Question

(a) The equilibrium separation of the two nuclei in an NaCl molecule is 0.24 nm. If the molecule is modeled as charges \(+e\) and \(-e\) separated by 0.24 nm, what is the electric dipole moment of the molecule (see Section 21.7)? (b) The measured electric dipole moment of an NaCl molecule is \(3.0 \times 10^{-29}\) \(C \cdot m\). If this dipole moment arises from point charges \(+q\) and \(-q\) separated by 0.24 nm, what is \(q\)? (c) A definition of the \(fractional\) \(ionic\) \(character\) of the bond is \(q/e\). If the sodium atom has charge \(+e\) and the chlorine atom has charge \(-e\), the fractional ionic character would be equal to 1. What is the actual fractional ionic character for the bond in NaCl? (d) Theequilibrium distance between nuclei in the hydrogen iodide (HI) molecule is 0.16 nm, and the measured electric dipole moment of the molecule is \(1.5 \times 10^{-30}\) \(C \cdot m\). What is the fractional ionic character for the bond in HI? How does your answer compare to that for NaCl calculated in part (c)? Discuss reasons for the difference in these results.

Short answer

NaCl has a fractional ionic character of 0.78, while HI has 0.059, due to differences in electronegativity.

Step-by-step solution

Calculate Dipole Moment for NaCl Model

The electric dipole moment \( p \) is given by \( p = q \, d \) where \( q \) is the charge magnitude and \( d \) is the separation distance. For NaCl modeled as charges \(+e\) and \(-e\), \( d = 0.24 nm = 0.24 \times 10^{-9} \, m \) and \( q = e = 1.6 \times 10^{-19} \) C. Thus, the dipole moment \( p = (1.6 \times 10^{-19} \, C) \times (0.24 \times 10^{-9} \, m) = 3.84 \times 10^{-29} \, C \cdot m \).

Determine Charge Magnitude for Measured Dipole Moment

Given the measured dipole moment \( p = 3.0 \times 10^{-29} \, C \cdot m \) and separation \( d = 0.24 \times 10^{-9} \, m \), use \( q = \frac{p}{d} \). Substituting, \( q = \frac{3.0 \times 10^{-29} \, C \cdot m}{0.24 \times 10^{-9} \, m} = 1.25 \times 10^{-19} \, C \).

Calculate Fractional Ionic Character for NaCl

The fractional ionic character \( \frac{q}{e} \) is \( \frac{1.25 \times 10^{-19} \, C}{1.6 \times 10^{-19} \, C} = 0.78125 \).

Calculate Fractional Ionic Character for HI

For HI, \( d = 0.16 \times 10^{-9} \, m \) and \( p = 1.5 \times 10^{-30} \, C \cdot m \). Calculate \( q = \frac{p}{d} = \frac{1.5 \times 10^{-30} \, C \cdot m}{0.16 \times 10^{-9} \, m} = 9.375 \times 10^{-21} \, C \). Thus, fractional ionic character is \( \frac{9.375 \times 10^{-21} \, C}{1.6 \times 10^{-19} \, C} = 0.05859 \).

Compare Ionic Characters for NaCl and HI

The fractional ionic character of NaCl is approximately 0.78 and that of HI is approximately 0.059. The difference arises due to the nature of the bonding; NaCl has a stronger ionic character due to a greater difference in electronegativity between sodium and chlorine compared to hydrogen and iodine.

Key concepts

Equilibrium Separation

Understanding the concept of equilibrium separation is crucial in the study of molecular structures. Equilibrium separation, often denoted as "d," refers to the optimal distance between the nuclei of two atoms in a molecule. This is the point at which the attractive and repulsive forces between the atoms balance out, resulting in a stable configuration.
In the context of ionic bonds, such as those seen in an NaCl molecule, the equilibrium separation is the distance where the potential energy of the system is at its minimum. For NaCl, this distance is 0.24 nm. At this separation, the opposing charges "+e" and "-e" of the sodium and chloride ions create an electric dipole moment, a key factor in determining the molecule's properties.
The equilibrium separation impacts the strength and characteristics of the bond, affecting the overall behavior of the molecule. Understanding this concept allows for deeper insights into molecular geometry and chemical interaction.

Fractional Ionic Character

The fractional ionic character is a dimensionless number that indicates the degree of ionic bonding in a compound. It is computed by comparing the actual charge separation to the full ionic charge separation, which is denoted by the charge of an electron, "e."
To calculate this, use the formula:

• Fractional Ionic Character = \( \frac{q}{e} \)
• Where "q" is the apparent charge calculated from the dipole moment and separation distance.

For example, in an NaCl molecule, the fractional ionic character is derived from the ratio of the measured charge separation to the expected full ionic separation (1.0 if both atoms had charges "+e" and "-e"). For NaCl, the fractional ionic character is approximately 0.78. This indicates a strong but not full ionic bond.
Higher fractional ionic character values suggest stronger ionic properties, while lower values imply more covalent characteristics. Understanding the fractional ionic character helps in predicting the properties and behaviors of the substance in various chemical contexts.

Ionic Bonding

Ionic bonding is a type of chemical bond that involves the transfer of electrons from one atom to another, resulting in the formation of ions. These ions are held together by electrostatic forces. The atom that loses an electron becomes a positively charged cation, while the one that gains an electron becomes a negatively charged anion.
In compounds like sodium chloride (NaCl), ionic bonding plays a critical role. Sodium (Na), with one electron in its outer shell, readily gives up its electron to achieve a stable configuration. Chlorine (Cl), with seven electrons in its outer shell, accepts this electron to fill its shell.
The resulting positive and negative charges create a strong electrostatic attraction between the ions, manifesting as an ionic bond. Ionic bonds are known for their strength and for producing hard, brittle substances. Understanding ionic bonding is essential in both chemical synthesis and analysis, providing foundational insights into reactions and material properties.

Charge Separation

Charge separation in chemical compounds refers to the distribution of electric charge within a molecule. In an ionic bond, this involves the displacement of electron density between two atoms, one becoming more positive and the other more negative.
The concept of charge separation is crucial in understanding the electric dipole moment, a measure of the separation of positive and negative charges in a molecule. It is calculated as the product of the magnitude of the charge and the distance between charges, stated as:

• Electric Dipole Moment = \( q \times d \)

For example, in the NaCl molecule, using model charges "+e" and "-e", charge separation across a distance of 0.24 nm leads to a calculated dipole moment of approximately \(3.84 \times 10^{-29} C \cdot m\).
Charge separation affects molecular polarity and interactions with other substances, influencing solubility, reactivity, and physical properties of compounds. A clear understanding of charge separation is critical for analyzing and predicting chemical behavior.