CH101 GENERAL CHEMISTRY I SPRING 2013

1. CH101 GENERAL CHEMISTRY I SPRING 2013 • Textbook: ‘Chemical Principles. The Quest for Insight’ by P Atkins and L Jones. Freeman, New York, 2010 (International Edition)

2. F1 CHEMISTRY The science of matter and the changes it can undergo. A science that deals with the composition, structure, and properties of substances and with the transformations that they undergo.

3. F2 Chemistry: A Science at Three Levels Symbolic level The expression of chemical phenomena in terms of chemical symbols and mathematical equations Macroscopic level The level dealing with the properties of large, visible objects Microscopic level An underworld of change at the level of atoms and molecules

4. F3 How Science Is Done

5. F4 The Branches of Chemistry • Traditional areas Organic chemistry (carbon compounds) Inorganic chemistry (all other elements and their compounds) Physical chemistry (principles of chemistry) • Specialized areas Biochemistry (chemistry in living systems) Analytical chemistry (techniques for identifying substances) Theoretical (computational) chemistry (mathematical and computational) Medicinal chemistry (application to the development of pharmaceuticals) • Interdisciplinary branches Molecular biology (chemical basis of genes and proteins) Materials science (structure and composition of materials) Nanotechnology (matter at the nanometer level)

6. Chapter 1. ATOMS: THE QUANTUM WORLD INVESTIGATING ATOMS 1.1 The Nuclear Model of the Atom 1.2 The Characteristics of Electromagnetic Radiation 1.3 Atomic Spectra QUANTUM THEORY 1.4 Radiation, Quanta, and Photons 1.5 The Wave-Particle Duality of Matter 1.6 The Uncertainty Principle 1.7 Wavefunctions and Energy Levels 2012 General Chemistry I

7. INVESTIGATING ATOMS (Sections 1.1-1.3) 1.1 The Nuclear Model of the Atom • Discovering the electron J.J. Thomson (English physicist, 1856-1940) in 1897 discovers the electron and determines the charge to mass ratio (e/me) as “cathode rays”. In 1906 he wins the Nobel Prize.

8. Robert Millikan designed an ingenious apparatus in which he could observe tiny electrically charged oil droplets. Fundamental charge, the smallest increment of charge e = 1.602×10-19 C From the value of e/me measured by Thomson, me = 9.109×10-31 kg

9. Brief Historical Summary

10. Two Models of the Atom

11. Nuclear Model Ernest Rutherford (1871-1937) and his students in England studied α emission from newly-discovered radioactive elements. Experiment by Geiger and Marsden Nucleus occupy a small volume at the center of the atom Nucleus contains particles called proton (+e) and neutron (uncharged).

12. Nuclear Model of the Atom In the nuclear model of the atom, all the positive charge and almost all the mass is concentrated in the tiny nucleus, and the negatively charged electrons surround the nucleus. The atomic number is the number of protons in the nucleus.

13. Some Questions Posed by the Nuclear Model • How are the electrons arranged around the nucleus? 2.Why is the nuclear atom stable? (classical physics predicts instability) 3. What holds the protons together in the nucleus? Atomic spectroscopy (involving the absorption by, or emission of electromagnetic radiation from atoms) provided many of the clues needed to answer questions 1 and 2.

14. 1.2 The Characteristics of Electromagnetic Radiation • Spectroscopy – the analysis of the light emitted or absorbed by • substances - Light is a form of electromagnetic radiation, which is the periodic variation of an electric field (and a perpendicular magnetic field). amplitude: the height of the wave above the center line intensity: the square of the amplitude wavelength,l: peak-to-peak distance wavelength × frequency = speed of light c = l n c = 2.9979 x 108 ms-1

15. The color of visible light depends on its frequency and wavelength; long-wavelength radiation has a lower frequency than short-wavelength radiation. infrared l > 800 nm the radiation of heat visible light l = 700 nm (red light) to 400 nm (violet light) ultraviolet l < 400 nm responsible for sunburn

16. Color, Frequency and Wavelength of Electromagnetic Radiation

17. Self-Test 1.1A Calculate the wavelengths of the light from traffic signals as they change. Assume that the lights emit the following frequencies: green, 5.75 x 1014 Hz; yellow, 5.15 x 1014 Hz; red, 4.27 x 1014 Hz.

