The Quantum Mechanical Model

Transcription

1 Recall

2 The Quantum Mechanical Model

3 Quantum Numbers Four numbers, called quantum numbers, describe the characteristics of electrons and their orbitals

4 Quantum Numbers

5 Quantum Numbers

6 The Case of Hydrogen

7 Orbitals For hydrogen, all orbitals with the same value of n have the same energy

8 Orbitals Energy states of a Hydrogen Atom In the ground state, electron resides in the 1s orbital An excited state can be produced by transferring the electron to a higher-energy orbital

9 Sample Question A ground-state electron in the hydrogen atom is given just enough energy to get to n = 2 Which orbital will the electron occupy? a. 2s orbital b. 2p x orbital c. 2p y orbital d. 2p z orbital e. Each of the above orbitals is equally likely

10 Electron Spin & the Pauli Principle

11 Electron Spin & the Pauli Principle Wolfgang Pauli Studied under Max Born and Niels Bohr Formulated his exclusion principle in 1925 for electrons (Wolfgang was 25) Helped establish the foundations of quantum theory Also the first to recognize the existence of the neutrino Won Nobel Prize in Physics in 1945

12 Electron Spin & the Pauli Principle Electron spin quantum number (m s ) Can be +1/2 or -1/2 Indicates that the e - can spin in one of two opposite directions Pauli Exclusion Principle In a given atom, no two e - s can have the same set of four quantum numbers An orbital can hold only two e - s, and they must have opposite spins

13 Figure The Spinning Electron

14 Sample Question Which of the following combinations of quantum numbers is not allowed? n l m l m s a ½ b ½ c ½ d ½ e ½

15 Polyelectronic Atoms

16 Polyelectronic Atoms Polyelectronic atoms Atoms with more than one electron, such as He, N, etc. Also called multi-electron atoms Hydrogen is the only atom that has one e - in the orbitals under ground state

17 Polyelectronic Atoms Polyelectronic atoms

18 Polyelectronic Atoms Polyelectronic atoms There are many energies/forces at play when there are multiple electrons present: Moving electrons have kinetic energy Attractive forces between the nucleus and electrons Repulsive forces between electrons You should be able to discuss all of these

19 Polyelectronic Atoms Polyelectronic atoms How do the additional e - s behave and affect the atom? Additional e - s means greater repulsion in the atom, and electrons tend to be as far away from each other as possible

20 Polyelectronic Atoms Effect of protons: However, more protons means a greater attractive force for e - s, so they will be pulled closer toward the nucleus

21 Polyelectronic Atoms Electron shielding When there are multiple energy levels, more e - s also create a shielding effect, where e - s closer to the nucleus block outer valence e - s from getting close to the nucleus It is easier to remove outer/ valence e - s due to this shielding effect

22 Polyelectronic Atoms Atoms other than hydrogen have variations in energy for orbitals having the same principal quantum number Electrons fill orbitals of the same n value in preferential order E ns < E np < E nd < E nf

23 Polyelectronic Atoms Polyelectronic atoms Electron density profiles show that s electrons penetrate to the nucleus more than other orbital types In other words, an electron in a 2s orbital is more strongly attracted to the nucleus than an electron in a 2p orbital Closer proximity to the nucleus = lower energy The 2s orbital is lower in energy than the 2p orbital

24 Sample Question When an electron is placed in a particular quantum level, they prefer the orbitals in what order? a. p, f, d, s b. s, p, f, d c. s, p, d, f d. f, d, p, s

25 The History of the Periodic Table

26 The History of the Periodic Table The Periodic Table

27 The History of the Periodic Table The Periodic Table Originally constructed to represent the patterns observed in the chemical properties of elements

28 The History of the Periodic Table The Periodic Table Johann Dobereiner à triad model Groups of three elements with similar properties

29 The History of the Periodic Table The Periodic Table John Newlands Suggested that elements should be arranged in octaves

