Entropy, free energy and equilibrium Spontaneity Entropy Free energy and equilibrium
Learning objectives Discuss what is meant by spontaneity Discuss energy dispersal and its relevance to spontaneity Describe the concept of a reversible process Define entropy and discuss relationships to distributions Use Boltzmann equation to calculate entropy Describe the second law of thermodynamics and its role in predicting chemical reactions Predict entropy changes in simple chemical reactions
Rules of the road: the laws of thermodynamics First law: energy is conserved Energy can neither be created nor destroyed but can be turned from one form into another Is that all there is to it? Heat engines convert heat into mechanical work Question: Can all heat be converted into work with 100 % efficiency?
Heat engines and the industrial revolution Newcomen steam engine invented 1712 Watt improves design 1760 Fundamental basis for efficiency was unknown Carnot (1820) described the operation of heat engines in abstract terms the Carnot cycle: the foundation of modern thermodynamics All engines based on burning fuels are heat engines
Carnot s cycle: net work obtained at energy cost Isothermal expansion work done by piston turns crank (heat drawn in to maintain T H ) Adiabatic expansion T, P - work done by gas Isothermal compression work done on gas to restore piston at T c Adiabatic compression work done on gas - T
Limitations on heat engines: the The answer is No! Carnot cycle shows net work is possible A temperature gradient Is essential Some energy lost to cold part (T C ) in cycle If T C = 0 K engine could achieve 100 % efficiency Footnote: Carnot cycle works infinitely slowly. Real engines are less efficient Carnot cycle
Fundamental limit tied to entropy Thermal motion is random Mechanical motion is coherent It is natural for coherent motion to become random Entropy and the heat tax The second law of thermodynamics Not all heat supplied to a heat engine can perform work (Entropy of universe always increases)
Equilibrium At an equilibrium point, the system resists small disturbances (not necessarily large ones) unstable Locally (meta) stable more stable At equilibrium, the rates of the forward and backward processes are equal
Spontaneity The tendency for a process to advance to equilibrium without external influence Something that happens naturally is spontaneous Any process will be spontaneous in one direction The reverse is non-spontaneous If work needs to be done, it is not spontaneous A rock naturally rolls down a hill - spontaneous It must be pushed back up - nonspontaneous A hot object naturally cools - spontaneous
Various spontaneities: dispersal Matter disperses gas fills a container, two liquids mix Heat disperses hot object cools on cold surface Motion disperses a ball stops bouncing The reverses of these three well known processes never occur spontaneously
Indicators of spontaneity What is the indicator of spontaneity? Heat evolved? But endothermic reactions occur spontaneously as well (ice melting, salt dissolving) Enthalpy is not an indicator of spontaneity, although most spontaneous processes are exothermic energy is conserved not created The amount of energy does not change in any process but it is redistributed...
Reversibility in thermodynamics A reversible process is one where the system and surroundings are restored to original values without any overall change An irreversible process is one where the system and surroundings cannot be restored to original values without change A reversible process produces the maximum possible work
Is reversibility possible? Gas expands spontaneously to fill vacuum Restoring system requires work to be done on it Some change in surroundings will have occurred, even if system looks the same
Reversibility and reality Reversibility only occurs when the system is in or almost at equilibrium at an infinitesimal rate In reality this does not obtain Real processes produce less work than ideal processes Spontaneous processes are irreversible Reverse of a spontaneous process is nonspontaneous
Spontaneity and speed The speed of a reaction is not an indicator of its spontaneity. Spontaneity is determined by the relative positions of the initial and final states (thermodynamic state functions) Speed is determined by the pathway (kinetics) Two independent regimes
Entropy the mixing (distributing) link entropy measures distribution of energy over states The more states available, the more entropy It is a state function depends only on initial and final states, not the pathway. The entropy change for a process is S S final S initial Systems move spontaneously to a state of greater entropy greater distribution of energy Disorder provides more states for energy distribution than ordered systems Thus we associate disorder and entropy
Entropy: microscopic and macroscopic views Microscopic: Measure of microstates and disorder Considers the atomic arrangements Macroscopic: Indicator of spontaneous process Treats matter like a black box
But you were wondering: Why do crystals form at all? Entropy is distribution of energy over microstates Crystals are highly ordered arrangements Shouldn t crystals should spontaneously fly apart to maximize disorder? Yes, but...this view ignores energy of the lattice Strong bonds hold the lattice together Energy input from surroundings to break bonds corresponds to entropy decrease (localization of energy in the crystal) So entropy is more than just shuffling playing cards also involves exchange of energy among paticles