18. 1.3 Atomic Spectra White light Discharge lamp of hydrogen (emission spectrum) discrete energy levels spectral lines

19. Johann Rydberg’s general empirical equation R (Rydberg constant) = 3.29×1015 Hz an empirical constant n1 = 1 (Lyman series), ultraviolet region n1 = 2 (Balmer series), visible region n1 = 3 (Paschen series), infrared region For instance, n1 = 2 and n2 = 3, l = 6.57×10-7 m

20. Self-Test 1.2A Calculate the wavelength of the radiation emitted by a hydrogen atom for n1 = 2 and n2 = 4. Identify the spectral line in Fig. 1.10b.

21. Absorption Spectra When white light passes through a gas, radiation is absorbed by the atoms at wavelengths that correspond to particular excitation energies. The result is an atomic absorption spectrum. Above is an absorption spectrum of the sun: elements can be identified from their spectral lines.

22. QUANTUM THEORY (Sections 1.4-1.7) 1.4 Radiation, Quanta, and Photons • This section involves two phenomena that classical physics was unable to explain (along with atomic line spectra): black body radiation and the photoelectric effect. • Black body radiation is the radiation emitted at different wavelengths by a heated black body, for a series of temperatures. Two empirical laws are associated with it (below) and plots of emitted radiation energy density versus wavelength give bell-shaped curves (right) Stefan-Boltzmann law: Total intensity = constant × T4 Wien’s law: T lmax = constant

23. Self-Test 1.3A In 1965, electromagnetic radiation with a maximum of 1.05 mm (in the microwave region) was discovered to pervade the universe. What is the temperature of ‘empty’ space?

24. Black Body Radiation Theories • Rayleigh-Jeans theory was based on classical physics. It assumed the black body atoms behave like mechanical oscillators that absorb and emit energy continuously. • The Rayleigh-Jeans equation did not agree with experimental data, except at high wavelengths. • Classical physics predicts intense UV or higher energy radiation from hot black bodies!

25. Planck’s Quantum Theory • Max Planck (1900) made the assumption that black body atoms could absorb and emit energy only in multiples of a fundamental quantity (a quantum), whose value is E = hn (4) • The constant h became known as Planck’s constant (= 6.626 x 10-34 Js) • The Planck equation describing the black body radiation profile agreed well with experiment.

26. Summary • Ultraviolet catastrophe: • Classical physics predicted that any hot • body should emit intense ultraviolet • radiation and even X-rays and g-rays! • Assumes continuous exchange of energy. Quantization of electromagnetic radiation suggested by Max Planck E =hn Assumes energy can be exchanged only in discrete amounts (quanta) Radiation of frequency n can be generated only if an oscillator of that frequency has acquired the minimum energy required to start oscillating.

27. The Photoelectric effect – • ejection of electrons from • a metal when its surface is • exposed to ultraviolet radiation Photoelectric effect: observations 1. No electrons are ejected < a certain threshold value of frequency, which depends on the metal. 2. Electrons are ejected immediately at that particular value. 3.The kinetic energy of ejected electrons increases linearly with the frequency of the radiation.

28. Albert Einstein proposed that electromagnetic radiation consists • of particles, called “photons”. – The energy of a single photon is proportional to the radiation frequency by E = hn. work function • Bohr frequency condition: • relates photon energy to energy • difference between two energy • levels in an atom:

29. Self-Test 1.5A (and part of 1.5B) The work function of zinc is 3.63 eV. (a) What is the longest wavelength of electromagnetic radiation that could eject an electron from zinc? (b) What is the wavelength of the radiation that ejects an electron with velocity 785 km s-1 from zinc?

32. Summary of 1.4

33. 1.5 The Wave-Particle Duality of Matter –Wave behavior of light: diffraction and interference effects of superimposed waves (constructive and destructive) – Louis de Broglie proposed that all particles have wavelike properties. lis the de Broglie wavelength of an object with linear momentum p = mv electron diffraction reflected from a crystal

34. De Broglie Wavelengths for Moving Objects

35. 1.6 The Uncertainty Principle • Complementarity of location (x) and momentum (p) –uncertainty in x is Dx; uncertainty in p is Dp • Heisenberg uncertainty principle where ħ = h / 2p = 1.0546×10-34 J·s –x and p cannot be determined simultaneously.

