Chapter 19Spontaneous Change: Entropy and Free Energy Dr. Peter Warburton firstname.lastname@example.org http://www.chem.mun.ca/zcourses/1051.php
Spontaneous processes • We have a general idea of what we consider spontaneous to mean: • A spontaneous process WILL OCCUR in a system WITHOUT any outside action being performed on the system.
Spontaneous processes Object falling to earth is spontaneous Ice melting above zero Celcius is spontatneous
Spontaneous processes • Icewillmelt above zero Celcius. • We don’t have to DO anything! • Objectswillfallto earth. • We don’t have to DO anything!
Spontaneous processes • Since we DON’T have to DO anything for these spontaneous processes to occur it APPEARS that an overall energy change from potential energy • to kinetic energy • IS SPONTANEOUS
Non-spontaneous processes • We have a general idea of what we consider non-spontaneous to mean: • A non-spontaneous process WILL NOT OCCUR in a system UNTIL an outside action is performed on the system.
Non-spontaneous processes Object rising from earth is non-spontaneous Ice freezing above zero Celcius is non-spontatneous
Non-spontaneous processes • We canmakewater freeze above zero Celcius by increasing the pressure. • We can make an object rise from the earth by picking it up.
Non-spontaneous processes • Since we DO have to ACT for these non-spontaneous processes to occur it APPEARS that an overall energy change from kinetic energy • to potential energy • IS NON-SPONTANEOUS
Chemistry and spontaneity • We know there are chemical processes that are spontaneousbecause we can put the chemical system together and reactants become products without us having to do anything. • H3O+ (aq) + OH- (aq) 2 H2O (l)
Chemistry and non-spontaneity • We know there are chemical processes that are non-spontaneousbecause we can put the chemical system together and reactants DO NOT become products. • The system we put together stays like it is • UNTIL WE CHANGE SOMETHING! • 2 H2O (l) 2 H2 (g) + O2 (g)
Spontaneous vs. non-spontaneous • It is obvious by the examples we’ve looked at that the opposite of every spontaneous process is a non-spontaneous process. • In chemical systems we’ve seen that if we put a chemical system together a reaction occursuntil the system reaches equilibrium. • Whether the forward reaction or the reverse reactiondominates depends on which of the two reactions is spontaneous at those conditions!
Spontaneity and energy • In our examples it APPEARED that the spontaneous process ALWAYS takes a system to a lower potential energy.
Spontaneity and energy • If this were true all exothermic processes would be spontaneous and all endothermic processes would be non-spontaneous. • THIS ISN’T TRUE! • H2O • NH4NO3 (s) NH4+ (aq) + NO3- (aq) • is spontaneous even though • DH = +25.7 kJ
Recall the First Law • The First Law of thermodynamics stated that the energy of an ISOLATED system is constant. • What’s the largest ISOLATED system we can think of? • It’s the UNIVERSE! • The energy of the universe is constant!
Recall the First Law • On the universal scale, there is no overall change in energy, and so lower energy CANNOT be the only requirement for spontaneity. • There must be something else as well!
Further proof lower energy isn’t enough • If an ideal gas expands into a vacuum at a constant temperature, then • no work is done • and • no heat is transferred
Further proof lower energy isn’t enough • No work done and no heat transferred means • NO OVERALL CHANGE in energy • of the system
Further proof lower energy isn’t enough • This spontaneous process has no overall change in energy!
Entropy • Entropy (from Greek, meaning • “in transformation”) • is a thermodynamic property • that relates • the distribution of the total energy of the system • to the available energy levels of the particles.
Entropy • A general way to envision entropy is • “differing ways to move” • Consider mountain climbers on a mountain. Two factors affect the distribution of mountain climbers on a mountain: • Total energy of all the climbers • and how many places can you stop on the mountain
Consider hungry mountain climbers • Hungry mountain climbers have • little total energy amongst themselves to climb a mountain, so most of them are near the bottom, while some are distributed on the lower parts of the mountain. Few energy levels can be reached!
Consider well fed mountain climbers • Well-fed mountain climbers have • more total energy amongst themselves to climb a mountain, so the climbers will be more spread out on the whole mountain. More energy levels can be reached!
Temperature and total energy • The total energy shared by molecules is related to the temperature. • A given number of molecules at a low temperature (less total energy) have less“differing ways to move”than the same number of molecules at a high temperature (more total energy).
