Periodic Properties of the Elements. Effective Nuclear Charge, Zeff

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1 Key Concepts: Periodic Properties of the Elements 1. Understand and be able to predict and explain trends in effective nuclear charge, Z eff. 2. Understand and be able to predict and explain the periodic trends in: 2.1. atom size 2.2. ion size 2.3. ionization energy 2.4. electron affinity 2.5. Properties of elements: Metals, nonmetals, groups (descriptive chemistry) 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. Larson-Foothill College 1 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, Z eff. 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) occupied by the electron being screened. 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. Larson-Foothill College 2

2 Z eff - Effective Nuclear Charge Sodium valence electron Z eff at 100% screening: Z eff = = +1 Lower energy (inner) electrons shield higher energy (outer) electrons from seeing a full nuclear charge. This screening is not 100%. Z eff = 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. Electrons in the same valence shell screen each other very little, but do have a slight screening effect. For valance electrons, the the core electrons provide most of the shielding. Screening electron density from the core electrons: 1s, 2s, and 2p Actual Na atom 3s valence electron screening by core electrons: Z eff = = Larson-Foothill College 3 Trends in Effective Nuclear Charge Equation 7.1: Zeff = Z - S Notice: The Zeff experienced by the innermost electrons, those in the 1s subshell (red circles), closely tracks the increase in nuclear charge, Z (black line). The Zeff experienced by the outermost valence electrons (blue squares) not only is significantly smaller than Z, it does not evolve linearly with increasing atomic number; it varies periodically. Graph showing the variations in effective nuclear charge for period 2 and period 3 elements. Slater s Rules: A Closer Look, page Electrons for which the principle quantum number n is larger than the value of n for the electron of interest contribute zero to the value of s. 2. Electrons with the same value of n as the electron of interest contribute 0.35 to the value of S. (Note: The electron does not screen itself.) 3. Electrons for which n is one less than n for the electron of interest contribute 0.85 to the value of S, while those with even smaller values of n contribute Larson-Foothill College 4

3 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. 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 The result is that the ns orbitals are lower in energy then the (n-1)d orbitals. This is why we fill the 4s before the 3d, 5s before 4d, etc. Graphs showing the 2s and 2p radial probability functions. Larson-Foothill College 5 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. Larson-Foothill College 6

4 Atomic Radius - Predictions When two atoms bond covalently, the bonding atomic radius of the two atoms can be used to predict the covalent bond length (the distance between the two nuclei). Bonding atomic radii are shorter than nonbonding atomic radii due to the attractive forces that lead to the bond. Bonding Atomic Radii in Angstroms 1 Å = m Use the figure of bonding atomic radii to predict: 1. the largest diatomic covalent molecule bond distance. 2. if a N-S bond is longer or shorter than a P-O bond. Larson-Foothill College 7 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. Metals lose electrons to become cations. Nonmetals gain electrons to become anions. We can use spdf notation to show this. 1. Al > Al e [Ne]3s 2 3p 1 > [Ne] + 3e (loses the 3s and 3p electrons) 2. Ca > Ca e [Ar]4s 2 > [Ar] + 2e (loses the 4s electrons) 3. O + 2e > O 2- [He]2s 2 2p 4 + 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 > Fe e [Ar]4s 2 3d 6 > [Ar]3d 6 + 2e (loses the 4s electrons) 2. Fe > Fe e [Ar]4s 2 3d 6 > [Ar]3d 5 + 3e (loses the 4s & a 3d electron) Write electron configurations for Li +, Zn 2+, Mn 4+, P 3, Sn 2+ and Sn 4+. Larson-Foothill College 8

5 Ions show a trend in ionic size as well. Ionic Size Trends Cations are smaller than the atoms they come from because they have lost outer electrons. Also, electron-electron repulsions are reduced. Anions are larger than the atoms they come from because of increased electron-electron repulsions. Also, Z eff decreases for added valence electrons. about 2x size about 1/2 size Larson-Foothill College 9 Period Trends - Comparison of Atomic and Ionic Radii (Units are angstroms: 1 Å = m) Grey: Neutral radius Pink: Cation radius Grey: Neutral radius Blue: Anion radius Larson-Foothill College 10

6 Isoelectronic Series - Same Valence Shell Electron Configuration Isoelectronic with [He] Isoelectronic with [Ne] Isoelectronic with [Ar] Isoelectronic with [Kr] Isoelectronic with [Xe] For isoelectronic series, what is the trend in size? Larson-Foothill College 11 Period Trends - Ionization Energy, IE Ionization Energy, IE, is the energy needed to remove an outer electron from an atom in the gas phase to make a positive ion. Each atom can have a series of ionizations to produce a multi-charged cation. For example consider the ionization of Mg(g): 1. First: Mg(g) > Mg + (g) + e IE 1 = +738 kj/mol 2. Second: Mg + (g) > Mg 2+ (g) + e IE 2 = kj/mol 3. Third: Mg 2+ (g) > Mg 3+ (g) + e IE 3 = kj/mol 1. Why the increase from IE 1 to IE 2? 2. Why the HUGE increase from IE 2 to IE 3? Larson-Foothill College 12

