TRT 401 PHYSICAL CHEMISTRY

1. TRT 401 PHYSICAL CHEMISTRY PART 1: INTRODUCTION TO PHYSICAL CHEMISTRY

2. What is physical chemistry? Physical chemistry is a study of the physical basis of phenomena related to the chemical composition and structure of substances. Or Physical chemistry is quantitative and theoretical study of the properties and structure of matter, and their relation to the interaction of matter with energy. • This course serves as an introduction to chemical thermodynamics, giving you an understanding of basic principles, laws and theories of physical chemistry the are necessary for chemistry, biochemistry, pre-medical, general science and engineering • students. • You will develop the ability to solve quantitative problems, and learn to use original thought and logic in the solution of problems and derivation of equations. • You will learn to apply mathematics in chemistry in such a way that the equations paint a clear picture of the physical phenomena

3. Physical chemistry includes numerous disciplines: • Thermodynamics - relationship between energy interconversion • by materials, and the molecular properties • Kinetics - rates of chemical processes • Quantum Mechanics - phenomena at the molecular level • Statistical Mechanics - relationships between individual • molecules and bulk properties of matter • Spectroscopy - non-destructive interaction of light (energy) and • matter, in order to study chemical structure • Photochemistry - interaction of light and matter with the intent of • coherently altering molecular structure

4. Atoms and Molecules Atoms are the submicroscopic particles that constitute the fundamental building block of ordinary matter. They are most found in molecules, two or more atoms joined in specific geometrical arrangement. Carbon dioxide molecule Carbon monoxide molecule Oxygen atom Carbon atom In the study of chemistry, atoms are often portrayed as colored spheres, with each color representing a different kind of atom. For example, a black sphere represents a carbon atom, a red sphere represents an oxygen atom.

5. Lanthanoids Actinoids For more interactive periodic table please refer http://www.ptable.com/

6. Chemical Bonding cation Sodium metal Chlorine gas anion NaCl Sodium Chloride Oppositely charged ions are held together by ionic bonding, forming a crystalline lattice. Ionic compound A compound that composed of cations and anions bound together by electrostatic attraction

7. Covalent Compund Compound that not contain a metallic element typically covalent compound consisting of discrete molecules. Single bond covalent • The shared pairs of electrons are bonding pairs. • The unshared pairs of electrons are lone pairs or non bonding pairs.

8. Polar Covalent Bond • In reality, fully ionic and covalent bonds represent the extremes of a spectrum • of bonding types. • Most of covalent bonds are polar covalent bonds, in which the electrons are • shared unequally, but are nit fully transfered from one atom to the other. • In polar bonds, one atom has a partial negative charge(δ-) and the other atom • has a partial positive charge(δ+).

9. Metallic Bonding • Metallic bonding, occurs in metals. Since metals have low ionization energies, they tend • to electron easily. • When metal atoms bonding together form a solid, each metal atom donates one or more • electron to an electron sea. Example: sodium metal as an array of positively charged Na+ ion immersed in a sea of negatively charges electron (e-). The table below summarize the three different types of bonding

10. Electronegativity The ability of an atom to attract electrons to itself in a chemical bond (which results in polar bonds) is called electronegativity, χ (chi). Fluorine is the most Electronegativity element Francium is the least electronegative element Electronegativity generally increase as we move across a row in periodic table and decrease as we move down a column.

11. Electronegativity and Bond Polarity Bond polarity expressed numerically as dipole moment, μwhich occurs when there is a separation between a positive and negative charge. μ = qr μ: dipole moment; q: separating a proton and an electron; r: distance

12. Example: q = 1.6 x 10-19 C r = 130 pm (the approximate length of a short chemical bond) μ= q x r = (1.6 x 10-19 C)(130 x 10-12m) = 2.1 x 10-29 . M = 6.2 D The debye (D) is a common unit used for reporting dipole moment (1D = 3.34 x 10-30 C.m) Table 1 Dipole moments of several molecules in the gas phase

13. Matter Matter: anything that occupies space and has mass. Example: book, desk, pen, pencil even your body is are all compose of matter. Air also matter but it too occupies space and matter. These specific instance of matter- such as air, sand, water- a substance. Matter can be classify to its state- solid, liquid, or gas according to its composition.

