Chemistry 1A. Chapter 7

Transcription

1 Chemistry 1A Chapter 7

2 Atomic Theory To see a World in a Grain of Sand And a Heaven in a Wild Flower Hold Infinity in the palm of your hand And Eternity in an hour William Blake Auguries of Innocence Thus, the task is not so much to see what no one has yet seen, but to think what nobody has yet thought, about that which everybody sees. Erwin Schrodinger

3 Ways to deal with Complexity and Uncertainty Analogies In order to communicate something of the nature of the electron, scientists often use analogies. For example, in some ways, electrons are like vibrating guitar strings. Probabilities In order to accommodate the uncertainty of the electron s position and motion, we refer to where the electron probably is within the atom instead of where it definitely is.

4 Electron like Light Dual Nature Particle Massless photons of varying energy for light. Negatively charged particles with a mass of g for the electron. Wave related to the effect on the space around them Oscillating electric and magnetic fields for light. 3-D Wave of varying negative charge for electron.

5 Guitar String Waveform

6 Allowed Vibrations for a Guitar String

7 Determination of the Allowed Guitar String Waveforms Set up the general form of the wave equation that describes the vibrating string. Determine the forms of the general equation that fit the boundary conditions. Each possible equation is solved over and over again for the amplitude at many different positions. We plot the values determined in Step 3 and get an image of the possible wave forms. Steps 3 and 4 can be repeated for other equations that meet the boundary conditions.

8 Equation for Guitar String A = A sin X O nπ x a A X = the amplitude at position x A O = the maximum amplitude at any point on the string n = 1, 2, 3,... x = the position along the string a = the total length of the string

9 Guitar String Amplitudes A 1 A 0 A 2

10 Guitar String Waveform 1 A = A sin X O π a x

11 Guitar String Waveform 2 A = A sin X O 2π x a

12 Guitar String Waveform 3 A = A sin X O 3π x a

13 Determination of the Allowed Electron Waveforms Set up the general form of the wave equation that describes the electron in a hydrogen atom. Ψ x,y,z = f(x,y,z) Determine the forms of the general equation that fit the boundary conditions. Each equation has its own set of three quantum numbers: n, l, and m l. Ψ 1s = f 1s (x,y,z) with 1,0,0 for quantum numbers Ψ 2s = f 2s (x,y,z) with 2,0,0 for quantum numbers Ψ 2p = f 2p (x,y,z) with 2,1,1 or 2,1,0 or 2,1, 1 for quantum numbers Etc.

14 Determination of the Allowed Electron Waveforms (cont.) Each allowed equation is solved to get the values for the wave function for many different positions. When we plot the solutions for one of the possible wave functions on a three-dimensional coordinate system, we get an image of one of the possible waveforms.

15 Waveform for 1s Electron (with quantum numbers 1,0,0)

16 Other Allowed Waveforms

17 1s Orbital

18 Particle Interpretation of 1s Orbital

19 Wave Character of the Electron Just as the intensity of the movement of a guitar string can vary, so can the intensity of the negative charge of the electron vary at different positions outside the nucleus. The variation in the intensity of the electron charge can be described in terms of a three-dimensional standing wave like the standing wave of the guitar string.

20 Wave Character of the Electron Although both the electron and the guitar string can have an infinite number of possible waveforms, only certain waveforms are possible. We can focus our attention on the waveform of varying charge intensity without having to think about the actual physical nature of the electron.

21 Summary The electron in a H atom can be described with a 3-dimensional wave equation. This equation has 3 quantum numbers associated with it. Each unique set of 3 quantum numbers (e.g. 1,0,0 for the 1s orbital) yields an equation that when calculations are done using this equation for various positions outside the nucleus and when the results of these calculations are plotted on a 3- dimensional coordinate system, we get an image of the variation in the intensity of negative charge generated by the electron. This image is called an orbital.

22 Electron-Wave Quantum Numbers for the Hydrogen Electron Principal quantum number n Describes the PE and relative size of orbital. Angular momentum quantum number (orbital shape quantum number) l Describes the general shape of orbital. Magnetic quantum number (orbital orientation quantum number) m l Describes the direction the orbital points relative to other orbitals of the same energy. Magnetic spin quantum number m s Necessary for describing electrons, not orbitals.