Don t let them fool you: order can arise from chaos A popular argument against evolution is that the formation of organized DNA molecules from a random soup of atoms and molecules contravenes Second Law of Thermodynamics Just as crystals appear in a dish spontaneously so can DNA molecules form by attraction of atoms (self-assembly) N.B. Order (energy concentration) can appear spontaneously locally provided greater disorder (energy dispersal) is occurring elsewhere Release of energy by attraction between particles increases entropy of surroundings
Solubility redux: intermolecular forces Energy costs (bond breaking) Solvent solvent interactions Solute solute interactions (lattice energy) High lattice energy low solubility Energy gain (bond making) Solvent solute interactions Small, more highly charged ions have stronger interactions
Entropy contributions to solubility Solubility is a subtle balance of opposing factors Opposing tendencies: Hydration increases entropy of of ions in lattice Ions in solution have greater disorder Decreases entropy of solvent Solvent molecules now have greater order Excessive hydration by highly polarizing ions reduces entropy of solvent NaCl is soluble AlPO 4 is insoluble
What will these socks ne er be matched? Would you be stunned if the tumble dryer matched the socks? Okay, you never match the socks Chaos in the sock drawer is natural The same principles apply to chemical change (sort of particles interact while socks don t)
Chance meeting: entropy and probability Ordered states are less likely because there are fewer ways to obtain them Do our socks become matched spontaneously? No, only one of many possible arrangements With only a few molecules the ordered state becomes massively less probable than a disordered state Only 1 possibility Many possibilities
Boltzmann and disorder S k lnw W is the number of possible arrangements of the state k is Boltzmann s constant = R/N A = 1.38x10-23 J/K The entropy is proportional to the natural log of the number of arrangements of the state
Entropy of a disordered system An ordered arrangement has W = 1, S = 0 (at 0 K) Entropy of one mole of disordered molecules which can occupy either of 2 states N S k lnw k ln 2 A kn ln2 R ln 2 A S = 5.76 J/K
Entropy and gas expansion There is only one possible way for N A molecules to fill A and leave B empty. There are N ways for N A molecules to occupy A and B 2 A Entropy associated with gas mixing Entropy associated with gas expansion: Doubling the volume doubles the number of positions (microstates) for distribution of energy S V R ln V final initial
Making sense of units and definition Units of entropy are J/K of entropy How do these units connect to disorder and probability? Disorder is not entropy Disorder increases the number of microstates available Clausius definition of entropy is: Change in entropy = (heat supplied)/temperature S sys q T
Les Regles du Jeu (Rules of the game) Thermodynamics is the Law First Law: The total energy of a system and its surroundings is constant in any process E q w sys Second Law: In any spontaneous process, the total entropy of a system and its surroundings increases S tot 0
Third Law of Thermodynamics The entropy of a perfectly ordered crystalline substance at 0K is zero
Entropy and temperature Increasing T causes increase in entropy through molecular motion (rotational, vibrational and translational), and changes of state Disorder and motion Greater motion corresponds to greater number of microstates entropy increases with T Each level populated according to Boltzmann exp(-e/kt)
Entropy of a system increases with T Increasing T increases entropy through greater molecular motion In a solid an increased number of vibrational energy states more ways to distribute energy Phase changes cause step change because of increased number of microstates in less condensed phase
Standard molar entropy S The entropy of one mole of the pure substance at 1 atm pressure and a specified temperature, usually 25 C Determined experimentally from heat capacity measurements
Comparison of different substances Gases have highest values Solids have the lowest values
Standard entropy of reaction S o S o products o S reactants In the reaction N 2 O 4 = 2NO 2 S 2 o o SNO S O Products have more particles than reactants Entropy change is positive o N 2 4 Predicting entropy change of reaction from chemical equation by counting particles 2
Global thinking N.B.:Negative entropy change for reaction does not mean process isn t spontaneous Why you ask? Because we need to consider the universe Consider the entropy change in the surroundings Hmmm How could entropy of surroundings increase?
Surroundings Entropy change for the system is obtained from the entropies of the initial and final states What about the surroundings? At constant pressure, the entropy change in the surroundings is related to the enthalpy change for the system S surr H T
Enthalpy change of system determines entropy change of surroundings Heat released by the system increases the disorder of the surroundings. The effect of this is modulated by the temperature: At low temperature the effect is much more significant At high temperature, where there is already considerable disorder, the effect is muted the difference between tossing a rock into a calm pool (low T) and a storm-tossed ocean (high T)
Three results S tot S sys S surr S total > 0 the process is spontaneous S total < 0 the process is nonspontaneous S total = 0 the process is at equilibrium