36. Example Calculation

37. 1.7 Wavefunctions and Energy Levels • Erwin Schrödinger introduced a central concept of quantum theory. wavefunction particle trajectory – Wavefunction (y, psi): a mathematical function with values that vary with position – Born interpretation: probability of finding the particle in a region is proportional to the value of y2 – Probability density (y2): the probability that the particle will be found in a small region divided by the volume of the region.

38. Schrödinger Equation:WaveEquation for Particles 38

39. Schrödinger equation: for a particle of mass m moving in one dimension • in a region where the potential energy is V(x) H = hamiltonian of the system - H represents the sum of potential energy and kinetic energy in a system - Origins of the Schrödinger equation: 2px If the wavefunction is described as y(x) = A sin , l l = h/p d2y(x) d2y(x) 2p 2p 2 2 p y(x) y(x) = - = - l h dx2 dx2 d2y(x) ħ2 p2 y(x) - = : kinetic energy V(x): potential energy 2m 2m dx2

40. Particle in a Box • The ‘particle in a box’ scenario is the simplest application of the Schrödinger equation – Mass m confined between two rigid walls a distance L apart –y = 0 outside the box and at the walls (boundary condition) – Potential energy is zero within and infinite outside the box n = quantum number

41. The Solutions of Particle in a Box For the kinetic energy of a particle of mass m, Whole-number multiples of half-wavelengths can follow the boundary condition, When this expression for l is inserted into the energy formula,

42. More General Approach From the Schrödinger equation with V(x) = 0 inside the box, Solution: k2 = 2mE/ħ2, and it follows From the boundary conditions of y(0) = 0 and y(L) = 0, L 0

43. Wavefunction obtained so far is (with just A left to identify) The normalization condition determines A: Hence,

44. Energies of a particle of mass m in a one dimensional box of length L, n = quantum number Energy of the particle is quantized, and restricted to energy levels. - Energy quantization stems from the boundary conditions on the wavefunction. - Energy separation between two neighboring levels with quantum numbers n and n+1: - L (the length of the box) or m (the mass of the particle) increases, the separation between neighboring energy levels decreases.

45. Zero-point energy: The lowest value of n is 1, and the lowest energy is E1 = h2/8mL2, not zero. According to quantum mechanics, a particle can never be perfectly still when it is confined between two walls: it must always possess an energy. consistent with the uncertainty principle –The shapes of the wavefunctions of a particle in a box E1 = h2/8mL2, E2 = h2/2mL2

46. EXAMPLE 1.8 Treat a hydrogen atom as a one-dimensional box of length 150 pm, containing an electron. Predict the wavelength of the radiation emitted when the electron falls to the lowest energy level from the next higher energy level. n = 1, n+1 = 2, m = me, and L = 150 pm = hn = hc/l

47. Chapter 1. ATOMS: THE QUANTUM WORLD THE HYDROGEN ATOM 1.8 The Principal Quantum Number 1.9 Atomic Orbitals 1.10 Electron Spin 1.11 The Electronic Structure of Hydrogen 2012 General Chemistry I

48. THE HYDROGEN ATOM (Sections 1.8-1.11) 1.8 The Principal Quantum Number An electron held within the atom by the pull of the nucleus • A particle in a box • For a hydrogen atom, V(r) = coulomb potential energy • Solutions of the Schrödinger equation lead to the expression • for energy: n is the principal quantum number R (Rydberg constant) = 3.29×1015 Hz, in good agreement with experiment

49. For other one-electron ions, such as He+, Li2+, and even C5+, - Z = atomic number, equal to 1 for hydrogen - n = principal quantum number - As n increases, energy increases, the atom becomes less stable, and energy states become more closely spaced (more dense). - Ground state of the atom: the lowest energy state, E = –hR when n = 1. - Ionization: the bound electron reaches E = 0, and freedom, and has left the atom. Ionization energy: the minimum energy needed to achieve ionization

50. 1.9 Atomic Orbitals The Schrödinger equation for the H atom is often written as below: