## 2. Electron Configuration and Periodic Properties. Electron Spin - Fourth Quantum Number, ms

Electron Configuration and Periodic Properties Key Concepts/Goals: 1. 2. 3. 4. 5. 6. Understand the “4th” quantum number, ms. Understand and be able ...
Author: Maurice Houston
Electron Configuration and Periodic Properties Key Concepts/Goals: 1. 2. 3. 4. 5. 6.

Understand the “4th” quantum number, ms. Understand and be able to describe the Pauli exclusion principle. Understand and apply the Aufbau principle and Hund’s rule for electron filling of energy levels. Be able to write orbital box diagrams and electron configurations for elements that follow the expected filling order. Know the exceptions for the first row d elements. Understand and be able to predict and explain trends in effective nuclear charge, Zeff. Understand and be able to predict and explain the periodic trends in: atomic radii, ion radii, ionization energy, electron affinity and properties of elements (metals, nonmetals, groups).

Periodic Table: first proposed in 1869 separately by Dmitri Mendeleev in Russia and Lothar Meyer in Germany. The Periodic Table proposed by Mendeleev and Meyer was arranged in order of increasing atomic weight. Some elements seemed “out of order” though. The modern period table is arranged by rows and columns in order of increasing ATOMIC NUMBER. The properties of the elements tend to repeat, are periodic, from row to row.

1

Larson-Foothill College

Electron Spin - Fourth Quantum Number, ms An electron in an atom has the magnetic properties expected for a spinning, charged particle. Electrons in effect behave as tiny electromagnets. Experiments have shown that relative to an applied magnetic field, only two orientations are possible for the magnetic moment associated with this “electron spin”: aligned with the field or opposed to the field. This gives us a fourth quantum number, ms to define the final state of an electron. ms is the electron spin magnetic quantum number. ms is assigned a value of either +1/2 or -1/2 (We signify these as “spin up” or “spin down”.)

Evidence for the magnetic behavior of electrons:

+1/2 Larson-Foothill College

-1/2 2

Electron Spin - Fourth Quantum Number, ms We now have 4 quantum numbers to express the energy, location and “spin” of an electron. The Pauli Exclusion Principle states that no two electrons in an atom can have the same four quantum numbers. 1. 2. 3. 4.

n = principle (orbital energy, size) l = angular momentum (orbital type, shape) ml = magnetic (specific orbital orientation) ms = electron spin (direction of electron spin, ±1/2)

This leads to the conclusion that any atomic orbital defined by (n, l, ml) can contain a maximum of two electrons. Experiments have shown that when two electrons occupy the same orbital, they have opposite spin orientations. Their electron spins are said to be “paired”, that means that the magnetic field of one electron is cancelled by the magnetic field of the second of opposite spin. Example: An electron in a 3d orbital might have the following four quantum numbers, n = 3, l = 2, ml = 0, ms = +1/2. A second electron in the same 3d orbital would have the following quantum numbers, n = 3, l = 2, ml = 0, ms = -1/2. 3

Larson-Foothill College

Subshell Energies in Multi-Electron Systems Compared to Hydrogen

Hydrogen atom, single electron Multi electron atom

Subshell energies different in multi-electron systems than in the H atom: • Electron-electron interactions complicate the analysis. • Fortunately, we can still describe the electronic structure of many electron atoms in terms of orbitals like those of the hydrogen atom.