14. Example: Glass, plastic & charcoal Example: Table salt, ice & diamond Solid matter may be crystalline, in which case its atoms or molecules are arranged in patterns with long range, repeating order. Or Its may be amorphous in which case its atoms or molecules do not have any long range order.

15. In Gaseous Matter Gases can be compressed-squeezed into a small volume because there is so much Empty space between atoms or molecules in the gaseous state.

16. The Composition of Matter Matter can be classified as either pure substances, which have fixed composition, or mixtures, which have variable composition. Pure substance (element and compounds) are unique materials with their own chemical and physical properties, and are composed of only one type of atom or molecule. Compound A pure substance that is composed of atoms or two more different elements. Element A substance that cannot be chemically broken down Into simpler substance. Molecular compound Ionic compound

17. The Composition of Matter Mixture are simply random combinations of two or more different types of atoms of molecules, and retain the properties of the individual substances. They can therefore be separated (although sometime with difficulty) by physical means (such as boiling, distillation, melting, crystallizing, magnetism, etc.) Heterogenus Mixture One in which the composition varies from one region to another. Homogenus Mixture One with the same composition Throughout.

18. Summary Composition of Matter Variable composition? YES NO NO YES YES NO Pure water Wet sand Helium gas Tea with sugar

19. Quantifying Matter Amount of substance(n): a measure of a number of specified entities (atoms, molecules, or formula unit) present (unit; mole; mol). 1 mol of a substance contains as many entities as exactly 12 g of carbon-12 (ca. 6.02 x 1023 objects) Avogadro’s Number: NA = 6.02 x 1023 mol-1 Extensive Property: Dependent upon the amount of matter in the substance (e.g., mass & volume) Intensive Property: Independent of the amount of matter in a substance (e.g., mass density, pressure and temperature) Molar Property: Xm, an extensive property divided by the amount of substance, n: Xm = X/n Molar Concentration:“Molarity” moles of solute dissolved in litres of solvent: 1.0 M = 1.0 mol L-1

20. Units • In science, the most commonly used set of units are those of the International System of Units (the SI System, for Système International d’Unités). • There are seven fundamental units in the SI system. The units for all other quantities (e.g., area, volume, energy) are derived from these base units. Table 2 Example list of units for more info: http://physics.nist.gov/cuu/Units/

21. SI Prefix – Small & Large Unit Table 3 SI Prefix Multipliers

22. SI Prefix – Large Unit Table 4 SI Prefix – large unit

23. Energy Energy is define as the ability to do work. Work is done when a force is exerted through a distance. Force through distance; work is done. Energy is measured in Joules (J) or Calories (cal). 1 J = 1 kg m2 s-2 Energy may be converted from one to another, but it is neither created nor destroyed (conversion of energy). In generally, system tend to move from situations of high potential energy (less stable) to situations having lower energy (more stable).

24. Energy is the capacity to supply heat or to do work. Energy can be exchanged between objects by some combination of either heat or work: Energy = heat + work ∆E= q + w • work is done when a force is exerted through a distance • work = force x distance • heat is the flow of energy caused by a temperature • difference. Example of a billiard ball rolling across the table and colliding straight on with a second, stationary billiard ball.

25. Potential and Kinetic Energy • Kinetic energy (EK) is the energy due to the motion of an object with mass m and velocity v: • EK = ½ mv2 • – Thermal energy, the energy associated with the temperature of an object, is a form of kinetic energy, because it arises from the vibrations of the atoms and molecules within the object. • Potential energy (EP) is energy due to position, or any other form of “stored” energy. There are several forms of potential energy: • – Gravitational potential energy • – Mechanical potential energy • – Chemical potential energy (stored in chemical bonds)

26. Potential energy increases when things that attract each other are separated or when things that repel each other are moved closer. • Potential energy decreases when things that attract each other are moved closer, or when things that repel each other are separated. • According to the law of conservation of energy, energy cannot be created or destroyed, but kinetic and potential energy can be interconverted. Example: Energy transformation I Energy transformation II

27. Water falling in a waterfall exchanges gravitational potential energy for kinetic energy as it falls faster and faster, but the energy is never destroyed. EK converted to thermal energy and sound high EPdecreasing EP low EP low EK increasing EK high EP

28. Chemical Energy The chemical potential energy of a substance results from the relative positions and the attractions and repulsions among all its particles. Under some circumstances, this energy can be released, and can be used to do work: Using chemical energy to do work – The compound produced when gasoline burns have Less chemical potential energy than the gasoline molecules.

