Question

Fluoromethane \(\left(\mathrm{CH}_{3} \mathrm{~F}, \mu=1.81 \mathrm{D}\right.\) ) has a smaller dipole moment than chloromethane \(\left(\mathrm{CH}_{3} \mathrm{Cl}, \mu=1.87 \mathrm{D}\right)\), even though fluorine is more electronegative than chlorine. Explain.

Short answer

Fluorine's higher electronegativity is countered by a shorter \(\mathrm{C-F}\) bond, leading to a smaller dipole moment in \(\mathrm{CH}_{3}\mathrm{F}\) compared to \(\mathrm{CH}_{3}\mathrm{Cl}\).

Step-by-step solution

Understand the Dipole Moment

The dipole moment (\( \mu \)) is a measure of the separation of positive and negative charges in a molecule, which is given by \( \mu = q \times d \), where \( q \) is the charge difference and \( d \) is the distance between the charges.

Analyze Electronegativity

Fluorine is more electronegative than chlorine, meaning fluorine pulls electrons more strongly towards itself compared to chlorine. This suggests that in isolation, a \( \text{C-F} \) bond should have a larger dipole moment than a \( \text{C-Cl} \) bond.

Consider Bond Length

Dipole moment is not only affected by electronegativity but also by bond length. In \( \mathrm{CH}_{3} \text{F} \), the \( \mathrm{C-F} \) bond is shorter than the \( \mathrm{C-Cl} \) bond in \( \mathrm{CH}_{3} \mathrm{Cl} \). The shorter bond length reduces the dipole moment in \( \mathrm{CH}_{3} \mathrm{F} \) despite the higher electronegativity of fluorine.

Evaluate Molecular Dipole

The overall molecular dipole moment includes contributions from all individual bond dipoles as well as the geometry of the molecule. The fluoromethane molecule has a geometry that reduces the effective dipole moment due to possible cancellation effects within the molecule.

Key concepts

Electronegativity

Electronegativity is a chemical property that illustrates how strongly an element can attract electrons towards itself. This concept is pivotal in understanding molecular interactions and properties. When we say that fluorine is more electronegative than chlorine, it means that fluorine has a greater ability to attract electrons compared to chlorine.
In a bond, the more electronegative atom will pull electron density towards itself, creating a partial negative charge on that atom and a partial positive charge on the other atom involved in the bond.
When considering dipole moments, a molecule like fluoromethane (\( ext{CH}_3 ext{F}\)) would seem to have a high dipole moment due to fluorine's high electronegativity. However, electronegativity alone doesn’t determine the dipole moment completely; factors like bond length and molecular geometry also play a crucial role.

Bond Length

Bond length refers to the distance between the nuclei of two bonded atoms. In the context of dipole moments, bond length is crucial because the dipole moment (\( u \)) is directly proportional to the distance between the charges, which is the bond length (\( d \)).
\[ \mu = q \times d \]
Even though fluorine is more electronegative, the bond length in \( ext{CH}_3 ext{F} \) between the carbon and the fluorine atoms is shorter than the bond length between carbon and chlorine in \( ext{CH}_3 ext{Cl} \).
This shorter bond length diminishes the dipole moment of \( ext{CH}_3 ext{F} \) compared to that of \( ext{CH}_3 ext{Cl} \), despite the greater electronegativity of fluorine. Bond length can therefore sometimes counteract the effects of electronegativity on dipole moment.

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. This geometry significantly impacts the overall dipole moment of a molecule.
Each bond in a molecule has its own bond dipole, and the way these dipoles combine depends on the geometry of the molecule. In certain structures, dipoles can cancel each other out due to the arrangement of bonds, leading to a smaller overall molecular dipole moment.
In the case of fluoromethane (\( ext{CH}_3 ext{F}\)), the geometry is tetrahedral, which affects how the individual bond dipoles combine. Although the \( ext{C-F}\) bond is polarized due to fluorine's electronegativity, the spatial arrangement of other bond dipoles can lead to partial cancellation, reducing the net dipole moment more than expected if considering electronegativity alone.
Thus, when evaluating dipole moments, it is essential to consider not only the electronegativity and bond lengths but also the entire molecular geometry which ultimately determines the polar character of the molecule.