30 The History of the Periodic Table The Modern Periodic Table Conceived by Julius Lothar Meyer and Dmitri Ivanovich Mendeleev

31 The History of the Periodic Table The Modern Periodic Table Mendeleev emphasized the usefulness of the periodic table in predicting the existence and properties of still unknown elements Used to table to correct several values of atomic masses

32 52

33 Electron Configurations

34 Arrangement of Electrons in Atoms Levels (n) Sublevels (l ) Orbitals (m l )

35 Electron Configurations: A Review n = 1 n = 2 n = 3 n = 4 Energy Levels

36 Arrangement of Electrons in Atoms Electron configuration = arrangement of e - s in atoms

37 Arrangement of Electrons in Atoms e - s assume an arrangement that gives the atom the lowest energy possible (more stable)

38 Arrangement of Electrons in Atoms What does this look like?

39 Electron Configurations 2p 4 Energy Level Number of electrons in the sublevel Sublevel 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 etc.

40 Arrangement of Electrons in Atoms What does this look like?

41 Aufbau Principle As protons are added one by one to the nucleus to build up elements, electrons are similarly added to these hydrogen-like orbitals

42 Aufbau Principle = e - s occupy the lowest E orbital available. Use the diagonal rule Aufbau Principle

43 1 s Diagonal Rule 2 s 2p s 3p 3d s 4p 4d 4f s 5p 5d 5f 5g? s 6p 6d 6f 6g? 6h? 7 s 7p 7d 7f 7g? 7h? 7i?

44 Pauli Principle Pauli Exclusion Principle = No more than two e - s can occupy a single orbital We note this using arrows in opposite directions

45 Hund s Rule The lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals

46 Hund s Rule Hund s Rule = Fill in single e - s in separate equal-energy orbitals before doubling up

47 Rules 1) Determine the # of e - s by looking up Z (atomic number) Assume the atom is neutral unless stated otherwise. Draw orbitals first to help you. Ex/ Nitrogen

48 Rules 2) Start filling orbitals in order of increasing E according to the Aufbau Principle. A single orbital can hold a max of 2 e - s Orbital Type Number of Orbitals s 1 p 3 d 5 f 7

49 Rules 3) Hund s Rule Applies: Draw all orbitals for each type, and fill in ONE e - in each orbital before doubling up.

50 Rules 4) Pauli Exclusion applies: Two e - s in the same orbital must have opposite spins

51 Rules 5) Double check numbers. Make sure total # of e - s in your configuration matches the atomic number (if your atom is neutral)

52 Orbitals and the Periodic Table Orbitals grouped in s, p, d, and f orbitals s orbitals d orbitals p orbitals f orbitals

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54 Examples

55 Write the orbital notation and e - Hydrogen configuration for

56 Write the orbital notation and e - Fluorine configuration for

57 Write the orbital notation and e - Magnesium configuration for

58 Write the orbital notation and e - Neon configuration for

59 Write the orbital notation and e - Arsenic configuration for

60 Orbitals and the Periodic Table Orbitals grouped in s, p, d, and f orbitals s orbitals d orbitals p orbitals f orbitals

61 Shorthand Notation

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63 Shorthand Notation We can abbreviate our long e- configurations by using our noble gases This is because our Noble Gases have complete full p orbitals Note: only do this when asked to

64 Shorthand Notation 1. Find the closest noble gas to your atom with a smaller Z 2. Add/fill orbitals from where the Noble Gas left off

65 Ex/Na Shorthand Notation

66 Shorthand Notation Try: Cl Ca

67 Sample Question How many of the following electron configurations for the species in their ground state are correct? Ca: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 Mg: 1s 2 2s 2 2p 6 3s 1 V: [Ar]3s 2 3d 3 As: [Ar]4s 2 3d 10 4p 3 P: 1s 2 2s 2 2p 6 3p 5 a. 1 b. 2 c. 3 d. 4 e. 5

68 Sample Question In which of the following groups do all the elements have the same number of valence electrons? a) P, S, Cl b) Ag, Cd, Ar c) Na, Ca, Ba d) P, As, Se e) None of these

69 Sample Question Element X has a ground-state valence electron configuration of ns 2 np 5 What is the most likely formula for the compound composed of element X and nitrogen? a. NX b. NX 7 c. NX 2 d. NX 3 e. NX 5

70 Sample Question Of the following elements, which has occupied d orbitals in its ground-state neutral atoms? a. Ba b. Ca c. Si d. P e. Cl

71 Periodic Table Review

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74 Periodic Trends

75 Periodic Trends in Atomic Properties Ionization Energy Electron Affinity Atomic Radius It is not sufficient to know the trends. You must be able to explain the trends.

76 Ionization Energy

77 Ionization Energy IE = Energy required to remove an e - from a gaseous atom or ion X (g) à X + (g) + e- Ionization energy increases for successive e - s First ionization energy (I 1 ): Energy required to remove the highest-energy e - of an atom The value of I 1 is smaller than that of the second ionization energy I 2

78 Ionization Energy As we go across a period from left to right, I 1 increases Why? e - s in the same quantum level (n) do not shield as effectively as e - s in inner levels Additional protons cause e - s in the same principal quantum level (n) to be more strongly bound as you go across a period

79 Ionization Energy As we go down a group, I 1 decreases Why? e - s being removed are farther from the nucleus As n increases, the size of the orbital increases à removal of e - s becomes easier

80 Ionization Energy

81 Figure Trends in Ionization Energies (kj/mol) for the Representative Elements

82 Exceptions Ionization Energy Half-filled and filled sublevels have irregularities due to extra repulsion of electrons paired in orbitals This makes them easier to remove

83 Sample Question The first ionization energy for phosphorus is 1060 kj/mol, and that for sulfur is 1005 kj/mol Why? Solution: Phosphorus and sulfur are neighboring elements in Period 3 of the periodic table and have the following valence electron configurations: Phosphorus is 3s 2 3p 3 Sulfur is 3s 2 3p 4

84 Sample Question Phosphorus and sulfur are neighboring elements in Period 3 of the periodic table and have the following valence electron configurations: Phosphorus is 3s 2 3p 3 Sulfur is 3s 2 3p 4 Ordinarily, the first ionization energy increases as we go across a period, so we might expect sulfur to have a greater ionization energy than phosphorus However, in this case the fourth p electron in sulfur must be placed in an already occupied orbital The electron electron repulsions that result cause this electron to be more easily removed than might be expected

85 Electron Affinity

86 Electron Affinity Electron Affinity = Energy change associated with the addition of an e - X (g) + e - à X - (g) In other words, electron affinity is a measure of how likely an atom is to gain an electron After the first e - is gained, an atom will release energy. The more energy that is released, the more negative the value will be. This indicates greater favorability for gaining an electron.

87 Electron Affinity Electron Affinity = Energy change associated with the addition of an e - X (g) + e - à X - (g) As we go across a period from left to right, e - affinities become more negative This is because it is more favorable to gain an electron as we go across the periodic table

88 Electron Affinity

89 Electron Affinity Electron Affinity = Energy change associated with the addition of an e - X (g) + e - à X - (g) Affinity tends to decrease as you go down a group Electrons are being added at increasing distances from the nucleus As electrons get farther from the nucleus, there are less nuclear attractive forces at play. However, these changes are relatively small compred to the changes across a period

90 Electron Affinity

91 Electron Affinity

92 Exceptions Electron Affinity There may be some irregularities due to repulsive forces in the relatively p orbitals

93 Atomic Radii

94 Atomic Radii Obtained by measuring the distance between atoms in a chemical compound Covalent atomic radii Determined from the distances between atoms in covalent bonds Metallic radii Obtained from half the distance between metal atoms in solid metal crystals

95 Atomic Radii Atomic radius decreases going across a period from left to right Increasing effective nuclear charge while going from left to right Valence e - s are closer to the nucleus, which decreases the size of the atom

96 Atomic Radii Atomic radius increases down a group Caused by the increase in orbital sizes in successive principal quantum levels

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98 Sample Question Predict the trend in radius for the following ions: Be 2+ Mg 2+ Ca 2+ Sr 2+

99 Solution All these ions are formed by removing two electrons from an atom of a Group 2A element In going from beryllium to strontium, we are going down the group, so the sizes increase: Be 2+ < Mg 2+ < Ca 2+ < Sr 2+ Smallest radius Largest radius

100 Sample Question Consider the following orders: I. Al < Si < P < Cl II. Be < Mg < Ca < Sr III. I < Br < Cl < F IV. Na + < Mg 2+ < Al 3+ < Si 4+ Which of these give(s) a correct trend in size? a. I b. II c. III d. IV e. At least two of the above give a correct trend in size

101 Sample Question Consider the following orders: Al < Si < P < Cl Be < Mg < Ca < Sr I < Br < Cl < F Na + < Mg 2+ < Al 3+ < Si 4+ Which of these give(s) a correct trend in ionization energy? a. III b. I, II c. I, IV d. I, III, and IV

102 Sample Question First ionization energy of magnesium is approximately 700 kj/mol What is a good estimate for the second ionization energy of magnesium? a. 700 kj/mol b kj/mol c. 70,000 kj/mol d. 700 kj/mol e kj/mol

103 Sample Question Which of the following statements concerning second ionization energy values is true? a. Second ionization energy of Al is higher than that of Mg since Mg wants to lose the second electron, so it is easier to take the second electron away b. Second ionization energy of Al is higher than that of Mg because the electrons are taken from the same energy level, but the Al atom has one more proton c. Second ionization energy of Al is lower than that of Mg because Mg wants to lose the second electron, so the energy change is greater d. Second ionization energy of Al is lower than that of Mg because the second electron taken from Al is in a p orbital, so it is easier to remove e. Second ionization energies are equal for Al and Mg

104 Sample Question For the atoms Li, N, F, and Na, which of the following is the correct order from smallest to largest atomic radius? a. Na, F, N, Li b. Na, Li, N, F c. Li, N, F, Na d. N, F, Na, Li e. F, N, Li, Na

105 Sample Question Which of the following correctly ranks the ionization energies of O, F, Na, S, and Cs from smallest to largest? a. Cs, Na, S, O, F b. Cs, S, Na, O, F c. F, O, Na, S, Cs d. F, O, S, Na, Cs e. Na, S, Cs, F, O

106 Pair-Share-Respond 1. Explain why ionization energy increases across a period and decreases down a group 2. Explain to your neighbor what electron affinity means 3. Explain why electron infinity increases across a period and decreases down a group. 4. Explain why atomic radii decrease across a period, and increase down a group

107 Notes on Group Properties

108 Properties of a Group Number and type of vse - s primarily determine an atom s chemistry e - configurations of representative elements can be determined from the organization of the periodic table Certain groups in the periodic table have special names

109 Properties of a Group Elements in the periodic table are divided into metals and nonmetals Metals have low ionization energies Nonmetals have large ionization energies and negative e - affinities Metalloids (semimetals): Elements that exhibit both metallic and nonmetallic properties

110 Figure Special Names for Groups in the Periodic Table

111 Figure Special Names for Groups in the Periodic Table (continued)

112 Alkali Metals Most chemically reactive metals React with nonmetals to form ionic solids Hydrogen Exhibits nonmetallic character due to its small size

113 Alkali Metals Trends: First ionization energy Decreases down the group Atomic radius Increases down the group Density increases Melting and boiling points smoothly decrease

114 Chemical Properties: Alkali Metals Group 1A elements are highly reactive Relative reducing abilities are predicted from the first ionization energies Reducing abilities in aqueous solution are affected by the hydration of M + ions by polar water molecules Energy change for a reaction and the rate at which it occurs are not necessarily related