Chapter 1 concepts and behavior of gas

PHYSICAL CHEMISTRY Dr Ngo Thanh An Introduction • The principal goal of physical chemistry is to understand the properties and behaviour of material systems and to apply this understanding in useful ways References Textbook Introduction Thermodynamics: phenomenological theory to describe equilibrium properties of macroscopic systems based on few macroscopically measureable quantities Or: The study of heat and its transformation into mechanical energy is called thermodynamics Introduction Definitions Definitions • • • • Macroscopic system: A large system containing many atoms or molecules Microscopic system: a system consisting of a single atom or molecule Macroscopic properties (such as temperature and pressure) apply only to a macroscopic system and are properties of the whole system Microscopic properties (such as kinetic energy and momentum) are mechanical in nature Definitions A body or system whose condition is altered without gaining heat from or losing heat to the surroundings (energy is transferred only as work.) Definitions Thermodynamic definition of work: It is a kind of interaction that would occur at the system boundaries It can be positive or negative Heat: Heat is a mode of energy transfer that takes place between the system and the surroundings solely due to the temperature difference Thus, heat is a transient phenomenon It can be recognized only during a process Energy exists in many forms, such as mechanical energy, heat, light, chemical energy, and electrical energy Energy is the ability to bring about change or to work Definitions A thermodynamic process is a passage of a thermodynamic system from an initial state 10 to a final state Real gas Several equations have been proposed to represent the P-v-T behavior of substances accurately over a larger region with no limitations Critical isotherm of a pure substance has an inflection point at the critical state This model includes two effects not considered in the ideal-gas model: the intermolecular attraction forces and the volume occupied by the molecules themselves The accuracy of the van der Waals equation of state is often inadequate 40 41 Real gas critical point is defined as the point at which the saturated liquid and saturated vapor states are identical At the critical point, only one phase exists There is an inflection point in the constanttemperature line (critical isotherm) on a PV diagram This means that at the critical point: 42 Real gas 43 Real gas 44 Real gas 45 Real gas Compressibility factor Z A factor that accounts for the deviation of real gases from ideal-gas behavior at a given temperature and pressure The farther away Z is from unity, the more the gas deviates from ideal-gas behavior Gases behave as an ideal gas at low densities (i.e., low pressure, high temperature) Question: What is the criteria for low pressure and high temperature? Answer: The pressure or temperature of a gas is high or low relative to its critical temperature or pressure 46 Real gas All substances obey the same equation of state in terms of reduced variables 47 Real gas Reduced pressure Reduced temperature Pseudo-reduced specific volume Comparison of Z factors for various gases Z can also be determined from a knowledge of PR and vR 48 49 50 Real gas 51 Real gas 52 Real gas 53 Real gas 54 [...]... total pressure of the gases: pT = nT RT / V nT represents the total number of moles of gas present in the mixture P1 and P2 are the partial pressures of gas 1 and gas 2, respectively • PT = P1 + P2 = nT (RT/V) • PT = P1 + P2 + P3 = ΣPi 32 Ideal gas law • • • Gaseous mixtures - gases exert the same pressure as if they were alone and occupied the same volume The partial pressure of each gas, Pi, is related... of a gas • • • • Pressure (P) Volume (V) Temperature (T) The amount of the gas in moles (n) 29 Ideal gas law Ideal gas law PV=nRT 30 Ideal gas law • Combine these relationships into a single fundamental equation of state - the ideal gas equation of state PV = nRT J L atm R = 8. 314 = 0.08206 K mole K mole 31 Ideal gas law • • • The pressure exerted by gas #1: P1 = n1 RT / V The pressure exerted by gas. .. invented by Torricelli Gas pressure conversion factors • 1 atm = 760 mm Hg = 760 torr • 1 atm = 10 1.325 kPa = 1. 013 25 bar • 1 bar = 1 x 10 5 Pa (exactly) 22 Some state variables Definition: Temperature measures the degree of hotness of a body (“how hot”) It doesn’t depend on the mass or the material of an object It can be thought of as a measure of the average kinetic energy of the atoms or molecules... f(x1,…,xn) be a function such that f (λ x1 , , λ xn ) = λ n f ( x1 , , xn ) Then f is said to be a homogeneous function of degree n 16 Definitions Intensive and extensive variables 17 Definitions Definitions • • • Gas - a substance that is characterised by widely separated molecules in rapid motion Mixtures of gases are uniform Gases will expand to fill containers Ex: - Common gases include - O2 and. .. components of "air" - Other common gases - F2, Cl2, H2, He, and N2O (laughing gas) 19 Some state variables • • • • The pressure of a gas is best defined as the forces exerted by gas on the walls of the container Define P = force/area The SI unit of pressure is the Pascal 2 2 2 1 Pa = N/m = (kg m/s )/m Force Pr essure = Area 20 Some state variables 21 Some state variables • • • How do we measure gas pressure?... different gases at different (but low) pressures T = lim p →0 PV nR (for ideal gas) 26 Some state variables 27 Equation of state Consider thermodynamic system described by state variables {Z1, Z2,…, Zn} Subspace of equilibrium states: f(Z1, Z2,…, Zn) = 0  This is the equation of state (EOS) Ideal gas: {T, P, V}  thermodynamics EOS: pV = nRT 28 Ideal gas law • Experiments with a wide variety of gases... the total pressure by Pi = Xi PT Xj is the mole fraction of gas i • Xj= nj / nT 33 Ideal gas • • An ideal gas is a gas that obeys totally the ideal gas law over its entire P-V-T range Ideal gases – molecules have negligible intermolecular attractive forces and they occupy a negligible volume compared with the container volume 34 Ideal gas 35 Ideal gas 36 ... by the value of 15 its state functions at a certain set of state variables Definitions State variables: Describe equilibrium state of thermodynamic system uniquely Intensive: homogeneous of degree 0, independent of system size Extensive: homogeneous of degree 1, proportional to system size Note: Intensive state variables serves as equilibrium parameters Ex: temperature (T), pressure (P) and chemical... 11 Definitions When a gas adiabatically expands, it does work on its surroundings and gives up internal energy, and thus becomes cooler Blow warm air onto your hand from your wide-open mouth Now reduce the opening between your lips so the air expands as you blow Adiabatic expansion—the air is cooled 12 Definitions A source supplies energy in the form of heat, and a sink absorbs it Bodies with relatively... amount of material in the system Ex: volume, mole number, mass, length, entropy, enthalpy, Gibbs free energy … State function State 1 (x1,y1,z1) (depending on state variables) State 2 (x2,y2,z2) (depending on state variables) • State functions: Can we find the exact form of functions?  We don’t need to know the functions because we just pay attention to the initial and final state • State 1 or state