Chemistry: the Central Science Fourteenth Edition

Chemistry: The Central Science Fourteenth Edition

Chapter 9 Molecular Geometry and Bonding Theories

• Lewis structures show bonding and lone pairs but do not denote shape. • However, we use Lewis structures to help us determine shapes. • Here we see some common shapes for molecules with two or three atoms connected to a central atom.

• The bond angles and bond lengths determine the shape and size of molecules. • Electron pairs repel each other. • Electron pairs are as far apart as possible; this allows predicting the shape of the molecule. • This is the valence-shell

electron-pair repulsion (V S E P R) model.

• We can refer to the directions to which electrons point as electron domains. This is true whether there is one or more electron pairs pointing in that direction. It is also true if it is a lone pair or a bond. • The central atom in this molecule, A, has four electron domains.

“The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them.” (The balloon analogy in the figure to the left demonstrates the maximum distances that minimize repulsions.)

• The table shows the electron-domain geometries for two through six electron domains around a central atom. • To determine the electron-domain geometry, count the total number of lone pairs, single, double, and triple bonds on the central atom.

Table 9.1 Electron-Domain Geometries as a Function of Number of Electron Domains Number of Arrangement of Electron Domain Predicted Electron Domains* Electron Domains Geometry Bond Angles Two domains opposite each other, forming a 2 Linear 180º straight line.

Three domains forming the points of an equilateral 3 Trigonal planar 120º triangle.

Four domains forming the 4 points of a pyramid. Tetrahedral 109.5º

[Table 9.1 Continued]

Number of Arrangement of Electron Domain Predicted Electron Domains* Electron Domains Geometry Bond Angles Three domains forming the points of an equilateral triangle. Two additional domains are found perpendicular, above and below, the triangle. Trigonal 120º 5 bipyramidal 90º

Four domains forming the points of a square. Two additional domains are found perpendicular, above and below, the square 6 Octahedral 90º

*The number of electron domains is sometimes called the coordination number of the atom.

1) Draw the best Lewis structure. 2) Determine the electron-domain geometry. 3) Use the arrangement of the bonded atoms to determine the molecular geometry. – Tables 9.2 and 9.3 show the potential molecular geometries.

• In the linear domain, there is only one molecular geometry: linear. • Note: If there are only two atoms in the molecule, the molecule will be linear no matter what the electron domain is. Table 9.2 Electron-Domain and Molecular Geometries for Two, Three, and Four Electron Domains around a Central Atom

Number of Electron Electron-Domain Bonding Nonbonding Molecular Domains Geometry Domains Domains Geometry Example Two domains opposite Linear. C O 2. A central C each other, forming a double bonded left straight line, linear. and right to O; each O has two pairs of 2 2 0 dots.

• There are two molecular geometries: – Trigonal planar, if all electron domains are bonding electrons – Bent, if one of the domains is a lone pair Table 9.2 Electron-Domain and Molecular Geometries for Two, Three, and Four Electron Domains around a Central Atom Number of Electron Electron-Domain Bonding Nonbonding Molecular Domains Geometry Domains Domains Geometry Example Three domains forming the Trigonal planar. B F 3. B is single left points of an equilateral and right, angled triangle, trigonal planar. down, and above to 3 3 0 F; each F has three pairs of dots.

N O 2. N is double bonded left, bent. angled down, to O, which has two pairs of dots, and single bonded right, angled down, to O, which has Blank three pairs. The entire molecule has Blank 2 1 a negative charge

• There are three molecular geometries: – Tetrahedral, if all are bonding pairs – Trigonal pyramidal, if one is a lone pair – Bent, if there are two lone pairs

Table 9.2 Electron-Domain and Molecular Geometries for Two, Three, and Four Electron Domains around a Central Atom Number of Electron Electron-Domain Bonding Nonbonding Molecular Domains Geometry Domains Domains Geometry Example Four domains forming the Tetrahedral. C H 4. C is single bonded points of a pyramid, right, into the page, and out of the page, all angled tetrahedral. down, to H, as well as 4 4 0 single bonded above to H.

N H 3. N is single bonded right, into Trigonal pyramidal. the page, and out of the page, all angled down, to H; N has a pair of dots above. Blank Blank 3 1

H 2 O. O is single bonded left and Bent right, angled down, to H; O has two pairs of dots. Blank Blank 2 2

• Nonbonding pairs are physically larger than bonding pairs. • Therefore, their repulsions are greater; this tends to compress bond angles.

• Double and triple bonds have larger electron domains than single bonds. • They exert a greater repulsive force than single bonds, making their bond angles greater.