29. Law of Conservation of Energy • A law stating that energy can neither be created nor destroyed, only converted from one form to another, and it can assume in different forms. • E.g.: The cycle held the gravitational energy The energy transformed into kinetic energy of motion.

30. Contributions to Energy Kinetic Energy, EK: Energy an object possesses as a result of its motion. KE = ½mv2 Potential Energy, V: Energy an object possesses as a result of its position. Zero of potential energy is relative: 1. Gravitational Potential Energy: zero when object at surface (V = 0 when h = 0) VG = mgh, m = mass, g = 9.81 m s-2, h = height 2. Electrical Potential Energy: zero when 2 charged particles infinitely separated qi = charge on particle i, r = distance ε0 = 8.85 x 10-12 C2 J-1 m-1 (vacuum permittivity)

31. Equipartition of Energy Molecules have a certain number of degrees of freedom: they can vibrate, rotate and translate - many properties depend on these degrees of freedom: Equipartition theorem: All degrees of freedom have the same average energy at temperature T: total energy is partitioned over all possible degrees of freedom Quadratic energy terms: ½mvx2 + ½mvy2 + ½mvz 2 Average energy associated with each quadratic term is ½kT, where k = 1.38 x 10-23 J K-1 (Boltzmann constant), where k is related to the gas constant, R = 8.314 J K-1 mol-1 by R = NAk However: this theorem is derived by classical physics, and can only be applied to translational motion.

32. Relationship Between Molecular and Bulk Properties The energy of a molecule, atom, or subatomic particle that is confined to a region of space Is quantized, or districted to certain discrete values. These permitted energies are called energy level.

33. Populations of States At temperatures > 0, molecules are distributed over available energy levels according to the Boltzmann Distribution, which gives the ratio of particles in each energy state: Boltzmann constant k=1.381 x 10-23 JK-1 At the lowest temperature T = 0, only the lowest energy state is occupied. At infinite temperature, all states are equally occupied. In real life, the population of states is described by an exponential function, with the highest energy states being the least populated. Degenerate states: States which have the same energy These will be equally populated!

34. Boltzmann Distributions Populations for (a) low & (b) high temperatures Boltzmann predicts an exponential decrease in population with increasing temperature At room T, only the ground electronic state is populated. However, many rotational states are populated, since the energy levels are so closely spaced. More states are significantly populated if energy level spacing are near kT!

35. The Electromagnetic Field Light is a form of electromagnetic radiation. In classical physics, electromagnetic radiation is understood in term of the electromagnetic field. Electric field – charged particles (whether stationary or moving) Magnetic field – acts only on moving charged particles.

36. Wavelength ,λ is the distance between the neighboring peaks of two wave, and is frequency, v (nu) the number of times in a given interval at which its displacement at a fixed point returns to its original value divided by the length of the time intervals. Frequency is measure in Hertz, 1 Hz= 1 s-1. Wavelength, λ = c/ v Wavenumber, ṽ (nu tilde) the number of complete wavelengths in a given length. Wavenumber, ṽ = v/c =1/λ e.g.: A wave number of 5 cm-1 indicates there are 5 complete wavelength in 1 cm.

38. PART 2: INTRODUCTION TO PHYSICAL CHEMISTRY

39. Matter: Substance, intensive and extensive properties, molarity and molality Substance • A substance is a distinct, pure form of matter. • The amount of a substance, n, in a sample is reported in terms of the unit called a mole (mol). In 1 mol are NA=6.0221023 objects (atoms, molecules, ions, or other specified entities). NA is the Avogadro constant. Extensive and intensive properties  An extensive property is a property that depends on the amount of substance in the sample. Examples: mass, volume… • An intensive property is a property that is independent on the amount of substance in the sample. Examples: temperature, pressure, mass density…  A molar property Xm is the value of an extensive property X divided by the amount of substance, n: Xm=X/n. A molar property is intensive. It is usually denoted by the index m, or by the use of small letters. The one exemption of this notation is the molar mass, which is denoted simply M.  A specific property Xs is the value of an extensive property X divided by the mass m of the substance: Xs=X/m. A specific property is intensive, and usually denoted by the index s. Measures of concentration: molarity and molality  The molar concentration(‘molarity’) of a solute in a solution refers to the amount of substance of the solute divided by the volume of the solution. Molar concentration is usually expressed in moles per litre (mol L-1 or mol dm-3). A molar concentration of x mol L-1 is widely called ‘x molar’ and denoted x M. • The term molalityrefers to the amount of substance of the solute divided by the mass of the solvent used to prepare the solution. Its units are typically moles of solute per kilogram of solvent (mol kg-1).