For multi-electron systems the energy of each orbital decreases (more negative) compared to the orbitals of hydrogen. Increased nuclear charge causes this: For example, the 1s orbital of H is higher in energy than 1s orbital of He. Different subshells within each principle energy level (n) no longer have the same energy. For a given n: s electrons closer than p electrons, s orbital lower in energy more stable. p subshells lower in energy than d subshells. d subshells lower in energy than f subshells. These effects can be explained by the concept effective nuclear charge. Effective Nuclear charge: The nuclear charge experienced by a particular electron in a multielectron atom, as modified by the presence of other electrons. Larson-Foothill College

4

Effective Nuclear Charge, Zeff The splitting of the principle energy level into the s, p, d, and f energy sublevels is best explained by using the concept of “effective” nuclear charge, Zeff. An electron in a higher energy level is “screened” from seeing 100% (all the protons) of the nuclear charge by the electrons in lower energy levels. We usually talk about the valence electrons and how they are screened from experiencing the complete nuclear charge. This screening depends on the sublevel (orbital type) that the electron being screened is occupying. The Effective Nuclear Charge is the NET NUCLEAR charge an electron experiences when other electrons “screen” the nuclear charge. An analogy is looking at a lightbulb that is covered by a frosted-glass lamp shade. The lampshade “screens” our eyes from the full brightness of the lightbulb.

5

Larson-Foothill College

Zeff - Effective Nuclear Charge Sodium valence electron Zeff at 100% screening: Zeff = 11-10 = +1

Lower energy (inner) electrons “shield” higher energy (outer) electrons from seeing a full nuclear charge. This screening is not 100%.

Actual Na atom 3s valence electron screening by core electrons: Zeff = 11-8.49 = +2.51

Zeff = Z - S where Z is the atomic number (number of protons) and S is the screening constant. S is a positive number with a value that is dependent on the energy subshell occupied by the electron. Electrons in the same valence shell screen each other very little, but do have a slight screening effect. For valance (highest energy, outermost) electrons, the core electrons provide most of the shielding. Larson-Foothill College

Screening electron density from the core electrons: 1s, 2s, and 2p 6

Trends in Effective Nuclear Charge Graph showing the variations in effective nuclear charge for period 1 through 3 elements. Period 3

Period 2

Period 1

Questions: •What do you notice about Zeff for hydrogen compared to atomic number that is different compared to the other elements? What is the reason for this difference? •What is the trend in Zeff across a period? Can you explain the trend? •What happens to Zeff at the beginning of a period? Can you explain this? •How does Zeff for the 1s electron in K compare to its atomic number? Can you explain why they are close in value, but not equal? 7

Larson-Foothill College

Other Details: “Splitting” of Subshell Energies with the Same n Value Remember that for many electron atoms, the energies of orbitals with the same n value increase in the order ns < np < nd < nf. Graph showing the 1s, 2s and 2p radial probability functions.

This can be explained by the following: • In general, for a given n value: s electrons penetrate closer to the nucleus than p p electrons penetrate closer to the nucleus than d d electrons penetrate closer to the nucleus than f

Thus, for a given n value, the attraction between the the electron and the nucleus decreases in the order: ns > np > nd > nf

One result is that the ns orbitals are lower in energy then the (n-1)d orbitals.This is why we fill the 4s before Orbital shape causes electrons in some the 3d, 5s before 4d, etc. orbitals to “penetrate” close to the nucleus. Penetration increases nuclear attraction and decreases shielding.

Larson-Foothill College

8

Multi Electron Atoms: Writing Electron Configurations “Aufbau” or “building up” principle. Electron configurations for each element are built upon the previous element in the table. One electron at a time is placed in the lowest energy orbital available. This gives the ground state electron configuration. The order of orbital filling is given by the periodic table with some exceptions! To write electron configurations using spdf notation, read the periodic table from left to right, row by row, filling the orbitals from the lowest energy up! Its that easy! Hund’s Rule (Bus seat rule): For orbitals of the same energy (degenerate orbitals), the lowest energy is attained when the number of electrons with the same spin is maximized. In other words, electrons occupy orbitals of the same energy one at a time until the sub-shell is half-filled (Can you think of the reason why this should occur?) In addition, all unpaired electrons will all have the same spin (parallel spins).

9

Larson-Foothill College

Orbital Filling and the Periodic Table The order in which the orbitals are filled can be obtained directly from the periodic table.