• Remember that some elements can break the octet rule and make more than four bonds (or have more than four electron domains). • The result is two more possible electron domains: five = trigonal bipyramidal; six = octahedral (as was seen in the slide on electron-domain geometries).

• There are two distinct positions in this geometry: – Axial – Equatorial • Lone pairs occupy equatorial positions.

• There are four distinct molecular geometries in this domain: – Trigonal bipyramidal – Seesaw – T-shaped – Linear

Table 9.3 Electron-Domain and Molecular Geometries for Five and Six Electron Domains around a Central Atom

Number of Electron-Domain Bonding Nonbonding Molecular Example Electron Domains Geometry Domains Domains Geometry Three domains forming the points of an equilateral triangle, and two more domains Trigonal bi-pyramidal. above and below, perpendicular to the plane of the triangle.

5 5 0 P C l5

Seesaw. Blank

Blank 4 1 S F 4

T shaped. Blank

Blank 3 2 C l F 3

Linear. Blank

Blank 2 3 X e F 2

• All positions are equivalent in the octahedral domain. • There are three molecular geometries: – Octahedral – Square pyramidal – Square planar

Table 9.3 Electron-Domain and Molecular Geometries for Five and Six Electron Domains around a Central Atom Number of Electron Electron-Domain Bonding Nonbonding Molecular Domains Geometry Domains Domains Geometry Example Four domains forming the Octahedral. points of a square, and two more domains above and below, perpendicular to the 6 6 0 S F6 plane of the square.

Square pyramidal.

Blank

Blank 5 X1 B r F 5

Square planar.

Blank

Blank 4 2 X e F 4

For larger molecules, look at the geometry about each atom rather than the molecule as a whole.

Ask yourself: Covalent or ionic? If covalent: Are the bonds polar? (Do they have a bond dipole?) a. No: The molecule is nonpolar! b. Yes: Continue—Do the average position of δ+ and δ– coincide? (Is the overall dipole moment equal to zero?) 1) Yes: The molecule is nonpolar. 2) No: The molecule is polar. Note: Different atoms attached to the central atom have different polarity of bonds.

• A nonpolar molecule • A polar molecule

• In valence-bond theory, electrons of two atoms begin to occupy the same space. • This is called “overlap” of orbitals. • The sharing of space between two electrons of opposite spin results in a covalent bond.

• Increased overlap brings the atoms together until a balance is reached between the like charge repulsions and the electron- nucleus attraction. • Atoms can’t get too close because the internuclear repulsions get too great.

• V S E P R predicts shapes of molecules very well. • How does that fit with orbitals?

• Let’s use H2O as an example:

• If we draw the best Lewis structure to assign V S E P R, it becomes bent. • If we look at oxygen, its electron configuration is 1ssp2 2 2 2 4 . If it shares two electrons to fill its valence shell, they should be in 2p. • Wouldn’t that make the angle 90°? • Why is it 104.5°? Copyright © 2018, 2015, 2012 Pearson Education, Inc. All Rights Reserved Hybrid Orbitals

• Hybrid orbitals form by “mixing” of atomic orbitals to create new orbitals of equal energy, called degenerate orbitals. • This process is called hybridization. • When two orbitals “mix” they create two orbitals; when three orbitals mix, they create three orbitals; and so on.

• When we look at the orbital diagram for beryllium (B e), we see that there are only paired electrons in full sublevels.

• B e makes electron-deficient compounds with two

bonds for B e. Why? s p hybridization (mixing of one s orbital and one p orbital).

• Mixing the s and p orbitals yields two degenerate orbitals that are hybrids of the two orbitals.

– The s p hybrid orbitals each have two lobes like a p orbital. – One of the lobes is larger and more rounded, as is the s orbital.

• These two degenerate orbitals would align themselves 180° from each other.

• This is consistent with the observed geometry of B e

compounds (like B e F2) and V S E P R: linear.

Using a similar model for boron leads to three degenerate sp2 orbitals.

With carbon, we get four degenerate sp3 orbitals.

• We started this discussion with H2O and the angle question: Why is it 104.5 degrees instead of 90 degrees? • Oxygen has two bonds and two lone pairs—four electron domains. • The result is sp3 hybridization!

• The elements that have more than an octet • Valence-bond model would use d orbitals to make more than four bonds. • This view works for period 3 and below. • Theoretical studies suggest that the energy needed would be too great for this. • A more detailed bonding view is needed than we will use in this course.

1) Draw the Lewis structure.

2) Use V S E P R to determine the electron-domain geometry. 3) Specify the hybrid orbitals needed to accommodate these electron pairs.

Table 9.4 Geometric Arrangements Characteristic of Hybrid Orbital Sets Atomic Orbital Set Hybrid Orbital Set Geometry Examples

Linear, 180 degrees.

s,p Two s p B e F2, H g C l2

Three, s p 2 Trigonal planar, 120 degrees

2 s,p,p Three sp B F3, S O3

Four, s p 2 Tetrahedral, 109.5 degrees C H 4. N H 3. H 2 O. N H 4, plus.

s,p,p,p 2 Four sp + CH4 , NH 3 , H 2 O, NH 4

• How does a double or triple bond form? • It can’t, if we use only hybridized orbitals. • However, if we use the orbitals that are not hybridized, we can have a “sideways” overlap. • Two types of bonds: – Sigma (σ) bond – Pi (π) bond

• Sigma bonds are characterized by – head-to-head overlap. – cylindrical symmetry of electron density about the internuclear axis. • Pi bonds are characterized by – sideways overlap. – electron density above and below the internuclear axis.

• Single bonds are always  -bonds. • Multiple bonds have one  -bond; all other bonds are  -bonds.

• Bonding electrons (  or ) that are specifically shared between two atoms are called localized electrons. • In many molecules, we can’t describe all electrons that way (resonance); the other electrons (shared by multiple atoms) are called delocalized electrons.

The organic molecule benzene (C66 H ) has six  -bonds and a p orbital on each C atom, which form delocalized bonds using one electron from each p orbital.

• Wave properties are used to describe the energy of the electrons in a molecule. • Molecular orbitals have many characteristics like atomic orbitals: – Maximum of two electrons per orbital – Electrons in the same orbital have opposite spin – Definite energy of orbital – Can visualize electron density by a contour diagram

• They differ from atomic orbitals because they represent the entire molecule, not a single atom. • Whenever two atomic orbitals overlap, two molecular orbitals are formed: one bonding, one antibonding. • Bonding orbitals are constructive combinations of atomic orbitals. • Antibonding orbitals are destructive combinations of atomic orbitals. They have a new feature unseen before: A nodal plane occurs where electron density equals zero.

Whenever there is direct overlap of orbitals, forming a bonding and an antibonding orbital, they are called sigma (σ) molecular orbitals. The antibonding orbital is distinguished with an asterisk as . Here is an example for the formation of a hydrogen molecule from two atoms.

• An energy-level diagram, or M O diagram, shows how orbitals from atoms combine to form molecular orbitals.

• In H2 the two electrons go into the bonding molecular orbital (lower in energy). 11 • Bond order = # of bonding electrons  = (2 0) = 1 bond . 22# of antibonding electrons

• Therefore, He2 does not exist.

1) The number of M O s formed equals the number of A O s combined.

2) A O s combine with A O s of similar energy.

3) The effectiveness with which two A O s combine is proportional to their overlap.

4) Each M O can accommodate at most two electrons with opposite spin. (They follow the Pauli exclusion principle.)

5) When M O s of the same energy are populated, one electron enters each orbital (same spin) before pairing. (They follow Hund’s rules.)

• Li 2 (g) occurs at high temperatures. • Lewis structure:

• The M O diagram is on the right. • Notice that core electrons don’t play a major part in bonding, so we usually don’t include them in the

M O diagram.

• p-orbitals also undergo overlap. • They result in either direct or sideways overlap.

• There are σ and   orbitals from s and p atomic orbitals. • There are π and   orbitals from p atomic orbitals. • Since direct overlap is stronger, the effect of raising and lowering energy is greater for σ and  .

• In some cases, s orbitals can interact with the pz orbitals more than the px and py orbitals.

• It raises the energy of the pz orbital and lowers the energy of the s orbital.

• The px and py orbitals are degenerate orbitals.

• Diamagnetism is the result of all electrons in every orbital being spin-paired. These substances are weakly repelled by a magnetic field. • Paramagnetism is the result of the presence of one or more unpaired electrons in an orbital.

• Is oxygen (O2 ) paramagnetic or diamagnetic? Look

back at the M O diagram! It is paramagnetic.

• Lewis structures would

not predict that (O2 ) is paramagnetic.

• The M O diagram clearly shows that is paramagnetic. • Both show a double bond (bond order = 2).

• Diatomic molecules can consist of atoms from different elements.

• How does a M O diagram reflect differences? • The atomic orbitals have different energy, so the interactions change slightly. • The more electronegative atom has orbitals lower in energy, so the bonding orbitals will more resemble them in energy.