23 Electron-Wave Quantum Numbers for the Hydrogen Electron (cont.) Possible values n = 1, 2, 3, l = 0, 1, 2,, (n 1) m l = +l,, 0,, l m s = +1/2 and 1/2 What they describe n principle energy level (shell) n, l sublevel (subshell) n, l, m l orbital n, l, m l, m s - electron

24 Possible Sublevels for the First 4 Principal Energy Levels of the Hydrogen Electron 1,0 1s 2,0 2s 2,1 2p 3,0 3s 3,1 3p 3,2 3d 4,0 4s 4,1 4p 4,2 4d 4,3 4f

25 Orbitals Within Sublevels Any s sublevel one orbital n,0,0 Any p sublevel three orbitals n,1,+1 n,1,0 n,1, 1 Any d sublevel five orbitals n,2,+2 n,2,+1 n,2,0 n,2, 1 n,2, 2 Any f sublevel seven orbitals n,3,+3 n,3,+2 n,3,+1 n,3,0 n,3, 1 n,3, 2 n,3, 3

26 Cutaway of 1s and 2s Orbitals (with quantum numbers 2,0,0)

27 Realistic and Stylized 2p y Orbital

28 2p x, 2p y, and 2p z Orbitals

29 3d Orbitals

30 Other Allowed Waveforms

31 Grand Orbital Table The website below, created by David Manthey, shows many more orbitals.

32 Orbitals for Ground States of Known Elements

33 Orbital Energies for Hydrogen

34 Calculating Frequencies for Hydrogen Spectrum Lyman (UV portion of hydrogen spectrum) frequency = ν = x 10 1/s n high = 2, 3, 1 nhigh Balmer (visible portion of hydrogen spectrum) ν = x 10 1/s n 2 n high = 3, 4, 5,... high Paschen (IR portion of hydrogen spectrum) ν = x 10 1/s n high = 4, 5, 6,... 3 nhigh 4,...

35 Line Spectrum of Hydrogen

36 Continuous and Line Spectrum

37 Frequency, Wavelength, and the Speed of Light speed of light (c) = wavelength( λ) frequency( ν ) distance cycles distance c = λν = = cycle time time m cycles 8 m or c = λν = = cycle s s

38 Lab Goal to determine wavelengths of lines in the visible portion of the hydrogen spectrum From Calculation frequency = ν = x 10 1/s - n 2 high = 3, 4, 5, 6, and 7 4 nhigh m/s 10 nm wavelength = λ = ν 1 m From Experiment

39 Wave Interference

40 Wave Diffraction Patterns

41 Lab With He Spectrum View lines and measure angle of diffraction for each. Assign to wavelengths on table based on color, intensity and relative position. Graph angle of diffraction vs. wavelength on graph paper provided.

42 Calibration Curve

43 When Graphing Label graph and axes. Set scale to use as much of the graph paper as possible. (Do not start numbering the scale at 0.) Make each box a value that makes the graph easy to read, e.g. 3 nm per box, not nm. Indicate each data point with a clear x. Draw the best straight line that averages the points.

44 Lab for H Spectrum View lines and measure angle of diffraction for each. Use the graph created from the helium data to determine the wavelength for each line.

45 Electron Spin

46 Pauli Exclusion Principle No two electrons in an atom can be the same in all ways. (No two electrons in an atom can have the same set of four quantum numbers, n, l, m l, and m s.) There are four ways that electrons can be the same: Electrons can be in the same principal energy level (same n). They can be in the same sublevel (same n and l). They can be in the same orbital (same n, l, and m l ). They can have the same spin (same m s ). Leads to the conclusion that there can only be 2 e /orbital 2 e /s sublevel, 6 e /p sublevel, 10 e /d sublevel, and 14 e /f sublevel.

47 Electron Configurations The sublevels are filled in such a way as to yield the lowest overall potential energy for the atom. No two electrons in an atom can be the same in all ways. This is one statement of the Pauli Exclusion Principle. When electrons are filling orbitals of the same energy, they prefer to enter empty orbitals first, and all electrons in half-filled orbitals have the same spin. This is called Hund s Rule.

48 Orbitals for Ground States of Known Elements

49 Why is 1s before 2s?

50 Electron Configurations (cont.)

51 Why 2s before 2p?

52 Electron Configurations through Neon H - 1s 1 He - 1s 2 Li - 1s 2 2s 1 Be - 1s 2 2s 2 B - 1s 2 2s 2 2p 1 C - 1s 2 2s 2 2p 2 N - 1s 2 2s 2 2p 3 O - 1s 2 2s 2 2p 4 F - 1s 2 2s 2 2p 5 Ne - 1s 2 2s 2 2p 6

53 Orbital Overlap

54 Why 4s before 3d?

55 Order of Orbital Filling 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f 6d 7p

56 Writing Electron Configurations Determine the number of electrons in the atom from its atomic number. Add electrons to the sublevels in the correct order of filling. Add two electrons to each s sublevel, 6 to each p sublevel, 10 to each d sublevel, and 14 to each f sublevel. To check your complete electron configuration, look to see whether the location of the last electron added corresponds to the element s position on the periodic table.