40. Some fundamental terms: System and surroundings: For the purposes of Physical Chemistry, the universe is divided into two parts, the system and its surroundings.  The system is the part of the world, in which we have special interest.  The surroundings is where we make our measurements. The type of system depends on the characteristics of the boundary which divides it from the surroundings: (a) An open system can exchange matter and energy with its (b) A closed system can exchange energy with its surroundings, but it cannot exchange matter. (c) An isolated system can exchange neither energy nor matter with its surroundings. Except for the open system, which has no walls at all, the walls in the two other have certain characteristics, and are given special names:  An adiabatic (isolated) system is one that does not permit the passage of energy as heat through its boundary even if there is a temperature difference between the system and its surroundings. It has adiabatic walls.  A diathermic (closed) system is one that allows energy to escape as heat through its boundary if there is a difference in temperature between the system and its surroundings. It has diathermic walls.

41. H2O (water) 25°C 1 bar H2 + ½ O2 25°C 1 bar stable unstable metastable stable metastable Homogeneous system: The macroscopic properties are identical in all parts of the system. Heterogeneous system: The macroscopic properties jump at the phase boundaries. Phase: Homogeneous part of a (possibly) heterogeneous system. Equilibrium condition:  The macroscopic properties do not change without external influence.  The system returns to equilibrium after a transient perturbation.  In general exists only a single true equilibrium state. Equilibrium in Mechanics: Equilibrium in Thermodynamics:

42. The concept of “Temperature”:  Temperature is a thermodynamic quantity, and not known in mechanics.  The concept of temperature springs from the observation that a change in physical state (for example, a change of volume) may occur when two objects are in contact with one another (as when a red-hot metal is plunged into water): If, upon contact of A and B, a change in any physical property of these systems is found, we know that they have not been in thermal equilibrium. A B A B + The Zeroth Law of thermodynamics: If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, than C is also in thermal equilibrium with A. All these systems have a common property: the same temperature. Energy flows as heat from a region at a higher temperature to one at a lower temperature if the two are in contact through a diathermic wall, as in (a) and (c). However, if the two regions have identical temperatures, there is no net transfer of energy as heat even though the two regions are separated by a diathermic wall (b). The latter condition corresponds to the two regions being at thermal equilibrium.

43. Assumption: Linear relation between the Celsius temperature  and an observable quantity x, like the length of a Hg column, the pressure p of a gas at constant volume V, or the volume V of the gas for constant pressure p: Left: The variation of the volume of a fixed amount of gas with the temperature constant. Note that in each case they extrapolate to zero volume at -273.15 C. Right: The pressure also varies linearly with the temperature, and extrapolates to zero at T= 0 (-273.15 C). For the pressure p, this transforms to: Observation: For all (ideal) gases one finds  Introduction of the thermodynamic temperature scale (in ‘Kelvin’): and The thermodynamic temperature scale: In the early days of thermometry (and still in laboratory practice today), temperatures were related to the length of a column of liquid (e.g. Mercury, Hg), and the difference in lengths shown when the thermometer was first in contact with melting ice and then with boiling water was divided into 100 steps called ‘degrees’, the lower point being labelled 0. This procedure led to the Celsius scale of temperature with the two reference points at 0 °C and 100 °C, respectively.

