Thermodynamics Thermodynamics Thermodynamics Way to calculate if a reaction will occur Way to calculate if a reaction will occur Kinetics Kinetics Way to determine the rate of reactions Way to determine the rate of reactions Thermodynamic equilibrium rarely attained: Thermodynamic equilibrium rarely attained: Biological processes – work against thermo Biological processes – work against thermo Kinetic inhibitions Kinetic inhibitions

Thermodynamics very useful Thermodynamics very useful Good approximation of reactions Good approximation of reactions Tells direction a reaction should go Tells direction a reaction should go Basis for estimated rates Basis for estimated rates Farther from equilibrium, faster rate Farther from equilibrium, faster rate

Thermodynamic definitions System – part of universe selected for study System – part of universe selected for study Surroundings (Environment) – everything outside the system Surroundings (Environment) – everything outside the system Universe – system plus surroundings Universe – system plus surroundings Boundary – separates system and surroundings Boundary – separates system and surroundings Real or imagined Real or imagined Boundary conditions – solutions to Diff Eq. Boundary conditions – solutions to Diff Eq.

Types of systems Open system Open system Exchanges with surroundings Exchanges with surroundings Mass, also heat and work Mass, also heat and work Closed system Closed system no exchange of matter between surrounding and system, energy can be exchanged no exchange of matter between surrounding and system, energy can be exchanged Isolated system Isolated system there is no interaction with surroundings, no exchange of energy or matter there is no interaction with surroundings, no exchange of energy or matter

Steady state system Steady state system Flux in = flux out Flux in = flux out There can be exchange, but no change in total abundance There can be exchange, but no change in total abundance

Parts of Systems Phase – physically and chemically homogeneous region Phase – physically and chemically homogeneous region Example: saturated solution of NaCl Example: saturated solution of NaCl Species – chemical entity (ion, molecule, solid phase, etc.) Species – chemical entity (ion, molecule, solid phase, etc.) E.g. NaCl (solid) + H 2 0 (liquid) E.g. NaCl (solid) + H 2 0 (liquid) Also Na +, Cl -, OH -, H +, NaCl o, others Also Na +, Cl -, OH -, H +, NaCl o, others

Components Components Minimum number of chemical entities required to define compositions of all species Minimum number of chemical entities required to define compositions of all species Many different possibilities Many different possibilities Na +, Cl -, H +, OH - Na +, Cl -, H +, OH - NaCl – H 2 O NaCl – H 2 O

Thermodynamic Properties Extensive Extensive Depends on amount of material Depends on amount of material E.g., moles, mass, energy, heat, entropy E.g., moles, mass, energy, heat, entropy Additive Additive Intensive Intensive Don’t depend on amount of material Don’t depend on amount of material Concentrations, density, T, heat capacity Concentrations, density, T, heat capacity Can’t be added Can’t be added

State function State function a property of a system which has a specific value for each state (e.g., condition) a property of a system which has a specific value for each state (e.g., condition) E.g., 1 g 25º C E.g., 1 g 25º C A couple of state functions for this sytem are amount of mass (1 g) and T (25º C) A couple of state functions for this sytem are amount of mass (1 g) and T (25º C) There are others we will learn about There are others we will learn about Path independent Path independent E.g., state would be the same if you condensed steam or melted ice E.g., state would be the same if you condensed steam or melted ice For the values of the state functions, it doesn’t matter how the state got there For the values of the state functions, it doesn’t matter how the state got there

Thermodynamic Laws Three laws – each derives a “new” state function Three laws – each derives a “new” state function 0 th law: yields temperature (T) 0 th law: yields temperature (T) 1 st law: yields enthalpy (H) 1 st law: yields enthalpy (H) 2 nd law: yields entropy (S) 2 nd law: yields entropy (S)

Zeroth law If two systems are in thermal equilibrium If two systems are in thermal equilibrium No heat is exchanged between the systems No heat is exchanged between the systems They have the same “temperature” They have the same “temperature” T is the newly defined state function T is the newly defined state function How is temperature defined? How is temperature defined?

Measurement of T Centigrade Centigrade 100 divisions between melting and boiling point of water 100 divisions between melting and boiling point of water Kelvin - Based on Charles law Kelvin - Based on Charles law At constant P and m, there is a linear relationship between volume of gas and T At constant P and m, there is a linear relationship between volume of gas and T Size of unit is same as centigrade Size of unit is same as centigrade V = a 1 + a 2 T Where V = volume T = temperature a 1 & a 2 = constants

Fig. Levine T (ºC) V (L) 1 mole of N 2 at constant P Experimental results: - extrapolation of results show intercept V = 0 is about -273ºC - Kelvin scale based on triple point of water - defined as being K

First law Change in the internal energy of a system is the sum of the heat added (q) and amount of work done (w) on system Change in the internal energy of a system is the sum of the heat added (q) and amount of work done (w) on system Energy conserved Energy conserved

Three types of energy Three types of energy Kinetic and potential – physically defined Kinetic and potential – physically defined Internal – chemically defined Internal – chemically defined