• Write condensed electron configurations and valence level orbital diagram for: C, K, Fe, As, and Cd.

• Some exceptions to the rule for transition elements: Cu, Cr. (Know exceptions for first row transition elements!)

• On exams, you will not be asked to write electron configurations beyond Barium.

Larson-Foothill College

10

Ground State Electron Configurations Some of the exceptions to the expected filling order are outlined in red.

Larson-Foothill College

11

General Electron Configurations of Groups of Elements Categories of Electrons • Inner (core) electrons are those an atom has in common with the previous noble gas and any • •

completed transition series. Outer electrons are those in the highest energy level (highest n value). Valence electrons are those involved in forming compounds. - For main group elements, the valence electrons are the outer electrons. - For transition elements, the valence electrons include the outer electrons and any (n -1)d electrons.

• The use of noble gas notation is useful for clearly showing the valence electrons. The valence electrons determine the chemical properties of an element. Why is this?

You must familiar with the following terminology and general electron configurations of groups: • Main Group Elements (Representative Elements): s and p block • Groups 1A (alkali metals) and 2A (alkaline earth metals) are the s-block elements. The last electrons are added to s orbitals. They have the general valence electron configuration: nsx • Groups 3A through 8A are the p-block elements. The last electrons are added to p orbitals. They have the general valence electron configuration: ns2npx • For the main group elements, the number of valence electrons equals the group number. • Transition Elements: For transition elements, the ns subshell fills before the (n-1)d subshell. The transition elements are the d-block elements. The last electrons are added to d orbitals. The transition elements have similar behavior because the electrons are being added to the (n-1) energy level, not the n level. • Lanthanides and Actinides: the 4f and 5f sublevels are being filled, respectively. Larson-Foothill College

12

Defining Atomic Radius When two of the same atoms bond covalently, the covalent bond length (the distance between the two nuclei) can be used to determine the covalent bonding atomic radius of the atom. Bonding atomic radii are shorter than nonbonding atomic radii due to the attractive forces that lead to the bond. The covalent radius of chlorine.

Known covalent radii and distances between nuclei can be used to find unknown radii.

13

Larson-Foothill College

Atomic Radius Trends (Outer Valence e–) Atomic radii decrease along a row. Why? Zeff increases as we add electrons to the same energy level. The increase in nuclear charge as we move across a row is not completely screened by the additional valence electrons so Zeff becomes larger for each valence electron. (Atomic radii of transition metals decrease only slightly across a period.) Atomic radii increase down a column. Why? As we move down a column n increases for the valence electrons, hence the orbital size also increases. Zeff also increases SLIGHTLY, but the valence electrons spend more time further from the nucleus in the larger orbitals, 2s compared to 1s, etc. Periodicity of Atomic Radius

Larson-Foothill College

14

Periodic Trends - Ionization Energy, IE Ionization Energy, IE, is the energy needed to remove an outer electron from an atom or ion in the gas phase. Ionization energies are usually given in units of kJ/mole of electrons. Do atoms with a low IE tend to form cations or anions? Each atom can have a series of ionizations to produce a multi-charged cation. For example consider the ionization of Mg(g): 1. 2. 3.

First:

Mg(g) —> Mg+(g) + e–

IE1 = +738 kJ/mol

Second:

Mg+(g)

IE2 = +1451 kJ/mol

Third:

Mg2+(g)

—>

Mg2+(g)

—>

+

Mg3+(g)

e–

+

e–

1.

Why the increase from IE1 to IE2?

2.

Why the HUGE increase from IE2 to IE3?