7 Periodic Trends - First Ionization Energy, IE 1 In general: first ionization energy increases across a row. Z eff increases across a row. As Z eff 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, IE 1 of N is greater than IE 1 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 13 Periodic Trends - Electron Affinity, EA Electron affinity is the energy change when an electron is added to a neutral atom in the gas phase. For example: F(g) + e > F (g) Na(g) + e > Na (g) N(g) + e > N (g) EA = -328 kj/mol EA = -53 kj/mol EA > 0 kj/mol so N (g) is unstable All second electron affinities are positive. For example: O - (g) + e > O 2 (g) EA2 = +744 kj/mol Does this make sense? Larson-Foothill College 14

8 Periodic Trends - Electron Affinity, EA The trends are not as regular as for ionization energies. Larson-Foothill College 15 Increase Summary of Atomic Trends Increase Z eff 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: Nonmetals have high electron affinities and tend to form (-) ions. Metals tend to have low ionization energies and form (+) ions. Compounds formed by a metal and a nonmetal tend to be ionic substances. Compounds formed by two nonmetals tend to be molecular substances. Larson-Foothill College 16

9 Metals Properties 1. Low ionization energies - oxidized easily 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) 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) The oxide ion is basic in water: O 2- (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) Larson-Foothill College 17 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) Larson-Foothill College 18

10 Questions: Trends in Properties of the Elements 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 +? Text Question 7.36 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 19 Problems From Text 7.55 Consider the first ionization energy of neon and the electron affinity of fluorine. (a) Write equations, including electron configurations, for each process. (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? 7.53 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 20

11 Problems From Text 7.95 (a) Use orbital diagrams to illustrate what happens when an oxygen atom gains two electrons. (b) Why does O 3 not exist in nature? Larson-Foothill College 21 Problems From Text Predict whether each of the following oxides is ionic or molecular: CO2 BaO SO3 Fe2O3 Li2O H 2 O 7.67 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

12 Problems From Text (Time permitting) (a) Write the electron configuration for Li, and estimate the effective nuclear charge experienced by the valence electron. (b) The energy of an electron in a one-electron atom or ion equals where Z is the nuclear charge and n is the principal quantum number of the electron. Estimate the first ionization energy of Li. (c) Compare the result of your calculation with the value reported in Table 7.4, and explain the difference. (d) What value of the effective nuclear charge gives the proper value for the ionization energy? Does this agree with your explanation in (c)? Larson-Foothill College 23 Problems From Text (Time permitting) Consider the gas-phase transfer of an electron from a sodium atom to a chlorine atom: (a) Write this reaction as the sum of two reactions, one that relates to an ionization energy and one that relates to an electron affinity. (b) Use the result from part (a), data in this chapter, and Hess s law to calculate the enthalpy of the above reaction. Is the reaction exothermic or endothermic? (c) The reaction between sodium metal and chlorine gas is highly exothermic and produces NaCl(s), whose structure was discussed in Section 2.6. Comment on this observation relative to the calculated enthalpy for the aforementioned gas-phase reaction. Larson-Foothill College 24

13 Alkali Metals Very reactive because of low ionization energy. Easily oxidized. Very good reducing agents. Found only as compounds in nature. Low melting points and densities when pure. All will form metal hydrides: 2 Na(s) + H 2 (g) > 2 NaH(s) All will react with water to form hydroxides and H 2 : 2 Na(s) + 2 H 2 O(l) > 2 NaOH(aq) + H 2 (g) Reactivity increases down the column, why? (a) The reaction of lithium is evidenced by the bubbling of escaping hydrogen gas. (b) The reaction of sodium is more rapid and is so exothermic that the hydrogen gas produced burns in air. (c) Potassium reacts almost explosively. Larson-Foothill College 25 Alkaline Earth Metals Harder and more dense than alkali metals. Not as reactive. Generally don t form metal hydrides. All form stable oxides, their most common form in nature. Only Ca, Sr and Ba react with water at room temperature to form hydroxides: Ca(s) + 2 H 2 O(l) > Ca(OH) 2 (aq) + H 2 (g) Reactivity again increases down the column. Why? Calcium metal reacts with water to form hydrogen gas and aqueous calcium hydroxide, Ca(OH)2(aq). The colors of firework displays originate from the characteristic emissions of elements, including the alkaline earths. Strontium oxide, SrO(s) Larson-Foothill College 26

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