Selective Recap of “Shell Model” (from Schrödinger equation; orbitals, etc.) Copyright © Houghton Mifflin Company. All rights reserved.7–17–1 An electron configuration describes the distribution of electrons in an atom (or ion) 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

Recap (continued) 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 < n valence ) Copyright © Houghton Mifflin Company. All rights reserved.7–27–2 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.

Example: a P atom (Z=15) Electron config is: 1s 2 2s 2 2p 6 3s 2 3p 3 Nuclear charge is 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 7–37– e - 8 e - 5 e - 2 e - 8 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.7–47–4

Ionization Energy (ies) (first) ionization energy (IE 1 ): the energy needed to remove an electron from a gaseous atom: X(g)  X + (g) + e - ;  E = IE 1 Copyright © Houghton Mifflin Company. All rights reserved.7–57–5 (second) ionization energy (IE 2 ): energy needed to remove the second electron from a gaseous atom: X + (g)  X 2+ (g) + e - ;  E = IE 2 (n th ) ionization energy (IE n ): etc. Note: IE 2 is not the energy to remove two electrons!

Copyright © Houghton Mifflin Company. All rights reserved.7–67–6 Table 8.1 Successive Ionization Energies (in kJ/mol) for the Elements in Period 3

p. 342, Tro:

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 (Z eff ) (Greater Z eff means stronger force) [Concept of Z eff sort of pushes the idea of electron-electron repulsion under the rug; focuses on charge “neutralization” —more on this later] Copyright © Houghton Mifflin Company. All rights reserved.7–87–8 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) Z eff = Z act – S(Z act = the actual charge of nucleus = Z)

Z eff (for the n = 2 e - ) Z eff (v. e - ) = Z act – S = +3 – 2 = +1 Z act (Shielding) Z eff (1s e - ) = Z act – S = +3 – 0 = +3

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 Z eff and smaller distances  strong Coulomb’s Law force attracting it to nucleus Copyright © Houghton Mifflin Company. All rights reserved.7–10 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 (IE 2 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 (IE 3 is huge)  +2 ion is “stable”)

Closer Look: Na vs Mg (also see pictures on board) Na (Z = 11) –1s 2 2s 2 2p 6 3s 1 –Z eff (3s electron [valence]) = +11 – 10 = +1 –Z eff (2p electron [core]) = +11 – 2 = +9 !!! (2 nd electron)  The 8 electrons in the n = 2 level were shielding for the 3s electron, but not for those in the n = 2 level! Copyright © Houghton Mifflin Company. All rights reserved.7–11 Mg ( Z = 12 ) –1s 2 2s 2 2p 6 3s 2 –Z eff (3s electron [valence]) = +12 – 10 = +2 –Z eff (2p electron [core]) = +12 – 2 = +10 !!! (3 rd electron)

Copyright © Houghton Mifflin Company. All rights reserved.7–12 Table 8.1 Revisited (focus on IE 1 )

Copyright © Houghton Mifflin Company. All rights reserved.7–13 Figure 8.10 The Values of First Ionization Energy for the Elements in the First 5 Periods

Copyright © Houghton Mifflin Company. All rights reserved.7–14 Figure Ionization energy increases across a row and decreases down a family I 1 ’s (in kJ/mol)

How does model explain why IE 1 values increase as you move across a row (focus on main groups) ? Across a row, Z eff (= Z act – S) increases –Z actual increases with each element (proton added to nucleus) –S remains same (b/c electrons being added to outer “shell”) Copyright © Houghton Mifflin Company. All rights reserved.7–15 No “base” distance issue to consider—outer electron coming from same energy level in all elements in row Larger Z eff, similar base distance  stronger force  Harder to pull away  larger IE !

Copyright © Houghton Mifflin Company. All rights reserved.7–16 Recall: First Ionization Energies decrease as you go down a family (Table from Zumdahl)

How does model explain why IE 1 values decrease as you move down a family? Down a family, Z eff is SAME –Try it out! (This is not “obvious”) Na and K both have Z eff = +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 Z eff drops back down to +1) Copyright © Houghton Mifflin Company. All rights reserved.7–17 Valence electrons are “one shell farther out” for each row you go “down” Same Z eff, farther away energy level  weaker force  Easier to pull away  smaller IE !