Three forms of energy Potential + Kinetic energy + internal energy Minimum or rest energy Here only internal energy, U

Internal energy (U) Internal energy (U) Molecular rotation, translation, vibration and electrical energy Molecular rotation, translation, vibration and electrical energy Potential energy of interactions of molecules Potential energy of interactions of molecules Relativistic rest-mass energy Relativistic rest-mass energy In thermo, a system at rest In thermo, a system at rest Kinetic and potential energy = 0 Kinetic and potential energy = 0 Thermodynamics considers only changes in internal energy Thermodynamics considers only changes in internal energy

New state function – Enthalpy (H) New state function – Enthalpy (H) PV = pressure * volume = work done on/by the system PV = pressure * volume = work done on/by the system Units – energy, e.g. J, kJ, cal etc. Units – energy, e.g. J, kJ, cal etc. Extensive – i.e., additive. Extensive – i.e., additive. H = U + PV

Second Law A system cannot undergo a cyclic process that extracts heat from a heat reservoir and also performs an equivalent amount of work on the surroundings A system cannot undergo a cyclic process that extracts heat from a heat reservoir and also performs an equivalent amount of work on the surroundings i.e., it is impossible to build a machine that converts heat to work with 100% efficiency i.e., it is impossible to build a machine that converts heat to work with 100% efficiency

New state function New state function Entropy = S Entropy = S Extensive = units of energy/T, e.g. kJ/K Extensive = units of energy/T, e.g. kJ/K Entropy is a variable used to defined Gibbs free energy (G) Entropy is a variable used to defined Gibbs free energy (G) G used to determine equilibrium of reactions G used to determine equilibrium of reactions

Equilibrium Thermodynamics Equilibrium occurs with a minimum of energy in system Equilibrium occurs with a minimum of energy in system Systems not in equilibrium move toward equilibrium through loss of energy Systems not in equilibrium move toward equilibrium through loss of energy

If system is at constant T and P, measure of energy of system is given by Gibbs free energy (G) If system is at constant T and P, measure of energy of system is given by Gibbs free energy (G) G = f(H,S,T) G = f(H,S,T) G and H units = kJ (kcal) G and H units = kJ (kcal) S units = kJ/K (kcal/K) S units = kJ/K (kcal/K) T is Kelvin scale (K) T is Kelvin scale (K) G = H - TS

Equilibrium A, B, C, and D present A + B ↔ C + D Imagine some system with A, B, C, and D components:

Consider processes in system at constant T & P Consider processes in system at constant T & P “Process” means system changes “Process” means system changes May be chemical reaction May be chemical reaction Here  is change in state: Here  is change in state: For all properties: G, H, T or S For all properties: G, H, T or S  G =  H - T  S  = State 2 – State 1

When system moves toward equilibrium: When system moves toward equilibrium: may release heat, e.g.  H < 0 may release heat, e.g.  H < 0 entropy may increase, e.g.  S > 0 entropy may increase, e.g.  S > 0 Both may happen Both may happen Thus: Thus:  G < 0 for spontaneous reaction  G < 0 for spontaneous reaction G 2 < G 1 ;  G = G 2 – G 1 < 0 G 2 < G 1 ;  G = G 2 – G 1 < 0  G = 0 for process at equilibrium  G = 0 for process at equilibrium Possible to calculate DG, and thus determine (1) if reaction will occur spontaneously, and (2) which way reaction will go. Possible to calculate DG, and thus determine (1) if reaction will occur spontaneously, and (2) which way reaction will go.

Non-equilibrium system: Non-equilibrium system: Equilibrium system Equilibrium system A + B ↔ C + D  G = 0 A + B → C + D  G ≠ 0 A + B ← C + D  G ≠ 0

G is an extensive state variable G is an extensive state variable It depends on the amount of material It depends on the amount of material The amount of G in a system is divided among components The amount of G in a system is divided among components Need to know how G changes for each component Need to know how G changes for each component First look at what variables control G First look at what variables control G What is G a function of? What is G a function of? Want to know how G changes if all (or any) other variable change Want to know how G changes if all (or any) other variable change Change = calculus Change = calculus

Math Review (on board)

If system is in thermal and mechanical equilibrium: If system is in thermal and mechanical equilibrium: G = f(P, T, n1, n2, n3…) G = f(P, T, n1, n2, n3…) Then total differential: Then total differential: (on board) Infinitesimal change in G caused by infinitesimal change in P, T, n1, n2, n3… Infinitesimal change in G caused by infinitesimal change in P, T, n1, n2, n3… These are values we need to know to know  G These are values we need to know to know  G

Last term defined by Gibbs as chemical potential (  ) Last term defined by Gibbs as chemical potential (  ) (on board)  is the amount that G changes (per mole) with addition of new component  is the amount that G changes (per mole) with addition of new component Intensive property (G extensive) Intensive property (G extensive) Doesn’t depend on mass of system Doesn’t depend on mass of system For one component system  = G/n For one component system  = G/n For system at equilibrium,  of all components are identical For system at equilibrium,  of all components are identical

Equilibrium, activities, chemical potentials (on board)