Helpful Hints Lewis Structures Octet Rule For Lewis structures of covalent compounds least electronegative

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1 Helpful Hints Lewis Structures Octet Rule Lewis structures are a basic representation of how atoms are arranged in compounds based on bond formation by the valence electrons. A Lewis dot symbol of an atom or ion is drawn by placing the valence electrons around the element symbol, one per side until the fifth is added where they begin being paired (similar to how the lugs are put back on when changing a tire). For example, the correct Lewis dot symbol for phosphorus is: Non-metals will often follow the octet rule, sharing or gaining enough electrons to obtain eight electrons in their valence. Based on the Lewis symbol phosphorus it can be seen that sharing or gaining three electrons will result in a full octet for phosphorus. For Lewis structures of covalent compounds the following points should be considered: 1) The least electronegative element will generally be the central atom with more electronegative elements as terminal atoms. For example the phosphorus atom in PF 3 will be the central atom while the fluorine atoms would be terminal atoms. 2) Valence electrons are shared as needed to fulfill all octets. The simplest way to distribute electrons properly is to start with all single bonds and fulfill octets on external atoms, and then place any remaining electrons on the central atom. 3) Generally all atoms need an octet; common exceptions include hydrogen and boron. If any atoms lack an octet it can be fixed by sharing one or more lone pairs from adjacent atoms that already have octets. 4) Formal charges can be useful in determining whether a more stable structure is possible. Structures with fewer formal charges are best and in cases where formal charges remain negatives are best on the most electronegative atoms while positives are best on the least electronegative atoms. The sum of the formal charges must be the total charge. FC = # of valence electrons (# of bonds + # of nonbonding electrons) FC F = 0; FC P = = 0 Therefore, the correct Lewis structure for PF 3 is:

2 Expanded Lewis Many compounds do not follow the octet rule either due to a deficiency or excess amount of electrons; only the elements C, N, O, F, and Ne must follow the octet rule except cases where not enough electrons are available. It is important to realize that the central atom should be the only one to violate the octet rule due to an expanded octet, terminal atoms will still attempt to follow the octet rule. Determining the correct Lewis structure for expanded valence molecules is effectively the same as for those that follow the octet rule. Using SF 4 as an example: 1) The least electronegative element is the central atom, more electronegative elements are terminal atoms. 2) Valence electrons are first put on the most electronegative elements to give octets, with any extra electrons are put on the central atom. 3) Formal charges are determined with least formal charges or lowest range being the best, such as above where all formal charges are zero. The most appropriate Lewis structure has sulfur surrounded by more than 8 electrons with terminal atoms following the octet rule. Only elements in the third energy level or higher can exceed an octet and only as a central atom. In cases where an odd number of electrons exist it will be impossible for each atom to have an octet, this is called a radical. The method stays exactly the same as for any other except that the single extra electron will go to the most electropositive element, other atoms will still try to form octets. An example molecule which is a radical is NO 2 which appears as the following; note that nitrogen, the most electropositive element is the location of the radical.

3 Resonance Sometimes multiple valid Lewis structures can be drawn for the same molecule, these are called resonance structures. In order to be a resonance structure the Lewis structures must have the same atomic arrangement and same number of electrons, but with different electron arrangements. The carbonate ion is a resonance structure due to the delocalized nature of the double bond. Realize that the molecule is not being rotated; the electrons are moving to create a double bond from the carbon central atom to different oxygen atoms. Resonance structures are necessary because in reality none of these Lewis structures are completely accurate as the electrons are not actually forming a double bond from the carbon to any of the oxygen atoms. In would be more accurate to say that the extra bonding electrons are shared equally to all the oxygen atoms giving something closer to a 1 1 bond between the carbon 3 and each oxygen. Sometimes a compound/ion can have resonance, but while each structure would be valid, not all would be equally accurate. For example, the cyanate ion (OCN - ) has three valid resonance structures: The middle structure would be the most unfavorable due to the higher range of formal charges; the first and last Lewis structures have the same range. Since the ranges between the first and last are identical it's time to compare the locations of the formal charges relative to the electronegativity of each atom; negative FCs should be on the most electronegative atom. Oxygen is the most electronegative atom in this molecule so the most valid resonance structure will be the last one where the formal charge of -1 is located on the oxygen:

