Selective Recap of “Shell Model” (from Schrödinger equation; orbitals, etc.) Electrons “exist in” orbitals, with only certain energy values (quantization) Orbitals have “fuzzy” 3D “shape”—NOT ORBITS Only 2 electrons max per orbital not all electrons can be in the lowest energy level An electron configuration describes the distribution of electrons in an atom (or ion) Copyright © Houghton Mifflin Company. All rights reserved.

Recap (continued) Notion of energy levels/shells (n = 1; n = 2, …) Each level comprised of sublevels (s, p, d, f) Each sublevel is made up of orbitals Shells are “fuzzy”! Only “average” distance increases w/ n  For today, we’ll generally focus on the “level” or “shell” as a whole—not worry so much about sublevels or individual orbitals. In general, electrons in the same shell will be considered to have a similar average distance from the nucleus. Valence electrons are those in outermost n level (called the “valence shell”) Core electrons are those in any level “closer in” than the valence shell (i.e. with n < nvalence) Copyright © Houghton Mifflin Company. All rights reserved.

Example: a P atom (Z=15) Electron config is: 1s2 2s2 2p6 3s2 3p3 Nuclear charge is +15 3 energy levels (highest n = 3) 3 “shells” [not orbits!] (imagine them “fuzzy”!) 5 valence electrons (in n = 3 level) 10 core electrons (in n = 1 & n = 2 levels) This model explains many “periodic” properties of elements +15 2 e- 2 e- 8 e- 8 e- 5 e- 5 e-

Periodic Properties (Observations) (first) Ionization Energy (of elements) Atomic radii (of elements) Charges of the monatomic cations and anions of the “Main Group” elements Review: Gp 1 is +1; Gp 2 is +2; etc. Some not exactly “periodic” properties: Cation/anion sizes Higher ionization energy patterns KNOWING TRENDS is not EXPLAINING Copyright © Houghton Mifflin Company. All rights reserved.

Ionization Energy (ies) (first) ionization energy (IE1): the energy needed to remove an electron from a gaseous atom: X(g)  X+(g) + e- ; DE = IE1 (second) ionization energy (IE2): energy needed to remove the second electron from a gaseous atom: X+(g)  X2+(g) + e- ; DE = IE2 Note: IE2 is not the energy to remove two electrons! (nth) ionization energy (IEn): etc. Copyright © Houghton Mifflin Company. All rights reserved.

Table 8.1 Successive Ionization Energies (in kJ/mol) for the Elements in Period 3 Copyright © Houghton Mifflin Company. All rights reserved.

p. 364, Tro 4/e: Chapter 8, Unnumbered Figure, Page 342

Explanation? (Factors Affecting Force Holding Electrons to Nucleus) Coulomb’s Law force between an electron and the nucleus is determined by: Average distance away (farther [higher n] means smaller force) Magnitude of effective (“apparent”) nuclear charge (Zeff) (Greater Zeff means stronger force) Core electrons are closer to nucleus and experience a greater effective nuclear charge (see next slide) Core electrons are held very tightly, have huge I.E.’s! Valence electrons are farther from the nucleus and experience a smaller effective nuclear charge (because they are shielded by core electrons!) Valence electrons are held relatively weakly, have lower I.E.’s! Copyright © Houghton Mifflin Company. All rights reserved.

# of shielding electrons +1 # of shielding electrons Zeff (for the n = 2 e-) Actual nuclear charge Chapter 8, Figure 8.12 Screening and Effective Nuclear Charge Zeff(1s [a core] e-) = +3 – 0 = +3

How do you calculate Zeff? Zeff = Zact – S (Zact = the actual charge of nucleus = Z) S is the number of “shielding” (or screening) electrons. -- In simplified model, a shielding electron is any electron in a “closer” energy level (i.e., smaller n value) Copyright © Houghton Mifflin Company. All rights reserved.

How do you calculate Zeff? Practice from Worksheet! Calculate the Zeff of the (outermost electron(s) in the) following: Li, C, S, Ar, Cl, Cl-, Cl+, Ca, Ca+, Ca2+ Copyright © Houghton Mifflin Company. All rights reserved.

How does model explain why Gp I and Gp II cations have different charges? Removal of a core e- is difficult because it has huge Zeff and smaller distances  strong Coulomb’s Law force attracting it to nucleus Diff. Groups  Diff. # v e-’s  diff. # of ionizations to “reach” the core  diff. charge of “stable” ion! Gp I atoms have 1 valence e-  gets really hard to remove an electron AFTER one is gone (IE2 is huge)  +1 ion is “stable”) Gp II atoms have 2 valence e-’s  gets really hard to remove an electron after TWO are gone (IE3 is huge)  +2 ion is “stable”) Copyright © Houghton Mifflin Company. All rights reserved.

