Problem 54 - Introductory Chemistry Atoms First

Question

Consider the molecule \(\mathrm{HNF}_{2}(\mathrm{~N}\) is the central atom in the molecule). (a) Draw the dot diagram. (b) Draw the molecule's three-dimensional shape, and label the numeric value of all bond angles. (c) What is the shape of this molecule? (d) Draw in the individual bond dipole moments. (e) Is the molecule polar? If yes, draw the molecular dipole moment vector.

Step-by-Step Solution

Answer

In conclusion: a) The Lewis structure (dot diagram) of HNF2 is: ``` F H \ / N = = = F ``` b) The three-dimensional shape of the molecule is trigonal pyramidal with bond angles slightly less than \(109.5^{\circ}\). c) The shape of this molecule is trigonal pyramidal. d) The individual bond dipole moments are \(0.9\) for H-N and \(0.98\) for N-F bonds. e) Yes, the molecule HNF2 is polar, with the molecular dipole moment vector pointing from the nitrogen atom to the outer atoms (hydrogen and fluorine).

Step 1: Determine the number of valence electrons

First, we need to determine the number of valence electrons present in the molecule. Here we have one hydrogen atom (H), one nitrogen atom (N), and two fluorine atoms (F). We use the periodic table to determine the number of valence electrons for each atom: • Hydrogen (H) has \(1\) valence electron. • Nitrogen (N) has \(5\) valence electrons. • Fluorine (F) has \(7\) valence electrons each. Therefore, there is a total of \(1 + 5 + 7 \times 2 = 20\) valence electrons in the HNF2 molecule.

Step 2: Draw the dot diagram (Lewis structure)

According to electron sharing rules, we'll draw a Lewis structure with Nitrogen as the central atom, as mentioned in the exercise. First, connect atoms with single bonds to fulfill the octet rule (except for hydrogen), then distribute the remaining electrons as lone pairs. 1. Place Nitrogen (central atom) in the middle and connect it to Hydrogen and two Fluorine atoms with single bonds. 2. Distribute the remaining valence electrons as lone pairs to fulfill the octet rule (except for hydrogen). Nitrogen has \(2\) remaining lone pairs, while each Fluorine atom keeps the \(6\) lone pairs. The Lewis structure of HNF2 is represented by: ``` F H \ / N = = = F ```

Step 3: Determine the molecule's three-dimensional shape

Using VSEPR (Valence Shell Electron Pair Repulsion) theory, we can determine the three-dimensional shape of the HNF2 molecule. Here, the central Nitrogen atom has \(3\) atoms bonded to it and \(1\) lone pair of electrons. This corresponds to an electronic geometry of "tetrahedral" with \(4\) electron domains.

Step 4: Determine bond angles and molecule shape

The three-dimensional shape of a molecule with an electronic geometry of "tetrahedral" and \(1\) lone pair of electrons forming \(3\) single bonds is "trigonal pyramidal." The bond angles between the three atoms bonded to the central atom in a tetrahedral geometry are approximately \(109.5^{\circ}\). However, lone pair-bonding pair repulsion causes a slight decrease, creating bond angles slightly less than \(109.5^{\circ}\). Thus, the shape of the HNF2 molecule is trigonal pyramidal with bond angles slightly less than \(109.5^{\circ}\).

Step 5: Calculate the individual bond dipole moments

Bond dipole moments occur due to the difference in electronegativity between two atoms in a bond. Using the electronegativity values, we can estimate the bond dipole moments of H-N and N-F bonds. Electronegativity values: • Hydrogen (H): \(2.1\) • Nitrogen (N): \(3.0\) • Fluorine (F): \(3.98\) The individual bond dipole moments: • H-N bond: \(\Delta EN = 3.0 - 2.1 = 0.9\) • N-F bond: \(\Delta EN = 3.98 - 3.0 = 0.98\) The H-N bond dipole moment points from hydrogen to nitrogen, and the N-F bonds dipole moment points from nitrogen to both fluorine atoms.