Ionic Radii Trends Copyright © Houghton Mifflin Company. All rights reserved.7–18

Copyright © Houghton Mifflin Company. All rights reserved.7–19 Fig (Zumdahl) and Fig (Tro) Atomic radii get smaller across a row, and larger down a family Atomic Radii (in pm)

How does model explain why atomic radii decrease as you move across a row (focus on main groups) ? Across a row, Z eff increases –See earlier slide for ionization energy trend! Copyright © Houghton Mifflin Company. All rights reserved.7–20 No “base” distance issue to consider—outer electron coming from same energy level in all elements in row Larger Z eff, similar base distance  stronger force  Outer electrons are pulled in closer Across a row, increasing Z eff and stronger force pulling inward results in both trends: Stronger force  greater ionization energy and shell is “pulled in closer”

How does model explain why atomic radii increase as you move down a family? Down a family, Z eff is SAME –See earlier slide for ionization energy Copyright © Houghton Mifflin Company. All rights reserved.7–21 Valence electrons are “one shell farther out” for each row you go “down” Same Z eff, 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

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);  E = EA Copyright © Houghton Mifflin Company. All rights reserved.7–22 Trends pretty “poor”. Main idea is that only HALOGENS have significantly exothermic EAs.

Copyright © Houghton Mifflin Company. All rights reserved.7–23 Fig (Tro)

(From Zumdahl)

How does model explain why adding an electron is favorable for halogens, but not noble gases ? Near the right of a row Z eff is quite large Copyright © Houghton Mifflin Company. All rights reserved.7–25 There’s “space left” in the p sublevel for halogens, but not noble gases! Config is s 2 p 5 for halogens, but s 2 p 6 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 Z eff will be ~0!)

Copyright © Houghton Mifflin Company. All rights reserved.7–26 How does model explain why adding an electron is favorable for halogens, but not noble gases ? ~0 Z eff ; No attraction for added electron! Added electron still “sees” nucleus because S is still low)

Model also explains why Gp VI anions are -2, Gp V anions are -3 Gp VI atoms have valence config s 2 p 4  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) Copyright © Houghton Mifflin Company. All rights reserved.7–27 Gp V atoms have valence config s 2 p 3  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)

Cations of same element are smaller; Anions of same element are larger Same element  same number of protons Thus: Copyright © Houghton Mifflin Company. All rights reserved.7–28 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, Z eff & valence n-level are considered.

Radius increases when an electron is added to an atom (more e - -e - repulsion) (Also See Fig in Tro)

Radius decreases when an electron is removed from an atom (less e - -e - repulsion) (Also See Fig in Tro)

Reminder: What we just discussed was: # of protons is the same (but the number of electrons differs) Copyright © Houghton Mifflin Company. All rights reserved.7–31 (largest radius) S 2- > S - > S > S + > S 2+ (smallest radius) (__________ IE 1 ) S 2- > S - > S > S + > S 2+ (__________ IE 1 ) Quick Quiz: What do you think is the trend in ionization energy? smallestlargest

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) Copyright © Houghton Mifflin Company. All rights reserved.7–32 If fewer protons, smaller Z eff  electrons pulled in LESS tightly (larger radius; smaller IE) If more protons, greater Z eff  electrons pulled in MORE tightly (smaller radius; larger IE) (______radius) O 2- > F - > Ne > Na + > Mg 2+ > Al 3+ (_______ radius) Thus: largestsmallest

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 Z eff here).

Why do Metals Tend to Form Cations & Nonmetals Tend to Form Anions? Again, Z eff ! Copyright © Houghton Mifflin Company. All rights reserved.7–34 Z eff smallest at left; increases as you move right Metal atoms: low Z eff -Easy to remove an electron(s) [so cations are formed] -Not very favorable to add an electron [metal “anions” rare] Nonmetal atoms: high Z eff -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]

Fig. 8.19: Trends in Metallic Character

Copyright © Houghton Mifflin Company. All rights reserved.7–36 IE 1 increases Radius decreases Metallic Character Decreases Less cation, more anion formation (except for noble gases, neither) Because (according to QM “shell” model of atoms) : Z eff (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

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.7–37

(Small IE 1 for alkali metals) (Large IE 1 for noble gases) (~0 EA for noble gas) (negative EA for halogens)