IE3 = +7733 kJ/mol

Name the Period 3 element with the following ionization energies (in kJ/mol) and write its electron configuration: IE1 IE2 IE3 IE4 IE5 IE6 1012

1903

2910

4956

6278

22,230

Larson-Foothill College

15

Periodic Trends - First Ionization Energy, IE1 In general: first ionization energy increases across a row. Zeff increases across a row. As Zeff increases there is more attraction of the electrons to the nucleus thus more difficult to remove. In general: first ionization energy decreases down a column. The outer electrons are in higher principle quantum shells and are further from the nucleus. Less attraction to the nucleus thus easier to remove. We see some exceptions however. For example, IE1 of N is greater than IE1 of O. Why? Half-filled p-sublevel for N is more stable than the partially filled p-sublevel for O. In N, we have no e– - e– repulsive pairing energy since all p-orbitals have only 1 e–. In O we have a p-orbital with two electrons, the pairing energy in this p-orbital leads to a slightly less stable electron configuration and thus lower ionization energy. Larson-Foothill College

16

Periodic Trends - Electron Affinity, EA Electron affinity is the energy change when an electron is added to a neutral atom or ion in the gas phase. Electron affinities are usually given in units of kJ/mole of electrons. Do atoms with a high EA tend to form cations or anions? For example: F(g) + e– —> F–(g) N(g) + e– —> N–(g)

EA = -328 kJ/mol EA = + 7 kJ/mol

Questions: All second electron affinities are positive. For example:

O-(g) + e– —> O2–(g) EA2 = +710 kJ/mol Does this make sense? Why does O3– not exist in compounds in nature? 17

Larson-Foothill College

Periodic Trends - Electron Affinity, EA The trends are not as “regular” as for ionization energies.

Electron affinities of the main-group elements (in kJ/mol).

Larson-Foothill College

18

Summary of Atomic Trends Increase

Increase

Zeff

The individual atomic properties of atoms can be related to the observed macroscopic behavior of the elements. The trends we observe across the periodic table help explain chemical behavior: • Reactive nonmetals have high IEs and highly negative EA; they tend to form (-) ions. • Reactive metals have low IEs and slightly negative EA; they tend to form (+) ions. • Noble gases have very high IEs and slightly positive EA; they tend to neither lose or gain electrons. • Compounds formed by a metal and a nonmetal tend to be ionic substances.

• Compounds formed by two nonmetals tend to be molecular substances. 19

Larson-Foothill College

Metals Properties 1. Low ionization energies - oxidized easily (good reducing agents) 2. Metallic bonding in elemental form

Chemistry 1. Metals and nonmetals react to form ionic compounds (salts): Metals + nonmetals —> salts 2 Fe(s) + 3 Cl2(g) —> 2 FeCl3(s)

Trends in Metallic Behavior

Metallic behavior decreases across a period.

Larson-Foothill College

2. Metal Oxides are basic since they contain a basic oxide ion: Soluble Metal oxide + water —> metal hydroxide Na2O(s) + H2O(l) —> 2 NaOH(aq)

Metallic behavior increases down a group

The oxide ion is basic in water: O2-(aq) + H2O(l) —> 2 OH–(aq) 3. Metal oxides react with acids: Metal oxide + acid —> salt + water Al2O3(s) + 6 HNO3(aq) —> 2 Al(NO3)3(aq) + 3 H2O(l)

20

Nonmetals Properties 1. Vary greatly in appearance 2. High electron affinities - tend to be reduced 3. Compounds of nonmetals are typically molecular substances (covalent bonding)

Chemistry 1. Nonmetal Oxides are acidic in solution: Nonmetal oxide + water —> acid CO2(g) + H2O(l) —> H2CO3(aq) 2. Nonmetal oxides react with bases: Nonmetal oxide + base —> salt + water SO3(g) + 2 NaOH(aq) —> Na2SO4(aq) + H2O(l)

Acid-base behavior of some element oxides.

Blue: Basic Purple: Amphoteric Red: Acidic 21

Larson-Foothill College

Questions •

Predict whether each of the following oxides is ionic or molecular:

CO2 BaO SO3 Fe2O3 Li2O

Write balanced chemical equations for the following reactions: (a) barium oxide with water

(b) iron(III) oxide with perchloric acid

(c) sulfur trioxide gas with water

(d) carbon dioxide gas with aqueous sodium hydroxide.

Larson-Foothill College

22

Highest and Lowest Oxidation Numbers of Main Group Elements

What is the oxidation number of nitrogen in nitric acid?

Do you expect nitric acid to be a good reducing agent or a good oxidizing agent?

23

Larson-Foothill College

Electron Configurations of Ions Main Group Elements: electrons are lost or gained so that the electron configuration of the ion matches that of the nearest Noble Gas. The ion is said to be isoelectronic (same electron configuration) with the Noble Gas. Metals lose electrons to become cations. Nonmetals gain electrons to become anions. We can use spdf notation to show this. 1. Al —> Al3+ + 3e– [Ne]3s23p1 —> [Ne] + 3e– (loses the 3s and 3p electrons) 2. Ca —> Ca2+ + 2e– [Ar]4s2 —> [Ar] + 2e– (loses the 4s electrons) 3. O + 2e– —> O2[He]2s22p4 + 2e– —> [Ne] (gains two e– to fill the 2p shell) In general, what type of orbitals are filled when nonmetals gain electrons?

Transition metals (d-block) lose the (n+1)s electrons first! 1. Fe —> Fe2+ + 2e– [Ar]4s23d6 —> [Ar]3d6 + 2e– (loses the 4s electrons) 2. Fe —> Fe3+ + 3e– [Ar]4s23d6 —> [Ar]3d5 + 3e– (loses the 4s & a 3d electron)

Write electron configurations for Li+, Zn2+, Mn4+, P3–, Sn2+ and Sn4+.

Larson-Foothill College

24

Magnetic Properties A species with one or more unpaired electrons exhibits paramagnetism – it is attracted by a magnetic field. A species with all its electrons paired exhibits diamagnetism – it is not attracted (and is slightly repelled) by a magnetic field. The apparent mass of a diamagnetic substance is unaffected by a magnetic field.

Determine if each of the following will have a mass that is unaffected by a magnetic field (Provide reasoning for each): • Fe

The apparent mass of a paramagnetic substance increases because it is attracted by the magnetic field.

• ZnCl2

25

Larson-Foothill College

Ionic Size Trends Ions show a trend in ionic size: • Cations are smaller than the atoms they come due to an increase in Zeff. Also, electron-electron repulsions are reduced. • Anions are larger than the atoms they come from because of increased electron-electron repulsions. Also, Zeff decreases for added valence electrons.

Larson-Foothill College

26

Period Trends - Comparison of Atomic and Ionic Radii (Units are picometers.) Grey: Anion radius Red: Atomic radius

An isoelectronic series

Questions: • What is the trend in ionic radius down a group, as n increases?

• What is an isoelectronic series?

• Within a isoelectronic

series, what trend do you notice for ion size? Does this trend make sense?

27

Larson-Foothill College

Questions • Compare B, Al, and C Which has the largest atomic radii? Which has the highest electron affinity? Rank them in order of INCREASING first ionization energy. Which has the most metallic Character? • Which experiences the greatest effective nuclear charge, a 2p electron in F−, a 2p electron in Ne, or a 2p electron in Na+?

• Consider S, Cl and K and their most common ions. (a) List the atoms in order of increasing size. (b) List the ions in order of increasing size. (c) Explain any differences in the orders of the atomic and ionic sizes.

Larson-Foothill College

28

Questions •

Consider the first ionization energy of neon and the electron affinity of fluorine. (a) Write the balanced chemical equations for each process. Include phase labels.

(b) These two quantities will have opposite signs. Which will be positive and which will be negative? (c) Would you expect the magnitudes of these two quantities to be the same. If not, which one would you expect to be larger and why?

While the electron affinity of bromine is a negative quantity, it is positive for Kr. Use the electron configurations of the two elements to account for this observation.

Larson-Foothill College

29