Step 6: Analyze if the molecule is polar or nonpolar

Since the molecule's shape is "trigonal pyramidal," the bond dipole moments do not cancel each other out. Therefore, the molecule is polar, with a dipole moment originating from the nitrogen atom and directed to the three outer atoms. In conclusion: a) The Lewis structure (dot diagram) of HNF2 is: ``` F H \ / N = = = F ``` b) The three-dimensional shape of the molecule is trigonal pyramidal with bond angles slightly less than \(109.5^{\circ}\). c) The shape of this molecule is trigonal pyramidal. d) The individual bond dipole moments are \(0.9\) for H-N and \(0.98\) for N-F bonds. e) Yes, the molecule HNF2 is polar, with the molecular dipole moment vector pointing from the nitrogen atom to the outer atoms (hydrogen and fluorine).

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons of an atom that participate in chemical bonding. Understanding the distribution of these electrons in a molecule is critical for predicting molecular interactions and geometry. They reside in the highest energy level of an atom and determine how atoms interact.

• Hydrogen, the simplest element, has 1 valence electron.
• Nitrogen has 5 valence electrons, as it is in group 15 of the periodic table.
• Fluorine, found in group 17, possesses 7 valence electrons.

In the molecule \(HNF_2\), the total valence electrons are the sum from each atom: 1 from hydrogen, 5 from nitrogen, and 7 from each fluorine. Sum them up to get a total of 20 valence electrons. Knowing the total number is the first step to constructing the Lewis structure.

Lewis Structure

A Lewis structure is a diagram that represents the bonding between atoms of a molecule, as well as any lone pairs of electrons that may exist. It helps to visualize the molecule's electron arrangement and bond formation.
To draw the Lewis structure for \(HNF_2\), begin with nitrogen in the center, the element that can form the most bonds:

• Connect nitrogen to hydrogen and the two fluorine atoms with single lines, representing bonds.
• Each bond uses two valence electrons.
• Distribute remaining electrons to fulfill the octet rule, where every atom (except hydrogen) should have 8 electrons surrounding it.
• In HNF2, nitrogen will have a lone pair, and each fluorine atom will retain three lone pairs.

This structure provides insights into the molecular geometry and facilitates the understanding of molecular behavior.

VSEPR Theory

VSEPR (Valence Shell Electron Pair Repulsion) theory helps predict the shape of molecules. It is based on the premise that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion.
In \(HNF_2\), nitrogen is surrounded by three bonding pairs (H and two Fs) and one lone pair of electrons. According to VSEPR theory, this setup leads to a 'trigonal pyramidal' shape, as lone pairs tend to repel more strongly than bonding pairs, pushing the attached atoms closer together. Thus, this molecular shape minimizes electron pair repulsion effectively.

Bond Angles

Bond angles refer to the angles between adjacent lines representing bonds. These angles determine the geometric shape of the molecule. In a perfect tetrahedral geometry, bond angles are \(109.5^\circ\).
However, for \(HNF_2\), the presence of the lone pair on nitrogen slightly alters the bond angles. The lone pair exerts greater repulsion than bonding pairs, reducing the bond angle slightly below \(109.5^\circ\). This adjustment aligns atoms in a way that best accommodates all electron pairs.

Dipole Moment

Dipole moments occur when there is an uneven distribution of electron density in a bond or molecule. They are represented as vectors with both direction and magnitude, pointing from the less electronegative atom to the more electronegative one.
In \(HNF_2\), dipole moments are due to:

• H-N bond where nitrogen is more electronegative than hydrogen, creating a dipole moment pointing towards nitrogen.
• N-F bonds where fluorine is more electronegative than nitrogen, creating moments pointing towards each fluorine atom.

These individual dipole moments combine vectorially to give an overall dipole moment for the molecule, affecting its physical properties, like solubility and reactivity.

Polarity

Polarity in molecules arises from differences in electronegativity between bonded atoms and the asymmetrical shape of the molecule. A molecule is polar if it has a net dipole moment.
For \(HNF_2\), polarity is determined by:

• The molecular shape, which is trigonal pyramidal, leading to non-canceling dipoles.
• The significant differences in electronegativity between N and F atoms.

Due to the arrangement of dipole moments in \(HNF_2\), the molecule has an overall polarity, with the net dipole moment directed from the central nitrogen atom toward the atoms at the base of the pyramid (H and F), impacting the molecule's interactions and properties.