Question

The ionic character of the bond in a diatomic molecule can be estimated by the formula $$ \frac{\mu}{e d} \times 100 \% $$ where \(\mu\) is the experimentally measured dipole moment (in \(\mathrm{C} \mathrm{m}\) ), \(e\) is the electronic charge \((1.6022 \times\) \(10^{-19} \mathrm{C}\) ), and \(d\) is the bond length in meters. (The quantity \(e d\) is the hypothetical dipole moment for the case in which the transfer of an electron from the less electronegative to the more electronegative atom is complete.) Given that the dipole moment and bond length of \(\mathrm{HF}\) are \(1.92 \mathrm{D}\) and \(91.7 \mathrm{pm},\) respectively, calculate the percent ionic character of the molecule.

Short answer

The percent ionic character of the HF molecule is approximately 39.2%.

Step-by-step solution

Convert units

Firstly, we need to have all quantities in compatible units. The dipole moment of the molecule is given in Debye (D)-a non-SI unit-where 1 D= \(3.336 \times 10^{-30} \, C·m \). So, the dipole moment in C·m will be \(1.92 \, D \times 3.336 \times 10^{-30} \, C·m/D= 6.405 \times 10^{-30} \, C·m\). For bond length, convert pm to m, making it \(91.7 \times 10^{-12} \, m\).

Calculating bond character

Now, we want to substitute the converted values as well as the known constant for electronic charge into the formula for ionic character. Thus, \(\mu/ed = 6.405\times 10^{-30}/(1.6022 \times 10^{-19} \times 91.7 \times 10^{-12})\)

Calculation

Performing the calculation, \(\mu/ed\) is approximately 0.392. To convert that to a percentage, we multiply by 100. Hence, \(0.392 \times 100= 39.2\% \)

Key concepts

Dipole Moment

In the realm of molecular chemistry, the dipole moment is a vector quantity that represents the separation of positive and negative electrical charges within a molecule. Consider it a measure of the polarity of a molecule: the greater the separation of charges, the larger the dipole moment. It's calculated by multiplying the amount of charge separation (in coulombs) by the distance (in meters) between the charges. Mathematically, it's represented as \(\mu = q \times d\), where \(q\) is the charge and \(d\) is the distance between charges.

In our textbook example, the dipole moment of hydrogen fluoride (HF) is given in Debye units (D), which we convert into the standard international unit of coulomb-meters (C⋅m). This conversion is crucial because it sets the stage for comparing the real-life polarity of the molecule to the theoretical maximum, enabling us to understand the degree of its ionic character.

Understanding the concept of dipole moment is vital, not just for solving this problem, but also for grasping molecular interactions, reactivity, and the physical properties of compounds that involve polar bonds.

Ionic Bond

An ionic bond is a type of chemical bond formed through the electrostatic attraction between two oppositely charged ions. Typically, this occurs between a metal, which loses electrons to become a positively charged cation, and a non-metal, which gains those electrons to become a negatively charged anion. Ionic bonds are the glue that holds salts together.

However, in the real world, very few bonds are purely ionic. Instead, they have varying degrees of ionic and covalent character, with the former arising from the difference in electronegativity between the two atoms. The bond in hydrogen fluoride (HF), as we are exploring, has partial ionic and covalent character, and by quantifying its ionic character, we can understand the nature of the bond more comprehensively.

When we talk about the 'hypothetical dipole moment' in the context of our problem, we’re referring to the theoretical scenario in which one atom has completely transferred its electron to the other, creating a fully ionic bond — a useful benchmark for our calculations.

Electronegativity

Electronegativity is a fundamental concept that describes an atom's tendency to attract shared electrons in a chemical bond. It is not a directly measurable property, but scales like the Pauling scale help us quantify it. The higher the electronegativity, the more an atom can attract electrons towards itself when it forms a bond with another atom.

In the case of HF, the fluorine atom is highly electronegative, much more so than hydrogen. This difference in electronegativity is the reason HF has a dipole moment – electrons in the HF bond are not shared equally but are drawn more towards fluorine, creating a separation of charges.

During the calculation of ionic character, the concept of electronegativity is implicitly used. The percentage we're calculating effectively tells us how much of the bond is ionic, meaning how much the bond resembles the situation where the electron is completely transferred to the more electronegative atom (in this case, fluorine). The resulting percentage communicates the extent to which the bond between two atoms approaches the characteristics of an ionic bond, guided by the differences in their electronegativities.