Question

Consider the molecule \(\mathrm{BrCl}_{3}\). (a) Draw a dot diagram for the molecule. (b) Predict the molecule's electron group geometry. (c) Predict the molecule's shape (name the shape and draw it using wedges, lines, and broken lines, and indicate the ideal value of the bond angles). (d) Predict if the molecule is polar or nonpolar. If polar, draw the dipole moment for the molecule.

Short answer

The BrCl3 molecule has a T-shaped molecular geometry with an electron dot structure of: .. Cl-Br-Cl | .. Cl The electron group geometry is trigonal bipyramidal, and the bond angles are 180° (axial-Br-axial) and 90° (equatorial-Br-axial). The molecule is polar due to the electronegativity difference between Br and Cl and its T-shaped geometry. The net dipole moment is represented as: Cl | Cl-Br-Cl →net_dipole

Step-by-step solution

Electron Dot Structure

To draw the electron dot structure for BrCl3, we need to determine the total number of valence electrons in the molecule. Bromine (Br) has 7 valence electrons, and Chlorine (Cl) has 7 valence electrons. Since there are three chlorine atoms, the total number of valence electrons is: \(7 (Br) + 3 \times 7 (Cl) = 28\) First, we place the central atom, Br, and surround it with three Cl atoms. Then, we distribute the 28 valence electrons around the atoms, starting with bonding electrons (single bonds) between the central atom and the surrounding atoms, and finally distributing the remaining electrons as lone pairs on the central and surrounding atoms. Br: .. Cl: .. .. Br-Cl-Cl-Cl The electron dot structure for BrCl3 is: .. Cl-Br-Cl | .. Cl ..

Electron Group Geometry

We will use the VSEPR theory to predict the electron group geometry of BrCl3. In this molecule, there are 3 bonding electron groups and 2 lone pairs on the central atom. Therefore, there are \(3+2=5\) electron groups around the central atom. According to VSEPR theory, if there are 5 electron groups around the central atom, the electron group geometry will be trigonal bipyramidal.

Predict Molecular Shape

The molecular shape is determined by the arrangement of the bonding electron groups and lone pairs around the central atom. In a trigonal bipyramidal electron group geometry with 2 lone pairs, the lone pairs occupy the equatorial positions, and the three Cl atoms occupy the axial and equatorial positions, forming a T-shaped molecular geometry. The bond angles in a T-shaped molecule are: Axial-Br-Axial (linear): 180° Equatorial-Br-Axial: 90° To draw the T-shaped molecule using wedges, lines, and broken lines, we represent the three-dimensional shape as follows: - Solid line: bonds in the plane of the paper - Solid wedge: bond coming out of the plane of the paper - Broken line: bond going into the plane of the paper Cl | .. Cl-Br-Cl

Determine Polarity

To determine if the molecule is polar or nonpolar, we need to consider the electronegativity difference between Br and Cl and the molecular shape. Br and Cl have an electronegativity difference of approximately 0.2, which indicates that the Br-Cl bonds are slightly polar. Due to the T-shaped molecular geometry, the bond dipoles do not cancel each other out, resulting in a net dipole moment for the molecule. Therefore, BrCl3 is a polar molecule. To draw the dipole moment, we need to represent the direction of the bond dipoles (toward more electronegative atom) and the resulting net dipole: Dipole direction: Br -> Cl Cl | Cl-Br-Cl →net_dipole Thus, we have successfully determined the electron dot structure, electron group geometry, molecular shape, bond angles, and polarity of BrCl3.

Key concepts

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a model that allows chemists to predict the shape of molecules based on the repulsion between electron pairs located in the valence shell of the central atom. The concept is straightforward: electron pairs, including bonding pairs and lone pairs, arrange themselves around a central atom in a manner that minimizes their mutual repulsion. This outcome determines the geometry of the molecule.

For example, in the case of BrCl3, there are five electron groups around the bromine atom. This includes three bonded pairs with chlorine atoms and two lone pairs of electrons. The VSEPR theory postulates that these electron groups will spread out to occupy space as far as they can from other electron groups, resulting in a trigonal bipyramidal electron group geometry. However, the presence of lone pairs alters this geometry, leading to the molecule's T-shaped structure.

Electron Dot Structure

The electron dot structure, also known as the Lewis structure, is a diagrammatic method used to represent the valence electrons of an atom. It shows how the electrons are arranged among the atoms in a molecule and identifies the types of bonds (single, double, triple) formed. Each dot represents a valence electron, while each line represents a bond formed between atoms.

Creating the electron dot structure for BrCl3 involves counting the valence electrons, placing them around the central atom, and arranging them to form bonds with surrounding atoms. Once the bonds are formed, the remaining valence electrons are distributed as lone pairs. In BrCl3, this results in two lone pairs on the central bromine atom. Understanding this structure aids in visualizing how the molecule's shape takes form based on electron pair repulsions, an insight that is crucial for predicting molecular geometry.

Molecular Polarity

Molecular polarity refers to the distribution of electrical charge over the atoms joined by the bond, determining whether a molecule is polar or nonpolar. Polarity arises from the differences in electronegativity between bonded atoms, with electrons being pulled more towards one atom than the other. This creates a difference in charge and a dipole moment across the bond.

For BrCl3, the electronegativity difference between Br and Cl, while small, does lead to polar bonds. However, the overall polarity of a molecule also depends on its shape. If a molecule's shape is such that the bond dipoles do not cancel each other out, the molecule exhibits a net dipole moment, making it polar. Since BrCl3 has a T-shaped structure due to its electron group arrangement, the polarities of the bonds do not cancel, rendering BrCl3 a polar molecule. This is crucial for predicting properties like solubility, boiling point, and reactivity.

Bond Angles

In molecular geometry, bond angles are the angles between adjacent lines representing bonds that emanate from the central atom. These angles can tell us a lot about the shape of a molecule and are largely determined by the electron groups around the central atom as per VSEPR theory.

For a molecule like BrCl3 with five electron groups, if there were no lone pairs, the ideal angles would be those of a trigonal bipyramidal geometry: 90°, 120°, and 180°. However, the presence of lone pairs on the central atom leads to the electron pairs pushing against each other and adjusting the bond angles to minimize repulsion. In a T-shaped molecule like BrCl3, where two lone pairs occupy equatorial positions and the chlorine atoms occupy the axial and one equatorial position, the bond angles are 90° between equatorial and axial positions, and 180° between the two axial positions.