4 Valence-Shell Electron-Pair Repulsion (VSEPR) VSEPR theory considers all electron pairs, lone pairs (LP) and bond pairs (BP), and how they repel each other to have the maximum amount of space. There are two types of geometry to consider, electron-pair and molecular. Electron-pair geometry: The shape when considering all electron groups as equivalent. All molecular geometries are derived from electron geometries, and these are particularly useful for determining the general bonding angles. Molecular geometry: The actual shape of the molecule where LPs influence the shape but only BPs are considered as part of the shape. An important factor to consider is that more highly electronegative species will have higher repulsive forces; electrons have the highest electronegativity and generate the highest repulsive force. Number of Electron Groups Around Central Atom Molecular Geometry Electron Geometry With 2 Lone With 1 Lone Pair Pairs 2 Linear Linear Trigonal Planar Bent Linear - 4 Tetrahedral Trigonal Pyramidal Bent With 3 Lone Pairs Linear 5 Trigonal Bipyramidal Seesaw T-shaped Linear 6 Octahedral Square Pyramidal Square Planar T-shaped Repulsion between groups is highest between LPs, and weakest between BPs so structures will arrange to minimize LP interaction, this is most noticeable in trigonal bipyramidal and octahedral arrangements: LP - LP > LP - BP > BP - BP For trigonal bipyramidal e - pair geometries, LPs replace equatorial atoms allowing for 120 o between LPs. Dashed wedges indicate atoms pointing into the plane; filled wedges indicate atoms pointing out of the plane. For octahedral e - pair geometries, LPs take up opposing positions 180 o apart when possible. Covalent Bonding

5 Polarity The dividing line between ionic and covalent bonding is set along a continuum based on the differences in electronegativity with larger differences leading to compounds that are more ionic than those with atoms having much lower differences between electronegativities. Electronegativity difference; ΔX Bond Type < 0.4 covalent polar covalent > 2.0 ionic When determining whether a polar bond exists but the given electronegativities are not available a quick approximation can be done by asking one question: Are the bonded atoms the same or different? If you chose different (hopefully because they actually were) then it s a polar bond; if the bonded atoms are the same then a non-polar bond exists. A molecule is polar if it has a net dipole moment, or put another way, if based on the geometry of attached groups (atoms or lone-pairs) it is not "balanced out" (based on electronegativities). To determine polarity, first draw the structure CH 4 and CCl 4 both have equivalent electronegative groups around them so any force is counteracted by other equivalent groups. CH 3 Cl, CH 2 Cl 2, and CHCl 3 all have a central carbon surrounded by groups with differing electronegativities, no matter the arrangement the atoms will not repulse equally giving a polar molecule. Another way is to consider it like tug of war with terminal groups pulling. If the terminal groups are all identical the central atom wouldn't move in any direction meaning a non-polar molecule; if the terminal groups change then the molecule will be polar unless the groups are opposed by identical groups in a pattern which balances it all out. 1.) If a structure has only one lone pair on the central atom it is always polar 2.) Ionic charges do not make structures polar or non-polar, it only determines the number of electrons. 3.) How the structure is drawn does not influence polarity only the groups present and arrangement do. 4.) Single, double, or triple bonds do not influence polarity.

6 Hybridization Electrons from one atom interacting with the nucleus of another atom causes bonding which would theoretically proceed by half-filled orbitals overlapping causing the electrons to pair their spins. When treating an actual molecule such as methane (CH 4 ) this method leaves a problem in that the p-subshell only has 3 p-orbitals with which to bond, only two of which are half-filled giving only two overlaps (bonds). Hybridized orbitals allow for mixing of two (or more) orbitals to give orbitals with characteristics of both; hybridizing s and p orbitals gives sp orbitals that have characteristics of both the s and p. Energetically, hybridized sp orbitals are considered to be between that of a typical s and p orbital. For methane it would appear in the following way: Hybridization of s and p orbitals accounts for the bonding, and its tetrahedral shape. These 4 single bonds caused by the overlap of the s-orbitals of hydrogen with the sp hybrid orbitals of carbon would each be considered sigma (σ) bonds. σ bonds are caused by end on overlap of orbitals, alternatively in with double or triple bonds there will still be a σ bond in either, but for the double there will also be one pi (π) bond, while a triple has two π bonds caused by a side-toside overlap of p-orbitals. Hybridization is easy to determine as it only involves counting groups (atoms and lone-pairs) attached to the element in question, and understanding of how many orbitals are possible for each type of subshell; there is only 1 orbital for an s-subshell, 3 orbitals for a p-subshell, and 5 orbitals for a d-subshell. To determine hybridization around the central atom count up the number of attached groups. In CH 2 O there are 4 bonds, but only 3 attached groups, 1 O and 2 H s. Three groups require 1 s- and 2 p-orbitals giving a hybridization of sp 2. This next one, ClF 3, has 5 attached groups, 2 lone-pairs and 3 F s. It will need 1 s-, 3 p-, and 1 d-orbital giving a hybridization of sp 3 d. The number of hybrid orbitals must be equal to the number of attached groups, for CH 2 O, there are 3 groups, so 3 orbitals are necessary, and for ClF 3, there are 5 groups, so 5 orbitals are necessary.

7 Intermolecular forces (IMFs) are attractive forces encountered between molecules that influence physical properties such as boiling and melting point; similar to bonds but much weaker. They include: London Dispersion: Also known as an induced dipole, or instantaneous dipole, is the weakest IMF; it deals primarily with attraction of the negatively charged electron cloud of one molecule to the positive core of another when the molecule is temporarily polarized: Higher polarizability is based on two factors: molar mass (higher molar mass ~ more electrons to polarize) and molecular shape (more surface area ~ more interaction). Dipole-Dipole: Dipole-dipole interactions involve two polar molecules. The polar nature means that there is a permanent dipole present. The opposite poles of polar molecules are attracted to one another; the positive pole of one is attracted to the negative pole of another molecule. The larger the dipoles are, the stronger the attraction between the molecules. Hydrogen Bonding: Hydrogen bonding is a special case of dipole-dipole interactions that involves a very large dipole. This occurs when a hydrogen atom directly attached to a highly electronegative element (N, O, or F) interacts with a highly electronegative element on another molecule also directly attached to a hydrogen atom. Ion-Dipole: Strong interaction between polar molecules and ions. This type of interaction is present in any mixture of a polar substance with an ionic substance, such as NaCl in water NaCl(aq). Ion-Ion: The interaction between two ions, the strength of which is based on the lattice energy. Lattice energy can be approximated using Coulomb's law which relates the ionic charges (q 1 and q 2 ) and internuclear distance (r) to the lattice energy (E). The remaining factor (1/4πɛ 0 ) can be thought of as a constant (k): E = 1 q 1q 2 = k q 1q 2 4πε 0 r r A higher product of charges and smaller internuclear distance indicates a higher lattice energy. The charges have a greater impact on the lattice energy, therefore it is generally only necessary to consider the internuclear distance when the product of the charges is the same. The internuclear distance should be estimated based on the ionic radii of each ion. Any molecule can exhibit multple IMFs, but it is generally only necessary to consider the strongest force present. Physical properties such as boiling point, melting point, surface tension (tendency to reduce surface area), viscosity (resistance to flow), and hardness (strength of crystal structure) are increased with increasing strength of IMFs as opposed to vapor pressure and solubility which increase with decreasing strength of IMFs.

8 Solids are the densest state of matter and can come in the form of different types of crystals including atomic solids which are comprised of units that are single atoms such as Xe, Fe, etc; these can be metallic, covalent, or even nonbonding dispersion based. There are also crystalline solids made up of covalent compounds (molecular solids) and ionic compounds (ionic solids). When a solid forms a definite arrangement it is called a crystalline solid, while if a solid has a disordered arrangement it is referred to as an amorphous solid. The lattice of a crystalline solid is comprised of regularly repeating units called a unit cell. The unit cell is the simplest representation of the 3D structure of a lattice; upon replication it gives the entirety of the lattice. The following table summarizes some characteristics of three basic cubic units cells. 2r 4r 3 2r 2 Atoms per cell: While something like a simple cubic seems to be made up of 8 atoms, one at each corner, in fact each of those atoms is shared equally with the adjacent unit cell therefore only a portion of each atom is included in each unit cell; the amount of each atom contained in a unit cell is dependent on the location of the atom. Atoms on the corner contribute 1, on the edge contribute 1, on the face contribute 1, while an atom in the center belongs completely to the cell. Coordination Number: Describes how many atoms are in direct contact with each individual atom, for a simple cubic each individual atom is in direct contact with 6 other atoms. Edge Length: The atomic arrangement requires geometry to determine how the radius (r) influences the edge length (l) of the unit cell which is important for describing cell density, amongst other features. Packing Efficiency: Describes the amount of space in a unit cell occupied by atoms. The remaining percentage is unoccupied void space in the lattice. Density is a measure of mass per unit volume, generally in units of g for solids. This can be cm3 related to a unit cell using the number of atoms in the given unit cell to find the mass and using the radius of the atom to find the edge length which when cubed gives the volume.