Closer Look: Na vs Mg (also see pictures on board) Na (Z = 11) 1s2 2s2 2p6 3s1 Zeff (3s electron [valence]) = +11 – 10 = +1 Zeff (2p electron [core]) = +11 – 2 = +9 !!! (2nd electron)  The 8 electrons in the n = 2 level were shielding for the 3s electron, but not for those in the n = 2 level! Mg (Z = 12) 1s2 2s2 2p6 3s2 Zeff (3s electron [valence]) = +12 – 10 = +2 Zeff (2p electron [core]) = +12 – 2 = +10 !!! (3rd electron) Copyright © Houghton Mifflin Company. All rights reserved.

Table 8.1 Revisited (focus on IE1) Copyright © Houghton Mifflin Company. All rights reserved.

Figure 8.10 The Values of First Ionization Energy for the Elements in the First 5 Periods Copyright © Houghton Mifflin Company. All rights reserved.

Figure 8.16. Ionization energy increases across a row and decreases down a family I1’s (in kJ/mol) Copyright © Houghton Mifflin Company. All rights reserved.

How does model explain why IE1 values increase as you move across a row (focus on main groups)? Across a row, Zeff (= Zact – S) increases Zactual increases with each element (proton added to nucleus) S remains same (b/c electrons being added to outer “shell”) No “base” distance issue to consider—outer electron coming from same energy level in all elements in row Larger Zeff, similar base distance  stronger force  Harder to pull away  larger IE ! Copyright © Houghton Mifflin Company. All rights reserved.

Recall: First Ionization Energies decrease as you go down a family (Table from Zumdahl) Copyright © Houghton Mifflin Company. All rights reserved.

How does model explain why IE1 values decrease as you move down a family? Down a family, Zeff is SAME Try it out! (This is not “obvious”) Na and K both have Zeff = +1 (only one valence electron  all BUT one are shielding electrons!) Results from the “shell” model; each time a new energy level starts to fill, a whole level of electrons becomes shielding, so Zeff drops back down to +1) Valence electrons are “one shell farther out” for each row you go “down” Same Zeff, farther away energy level  weaker force  Easier to pull away  smaller IE ! Copyright © Houghton Mifflin Company. All rights reserved.

Atomic Radii Trends Copyright © Houghton Mifflin Company. All rights reserved.

Fig. 7.34 (Zumdahl) and Fig. 8.10 (Tro) Atomic radii get smaller across a row, and larger down a family Atomic Radii (in pm) Copyright © Houghton Mifflin Company. All rights reserved.

How does model explain why atomic radii decrease as you move across a row (focus on main groups)? Across a row, Zeff increases See earlier slide for ionization energy trend! No “base” distance issue to consider—outer electron coming from same energy level in all elements in row Larger Zeff, similar base distance  stronger force  Outer electrons are pulled in closer Across a row, increasing Zeff and stronger force pulling inward results in both trends: Stronger force  greater ionization energy and shell is “pulled in closer” Copyright © Houghton Mifflin Company. All rights reserved.

How does model explain why atomic radii increase as you move down a family? Down a family, Zeff is SAME See earlier slide for ionization energy Valence electrons are “one shell farther out” for each row you go “down” Same Zeff, farther away energy level  larger atomic radius ! Down a column, outer electrons are in higher energy (bigger n) levels and are thus farther away. This makes ionization energy smaller, but radius bigger Copyright © Houghton Mifflin Company. All rights reserved.

What about forming anions? (Electron Affinity) Electron affinity (EA): the energy change associated with adding an electron to a gaseous atom: X(g) + e-  X-(g); DE = EA Trends pretty “poor”. Main idea is that only HALOGENS have significantly exothermic EAs. Copyright © Houghton Mifflin Company. All rights reserved.

Fig. 18.17 (Tro) Copyright © Houghton Mifflin Company. All rights reserved.

(From Zumdahl) Figure: 06-06 Title: Electron affinity Caption: Figure 6.6  Measured electron affinities for elements 1–57 and 72–86. A negative value means that energy is released when an electron adds to an atom, while a value of zero means that energy is absorbed but the exact amount can’t be measured experimentally. Note that the group 2A elements (alkaline earths) and the group 8A elements (noble gases) have Eea values near zero, while the group 7A elements (halogens) have large negative Eea’s. Accurate electron affinities are not known for elements 58–71.

How does model explain why adding an electron is favorable for halogens, but not noble gases? Near the right of a row Zeff is quite large There’s “space left” in the p sublevel for halogens, but not noble gases! Config is s2 p5 for halogens, but s2 p6 for noble gases Added electron goes into the valence shell in a halogen (where it can “see” the nucleus), but into the next higher energy level in a noble gas (where Zeff will be ~0!) Copyright © Houghton Mifflin Company. All rights reserved.