44. Work, heat, and energy:  The fundamental physical propertyin thermodynamics is work: work is done when an object is moved against an opposing force. (Examples: change of the height of a weight, expansion of a gas that pushes a piston and raises the weight, or a chemical reaction which e.g. drives an electrical current)  The energy of a system is its capacity to do work. When work is done on an otherwise isolated system (e.g. by compressing a gas or winding a spring), its energy is increased. When a system does work (e.g. by moving a piston or unwinding the spring), its energy is reduced.  When the energy of a system is changed as a consequence of a temperature difference between it and the surroundings, the energy has been transferred as heat. When, for example, a heater is immersed in a beaker with water (the system), the capacity of the water to do work increases because hot water can be used to do more work than cold water. Heat transfer requires diathermic walls.  A process that releases energy as heat is called exothermic, a process that absorbs energy as heat endothermic. (a) When an endothermic process occurs in an adiabatic system, the temperature falls; (b) if the process is exothermic, then the temperature rises. (c) When an endothermic process occurs in a diathermic container, energy enters as heat from the surroundings, and the system remains at the same temperature; (d) if the process is exothermic, then energy leaves as heat, and the process is isothermal.

45. When energy is transferred to the surroundings as heat, the transfer stimulates disordered motion of the atoms in the surroundings. Transfer of energy from the surroundings to the system makes use of disordered motion (thermal motion) in the surroundings. When a system does work, it stimulates orderly motion in the surroundings. For instance, the atoms shown here may be part of a weight that is being raised. The ordered motion of the atoms in a falling weight does work on the system. Work, heat, and energy (continued): Molecular interpretation • In molecular terms, heat is the transfer of energy that makes use of chaotic molecular motion (thermal motion). • In contrast, work is the transfer of energy that makes use of organized motion. • The distinction between work and heat is made in the surroundings.

46. State functions and state variables STATEMENT • If only two intensive properties of a phase of a pure substance are known, all intensive properties of this phase of the substance are known, or • If three properties of a phase of a pure substance are known, all properties of this phase of the substance are known. example: - p and T as independent variables means: Vm (=v) = f(p,T), i.e. the resulting molar volume is pinned down, or - p, T, n as independent variables means: V = f(p,T,n) • The resulting function is termed a state function. • The variables which describe the system state, are termed - state variables, and are related to each other via the - state functions.

47. 1 2 3 The thermal equation of state and the perfect gas equation Thermal equation of state: • The thermal equation of state combines volumeV, temperatureT, pressurep, and the amount of substancen: V = f(p,T,n)orVm = v = f(p,T) The “perfect gas” (or “ideal gas”): • mass points without expansion • no interactions between the particles • a real gas, an actual gas, behaves more and more like a perfect gas the lower the pressure, and the higher the temperature Some empirical gas laws: V = f(T) for p=const.: “isobars” p = f(T) for V=const.: “isochores” p = f(V) for T=const.: “isotherms” V = const.  ( + 273.15°C) = const.’  T p = const.  ( + 273.15°C) = const.’  T p  V = const. Boyle’s Law Charles’s Law

48. Step 1: Isobaric change Step 2: Isothermal change } = const. ! • Combination of 1 and 3 for: •  1 mol gas at •  p0 = 1.013 bar •  T0 = 273.15 K •  v0 = 22.42 l A region of the p,V,T surface of a fixed amount of perfect gas. The points forming the surface represent the only states of the gas that can exist. Sections through the surface shown in the figure at constant temperature give the isotherms shown for the Boyle-Mariotte law and the isobars shown for the Gay-Lussac law. p  v = R  T p  V = n  R  T ‘perfect gas equation’ R : ‘gas constant’ (= 8.31434 J K-1 mol-1)

49. Step 1: Isothermal change Step 2: Isobaric change } = const. ! • Swap the changes: • a combination of 3 and 1 for •  1 mol gas at •  p0 = 1.013 bar •  T0 = 273.15 K •  v0 = 22.42 l The change of a state variable is independent of the path, on which the change of the state has been made, as long as initial and final state are identical.  • Some mathematical consequences: • The change can be described as an ‘exact differential’, i.e. the variables can be varied independently; e.g. for z=f(x,y): • The mixed derivatives are identical (Schwarz’s theorem): • Upon variation of x, y for z=const (Euler’s theorem):  same result !!!

50. A more general approach to thermal expansion and compression:  V = f(T) for p=const.:V = V0 (1 + ) (Gay-Lussac)  : (thermal) expansion coefficient  p = f(T) for V=const.:p = p0 (1 + )  p = f(V) for T=const.:pV = const. and d(pV) = pdV + Vdp = 0 (Boyle-Mariotte)  : (isothermal) compressibility generally valid!  Due to generally valid! Exact differential of V=f(p,T):