57 Order of Filling from the Periodic Table

58 Long Periodic Table

59 Drawing Orbital Diagrams Draw a line for each orbital of each sublevel mentioned in the complete electron configuration. Draw one line for each s sublevel, three lines for each p sublevel, five lines for each d sublevel, and seven lines for each f sublevel. Label each sublevel. For orbitals containing two electrons, draw one arrow up and one arrow down to indicate the electrons opposite spin. For unfilled sublevels, follow Hund s Rule.

60 Abbreviated Electron Configurations The highest energy electron are most important for chemical bonding. The noble gas configurations of electrons are especially stable and, therefore, not important for chemical bonding. We often describe electron configurations to reflect this representing the noble gas electrons with a noble gas symbol in brackets. For example, for sodium 1s 2 2s 2 2p 6 3s 1 goes to [Ne] 3s 1

61 Writing Abbreviated Electron Configurations Find the symbol for the element on a periodic table. Write the symbol in brackets for the noble gas located at the far right of the preceding horizontal row on the table. Move back down a row (to the row containing the element you wish to describe) and to the far left. Following the elements in the row from left to right, write the outer-electron configuration associated with each column until you reach the element you are describing.

62 Abbreviated Electron Configurations Optional Step Rewrite the abbreviated electron configuration, listing the sublevels in the order of increasing principal energy level (all of the 3 s before the 4 s, all of the 4 s before the 5 s, etc.)

63 Group 1 Abbreviated Electron Configurations

64 Abbreviated Electron Configuration Steps for Zinc

65 Common Mistakes Complete electron configurations miscounting electrons (Use the periodic table to determine order of filling.) Orbital diagrams forgetting to leave electrons unpaired with the same spin when adding electrons to the p, d, or f sublevels (Hund s Rule) Abbreviated electron configurations Forgetting to put 4f 14 after [Xe] Forgetting to list sublevels in the order of increasing principal quantum number For cations, forgetting to remove highest energy level electrons first

66 Anomalies Cu [Ar] 3d 10 4s 1 Ag [Kr] 4d 10 5s 1 Au [Xe] 4f 14 5d 10 6s 1 Cr [Ar] 3d 5 4s 1 Mo [Kr] 4d 5 5s 1 Pd [Kr] 4d 10

67 Paramagnetic and Diamagnetic Atoms Diamagnetic atoms have no permanent net magnetic field because all of their electrons are paired. Uncharged palladium atoms and the uncharged atoms that are in columns that end either the s, p, d, or f blocks are diamagnetic. Paramagnetic atoms have a permanent net magnetic field due to having at least one unpaired electron. All uncharged atoms are paramagnetic except palladium atoms and the uncharged atoms that are in columns that end either the s, p, d, or f blocks.

68 Writing Abbreviated Electron Configurations for Transition Metal Monatomic Cations Draw the abbreviated electron configuration for the uncharged atom, listing the sublevels in the order of increasing principal quantum number. Remove the number of electrons equal to the charge, removing them from the right to left in the electron configuration.

69 Factors that Affect Ionic Charge (1) Ions form in such a way as to yield the most stable, lowest potential energy ionic compound. Ions are less stable than their neutral counterparts. Therefore, it takes energy to form ions. The higher the charges are, the less stable they are and the more energy it takes to form them. Therefore, this factor favors low charges.

70 Factors that Affect Ionic Charge (2) The formation of ionic bonds stabilizes the ions, so energy is released when the cations and anions form ionic bonds. The higher the charges are, the stronger the bonds and the more energy is released when they form. Therefore, this factor favors higher charges.

71 Factors that Affect Ionic Charge (3) Ions form the charges that yield the best balance between (1) the tendency to keep charges low to minimize the energy necessary to form ions and (2) the tendency to maximize charge to yield the strongest, most stable ionic bond. The best balance is often reached when the ions form stable electron configurations, which require the least energy to form.

