a slight increase when hydrogen is substituted by deuterium, indicating that isotopic substitution impacts the electron cloud and polarizability. This subtle change informs us that isotopic effects, although often small, can be significant in certain contexts and should not be overlooked.

Subtle Yet Significant Isotope Influence

Homework exercises involving isotopes should prompt students to consider not only the change in mass but also the resulting effect on molecular vibrations and how this might affect the overall dipole moment of a molecule.