How does model explain why adding an electron is favorable for halogens, but not noble gases? ~0 Zeff; No attraction for added electron! Added electron still “sees” nucleus because S is still low) Copyright © Houghton Mifflin Company. All rights reserved.

Model also explains why Gp VI anions are -2, Gp V anions are -3 Gp VI atoms have valence config s2 p4 There “room” for 2 electrons in the p sublevel (after that it will be unfavorable to add any more because they’ll have to go into the next higher energy level and be shielded from the nucleus) Gp V atoms have valence config s2 p3 There “room” for 3 electrons in the p sublevel (after that it will be unfavorable to add any more because they’ll have to go into the next higher energy level and be shielded from the nucleus) Copyright © Houghton Mifflin Company. All rights reserved.

Cations of same element are smaller; Anions of same element are larger Same element  same number of protons Thus: If fewer electrons, less electron-electron repulsion  electrons (shells) pulled in CLOSER (smaller radius) If more electrons, greater electron-electron repulsion  electrons (shells) pushed farther away (larger radius) In cases where the only difference between two species is the number of electrons, THEN electron-electron repulsion is key (and is looked at “explicity”). Otherwise, Zeff & valence n-level are considered. Copyright © Houghton Mifflin Company. All rights reserved.

CHM 121 R, W12 & T, W13 Radius increases when an electron is added to an atom (more e--e- repulsion) (Also See Fig. 8.14 in Tro)

CHM 121 R, W12 & T, W13 Radius decreases when an electron is removed from an atom (less e--e- repulsion) (Also See Fig. 8.13 in Tro)

Reminder: What we just discussed was: # of protons is the same (but the number of electrons differs) (largest radius) S2- > S- > S > S+ > S2+ (smallest radius) Quick Quiz: What do you think is the trend in ionization energy? (__________ IE1) S2- > S- > S > S+ > S2+ (__________ IE1) smallest largest Copyright © Houghton Mifflin Company. All rights reserved.

Let’s flip it around: What if the number of electrons is the same (but the number of protons differs)? Same # TOTAL electrons  “isoelectronic”  same exact electron configuration!  same exact # of shielding electrons (S) Thus: If fewer protons, smaller Zeff  electrons pulled in LESS tightly (larger radius; smaller IE) If more protons, greater Zeff  electrons pulled in MORE tightly (smaller radius; larger IE) (______radius) O2- > F- > Ne > Na+ > Mg2+ > Al3+ (_______ radius) largest smallest Copyright © Houghton Mifflin Company. All rights reserved.

CHM 121 R, W12 & T, W13 Figure 8.8 (Zumdahl) Sizes of Ions Related to Positions of the Elements on the Periodic Table The enclosed five ions are isoelectronic—they have the same number of electrons [and the same configuration]. The size decreases as there are MORE PROTONS in the nucleus (greater Zeff here).

Why do Metals Tend to Form Cations & Nonmetals Tend to Form Anions? Again, Zeff! Zeff smallest at left; increases as you move right Metal atoms: low Zeff Easy to remove an electron(s) [so cations are formed] Not very favorable to add an electron [metal “anions” rare] Nonmetal atoms: high Zeff Is (relatively) favorable to add an electron [to form anions] AS LONG AS THERE IS “ROOM” (no room in noble gases!) Hard to remove an electron(s) [so nonmetal “cations” rare] Copyright © Houghton Mifflin Company. All rights reserved.

Fig. 8.19: Trends in Metallic Character Chapter 8, Figure 8.19 Trends in Metallic Character II

Metallic Character Decreases Less cation, more anion formation IE1 increases Radius decreases Metallic Character Decreases Less cation, more anion formation (except for noble gases, neither) Because (according to QM “shell” model of atoms): Zeff (for v. e-’s) increases to right (avg) distance of v. shell decreases up a family Stronger attraction for v. shell e-’s up and right! But not favorable to add e-’s to (n + 1) level Copyright © Houghton Mifflin Company. All rights reserved.

Review: Periodic Properties We’ve Discused and Explained with Shell Model (first) Ionization Energy (of elements) Atomic radii (of elements) Electron Affinities Metallic Character Charges of the monatomic cations and anions of the “Main Group” elements Review: Gp I, II cations; Gp V,VI, VII anions Some not exactly “periodic” properties: Cation/anion sizes (radii); 1) of same element and 2) in isoelectronic series Higher ionization energy patterns Copyright © Houghton Mifflin Company. All rights reserved. 7–39 39

(Small IE1 for alkali metals) (Large IE1 for noble gases) Figure: 06-09-17UN Title: The Octet Rule Caption: Atoms tend to gain or lose electrons in order to attain an electron configuration resembling a noble gas. Since the outermost shell in these cases is comprised of an s orbital and three p orbitals, the maximum number of electrons in the valence shell is eight (the octet). (~0 EA for noble gas) (negative EA for halogens)