Physical Chemistry I (TKK-2246) 14/15 Semester 2 Instructor: Rama Oktavian Office Hr.: M – F.13-15

Outlines 1. Review (week 1 – 8) 2. Phase equilibrium (1-comp) 3. Phase rule 4. Clausius-Clapeyron equation

Review Boyle’s law Boyle’s Law is one of the laws in physics that concern the behaviour of gases When a gas is under pressure it takes up less space: The higher the pressure, the smaller the volume Boyles Law tells us about the relationship between the volume of a gas and its pressure at a constant temperature The law states that pressure is inversely proportional to the volume

Gas laws Charles’s law Jacques Charles French chemist Jacques Charles discovered that the volume of a gas at constant pressure changes with temperature. As the temperature of the gas increases, so does its volume, and as its temperature decreases, so does its volume. The law says that at constant pressure, the volume of a fixed number of particles of gas is directly proportional to the absolute (Kelvin) temperature

Ideal gas and Real gas Ideal gas The ideal gas law is used to describe the behavior of an ideal gas. Ideal gas: hypothetical gas that obeys kinetic molecular theory and the ideal gas law

Ideal gas and Real gas Real gas The compression factor For ideal gas P moderate  Z < 1

Equation of state The general form of an equation of state is p=f(T,V,n) Ideal gas equation is equation of state

Equation of state P, V, n, T are properties Intensive properties – independent on the quantity of material P, T Extensive properties – dependent on the quantity of material n, V Intensive properties The ratio of any two extensive variables is always an intensive variable

Dalton’s law Dalton’s Law of Partial Pressures indicates that pressure depends on the total number of gas particles, not on the types of particles. the total pressure exerted by gases in a mixture is the sum of the partial pressures of those gases. P T = P 1 + P 2 + P

Condensed Phase The definition of “condensed” 1. reduced in volume, area, length, or scope; shortened: a condensed version of the book. 2. made denser, especially reduced from a gaseous to a liquid state. 3. thickened by distillation or evaporation; concentrated: condensed lemon juice.

Condensed Phase The definition of “condensed phase” Solid and Liquid are condensed phase because the particles are very close together. There are strong intermolecular forces

Condensed Phase The definition of “condensed phase” made denser, especially reduced from a gaseous to a liquid state.

Thermodynamic terms What is thermodynamic? the study of the transformations of energy enables us to discuss all matters quantitatively and to make useful predictions e.g: The release of energy can be used to provide heat when a fuel burns in a furnace, to produce mechanical work when a fuel burns in an engine, and to generate electrical work when a chemical reaction pumps electrons through a circuit

Thermodynamic terms A thermodynamic system is that part of the physical universe the properties of which are under investigation A system is isolated when the boundary prevents any interaction with the surroundings A system is called open when mass passes across the boundary, closed when no mass passes the boundary

Thermodynamic terms State of a System. A system is in a definite state when each of its properties has a definite value. Change in State, Path, Cycle, Process. Let a system undergo a change in its state from a specified initial to a specified final state The change in state is completely defined when the initial and the final states are specified The path of the change in state is defined by giving the initial state, the sequence of intermediate states arranged in the order traversed by the system, and the final state

Thermodynamic terms A process is the method of operation by means of which a change in state is effected State Variable,.... A state variable is one that has a definite value when the state of a system is specified.... Path Variable,… Variable that do depend on path

1 st law of thermodynamics Mathematical statement for The 1st Law of Thermodyamics ΔU = q + w in which w > 0 or q > 0 if energy is transferred to the system as work or heat and w < 0 or q < 0 if energy is lost from the system as work or heat

Change in state at constant volume Heat calculation at constant volume Valid for constant volume process Heat calculation at constant volume process

Change in state at constant pressure Heat calculation at constant pressure process Heat capacity at constant pressure process Valid for constant pressure process If Cp is constant

Adiabatic change Adiabatic change PV-graph

Process in ideal gas Isothermal Process (constant temperature) for closed system process Governing equation

Process in ideal gas Isobaric Process (constant pressure) for closed system process

Process in ideal gas Isochoric Process (constant volume) for closed system process

Hess’ law “The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided” path-independence of the value of ∆ r H 0

Phase equilibrium Phases: A homogenous portion of a system that has uniform physical and chemical characteristics, e.g. pure material, solid solution, liquid solution, and gaseous solution, ice and water, syrup and sugar. Equilibrium is a word denoting a static condition, the absence of change Phase equilibrium is the state of balance between two phases of a molecule For one component, the three different phases of compounds are solid, liquid and gas

Phase equilibrium Phases: A homogenous portion of a system that has uniform physical and chemical characteristics, e.g. pure material, solid solution, liquid solution, and gaseous solution, ice and water, syrup and sugar. examples of phase equilibrium are the equilibrium of a liquid and its saturated vapor Give me more examples…

Phase rule the phase rule for a one-component system Gibbs Phase Rule Josiah Willard Gibbs ( ), American mathematical physicist. Assignment: Summarize the justification of this phase rule from J.M. Smith, H.C. Van Ness, M.M. Abott, 2011, Introduction to Chemical Engineering Thermodynamics, 6 th ed., sec The number of degrees of freedom(or the variance) f of an equilibrium system is defined as the number of independent intensive variables needed to specify its intensive state

Phase rule

Phase equilibrium Equilibrium condition the chemical potential of each substance must have the same value in every phase in which that substance appears a state in which there are no observable changes as time goes by.

Phase equilibrium

Phase rule the phase rule for a one-component system phase equilibrium is usually represented in P-T diagram

Phase equilibrium Phase diagram (P-T diagram)

The Clapeyron equation At equilibrium condition

The Clapeyron equation At equilibrium condition