Thermodynamics

Thermodynamics Way to calculate if a reaction will occur

Kinetics Way to determine the rate of reactions

Thermodynamic equilibrium rarely attained: Biological processes – work against

thermo Kinetic inhibitions

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

Thermodynamic definitions System – part of universe selected

for study Surroundings (Environment) –

everything outside the system Universe – system plus surroundings Boundary – separates system and

surroundings Real or imagined Boundary conditions – solutions to Diff

Eq.

Types of systems

Open system Exchanges with surroundings Mass, also heat and work

Closed system no exchange of matter between

surrounding and system, energy can be exchanged

Isolated system there is no interaction with

surroundings, no exchange of energy or matter

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

in total abundance

Parts of Systems

Phase – physically and chemically homogeneous region Example: saturated solution of NaCl

Species – chemical entity (ion, molecule, solid phase, etc.) E.g. NaCl (solid) + H20 (liquid) Also Na+, Cl-, OH-, H+, NaClo, others

Components Minimum number of chemical entities

required to define compositions of all species

Many different possibilities Na+, Cl-, H+, OH-

NaCl – H2O

Thermodynamic Properties Extensive

Depends on amount of material E.g., moles, mass, energy, heat, entropy Additive

Intensive Don’t depend on amount of material Concentrations, density, T, heat

capacity Can’t be added

State function a property of a system which has a

specific value for each state (e.g., condition) E.g., 1 g water @ 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

Path independent 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

Thermodynamic Laws

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

Zeroth law

If two systems are in thermal equilibrium No heat is exchanged between the

systems They have the same “temperature”

T is the newly defined state function How is temperature defined?

Measurement of T Centigrade

100 divisions between melting and boiling point of water

Kelvin - Based on Charles law At constant P and m, there is a linear

relationship between volume of gas and T

Size of unit is same as centigrade

V = a1 + a2TWhere V = volume

T = temperaturea1 & a2 = constants

Fig. Levine

T (ºC)

V (L)

• 1 mole of N2 at constant P• Experimental results:

- extrapolation of results show intercept T @ V = 0 is about -273ºC

- Kelvin scale based on triple point of water

- defined as being 273.16 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 Energy conserved

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

Three forms of energy

Potential + Kinetic energy + internal energy

Minimum or rest energyHere only internal energy, U

Internal energy (U) Molecular rotation, translation, vibration

and electrical energy Potential energy of interactions of

molecules Relativistic rest-mass energy

In thermo, a system at rest Kinetic and potential energy = 0 Thermodynamics considers only

changes in internal energy

New state function – Enthalpy (H)

PV = pressure * volume = work done on/by the system

Units – energy, e.g. J, kJ, cal etc. 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 i.e., it is impossible to build a machine

that converts heat to work with 100% efficiency

New state function Entropy = S

Extensive = units of energy/T, e.g. kJ/K

Entropy is a variable used to defined Gibbs free energy (G)

G used to determine equilibrium of reactions

Equilibrium Thermodynamics

Equilibrium occurs with a minimum of energy in system

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) G = f(H,S,T)

G and H units = kJ (kcal) S units = kJ/K (kcal/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 “Process” means system changes May be chemical reaction

Here D is change in state:

For all properties: G, H, T or S

DG =DH - TDS

D = State2 – State1

When system moves toward equilibrium: may release heat, e.g. DH < 0 entropy may increase, e.g. DS > 0 Both may happen

Thus: DG < 0 for spontaneous reaction

G2 < G1; DG = G2 – G1 < 0

DG = 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.

Non-equilibrium system:

Equilibrium system

A + B ↔ C + D DG = 0

A + B → C + D DG ≠ 0

A + B ← C + D DG ≠ 0

G is an extensive state variable It depends on the amount of material

The amount of G in a system is divided among components Need to know how G changes for each

component First look at what variables control G

What is G a function of? Want to know how G changes if all (or

any) other variable change Change = calculus

Math Review

(on board)

If system is in thermal and mechanical equilibrium: G = f(P, T, n1, n2, n3…)

Then total differential:(on board)

Infinitesimal change in G caused by infinitesimal change in P, T, n1, n2, n3…

These are values we need to know to know DG

Last term defined by Gibbs as chemical potential (m)

(on board) m is the amount that G changes (per

mole) with addition of new component Intensive property (G extensive) Doesn’t depend on mass of system For one component system m = G/n

For system at equilibrium, m of all components are identical

Equilibrium, activities, chemical potentials

(on board)