72 Very Rough PE Diagram for NaCl Formation

73 Very Rough PE Diagram for AlN Formation

74 Stable Configurations 1s 2 (2 electrons) H, Li +, Be 2+ ns 2 np 6 (10, 18, 36, 54, and 86 electrons) All monatomic anions, except H Cations from Group 1, 2, or 3 and Al 3+ nd 10 (n+1)s 2 (30, 48, and 80 electrons) Ga +, In +, Tl +, Sn 2+, Pb 2+, and Bi 3+ nd 10 (28, 46, and 78 electrons) Cu +, Ag +, Au +, Zn 2+, Cd 2+, Hg 2+, Ga 3+, In 3+, and Tl 3+

75 Monatomic Ion Charges

76 Trends on the Periodic Table Chemistry 1A

77 Atomic Size Covalent Radius for Covalently Bonded Atoms F-F bond length is 144 pm, so F covalent radius is 72 pm. H-F bond length is 109 pm, so H covalent radius is 37 nm. Atomic Radius for Elements like the Noble Gases Ar atomic radius is 131 pm Metallic Radius for Metals Al metallic radius is 143 pm.

78 Trends in Atomic Size (1)

79 Trends in Atomic Size (2)

80 Ionization Energy, ΔH i.e. First Ionization Energy A(g) A + (g) + e Second Ionization Energy A + (g) A 2+ (g) + e Third Ionization Energy A 2+ (g) A 3+ (g) + e

81 Ionization Energy Trends (1)

82 Ionization Energy Trends (2)

83 Electron Affinity, ΔH e.a. First Electron Affinity A(g) + e A (g) Second Electron Affinity A (g) + e A 2 (g) Third Electron Affinity A 2 (g) + e A 3 (g)

84 Electron Affinity Trends

85 Trends Representative Elements Atomic Size Increases to left and down ΔH i.e. ΔH e.a. EN Increases to right and up More favorable to right and up Increases to right and up

86 Two Factors Used to Explain Trends The principal energy level reflects the size of orbitals and potential energy of the electrons in those orbitals. All other factors being equal, increased n for the orbitals in which electrons are found means increased size of orbitals, which leads to decreased attraction for electrons and increased potential energy of those electrons.

87 Effective Charge Effective charge is the approximate nuclear charge felt by the highest energy electrons. nuclear charge minus #e in lower energy levels The effective charge on the highest energy electrons of the representative elements is equal to their A-group number. The effective charge on the highest energy electron of the transition metals (other than the anomalies) is +2. All other factors being equal, increased effective charge means increased attraction for electrons, which leads to decreased size of orbitals and decreased potential energy of electrons.

88 Explanation of Trends (1)

89 Explanation of Trends (2)

90 Explanation of Trends (3)

91 Ionic or Molecular? Is aluminum iodide, AlI 3, ionic or molecular? If you are told that aluminum iodide s formula was better described as Al 2 I 6, would it change your prediction? Many metal and nonmetal combinations are better described as forming molecular compounds rather than ionic compounds. To see why, a new classification of chemical bonds is added to our list ionic bonds with covalent character.

92 Ionic Bonds with Covalent Character The attraction for the anion s negative charge cloud from the cation draws the anion s charge cloud toward the cation and distorts the anion electron cloud. This distortion is described as covalent character, that is, sharing of electrons.

93 Bond Types

94 Degree of Covalent Character Greater distortion of anion electron cloud (more covalent character) in an ionic bond comes from More highly charged cation more attraction for anion electron cloud. Smaller cation more focused attraction for anion electron cloud. Larger anion electron cloud less strongly attracted, so anion is more easily distorted. More highly charged anion more repulsion between electrons, so anion is more easily distorted.

95 Ionic Size Cations are much smaller than the uncharged atoms they come from. Fewer electrons means less repulsion between electrons, allowing the electron cloud to be pulled closer to the nucleus. Anions are much larger than the uncharged atoms they come from. More electrons means more repulsion between electrons, causing the electron cloud to expand to minimize this increased repulsion.

96 Ionic and Atomic Size

97 Isoelectronic Series A collection of ions and an uncharged atom with the same number of electrons is called an isoelectronic series. For isoelectronic atoms or ions, higher nuclear charge leads to smaller size.

98 Predicting Degree of Covalent Character CsF low covalent character Large, low charge cation-low attraction and unfocused attraction. Small, low charge anion electrons strongly attracted hard to distort AlI 3 high covalent character Small, highly charged cation strong attraction and focused attraction. Large anion electrons weakly attracted easy to distort Li 3 P high covalent character Small cation focused attraction. Large anion, highly charged anion electrons weakly attracted easy to distort