Higher mountain means more places to stop • If a well-fed mountain climber tries to climb Signal Hill, they will most likely reach the top. They have only a few places to stop (levels)because Signal Hill is a small mountain. • The same well-fed mountain climber on Mount Everest has a greater number of places to stop(levels) because it is a larger mountain.
Volume and energy levels • The number of levels of energy distribution of molecules is related to the volume. • A given number of molecules in a small volume have less“differing ways to move”than the same number of molecules in a larger volume.
Entropy • The greater the number of “differing ways to move” molecules can take amongst the • available energy levels of a system • of a given state (defined by temperature and volume, and number of molecules), • the greater the entropy of the system.
Expansion into vacuum • A gas expands into a vacuum because the increased volume allows for a greater number of“differing ways to move” for the molecules, even if the temperature is the same.
Expansion into vacuum • That is, the entropy increases when the gas is allowed to expand into a vacuum. • Entropy increase plays a role in spontaneity!
Entropy is a state function • Entropy, S, is a state function like enthalpy or internal energy. • The entropy of a system DEPENDS ONLY on the current state • (n, T, V, etc.) of the system, and NOT how the system GOT TO BE in that state.
Boltzmann equation and entropy More available energy levels when the size of a box increases – like expanding a gas into a vacuum – ENTROPY INCREASES! More energy levelsare accessible when the temperature increases – ENTROPY INCREASES!
Change in entropy is a state function • Because entropy is a state function, then change in entropy DS is ALSO a state function. • The difference in entropy between two states ONLY depends on the entropy of the initial and final states, and NOT the path taken to get there.
Hess’s Law • Recall Hess’s Law – as long as we get from the same initial state to the same final statethen DH will be the same regardless of the steps we add together. • Change in entropy DS will work exactly the same way! As long as we get from the same initial state to the same final statethen DS will be the same regardless of the steps we add together.
Boltzmann equation and entropy • n, T, V help define the number of states(number of available energy levels) the system can have. • The many “different ways to move” of molecules in a particular state are called microstates. • Hopefully it makes sense that more total states should automatically mean more total microstates. • The number of microstates is often symbolized by W.
Say we have a deck of 52 playing cards. Choosing oneplaying card is a state. If we choose the first card out of the pack, there are 52 microstatesfor thisfirst state. The second card (second state)we choose has 51 microstates, and so on. Playing cards
Overall there are W =52! 8 x 1067 possible distributions (total microstates) for 52 playing cards! Playing cards
If we flip 52 coins(a coin is one state), with two possible microstates(heads or tails) each, there are W =252 = 4.5 x 1015 possibledistributions. (total microstates) A deck of 52 playing cards has greater entropy than 52 coins! Playing cards and coin flips
Boltzmann equation and entropy • Ludwig Boltzmann formulated the relationship between the number of microstates (W) and the entropy (S). • S = k ln W • The constant k is the Boltzmann constant which has a value equal to the gas constant R divided by Avagadro’s number NA
Boltzmann equation and entropy • S = k ln W • where k = R / NA • k = (8.3145 JK-1mol-1) / (6.022 x 1023mol-1) • k = 1.381 x 10-23 JK-1 • We can see the units for entropy will be Joules per Kelvin(JK-1)
Measuring entropy change • From the • units for entropy(JK-1) • we get an idea of how we might measure entropy change DS • It must involve some sort ofenergy changerelative to thetemperature change!
Measuring entropy change • DS = qrev / T • The change in entropy is the heat involved in areversible process at a constant temperature.
Heat IS NOT a state function • Since heat IS NOT a state function we need a reversible process to make it ACT LIKE a state function.
Reversible processes • In a reversible process a change in one direction is exactly equal and opposite to the change we see if we do the change in the reverse direction. • In reality it is impossible to make a reversible process without making an infinite number of infinitesimally small changes.
Reversible processes • We can however imagine the process is done reversibly and calculate the heat involved in it, so we can calculate the reversible entropy change that could be involved in a process. DSrev = qrev / T
Endothermic increases in entropy In these three processes the molecules gain greater “differing ability to move.” The molecules occupy more available microstates at the given temperature, and so the entropy increases in all three processes!
Generally entropy increases when… • …we go from solid to liquid. • …we go from solid or liquid to gas. • …we increase the amount of gas in a reaction. • …we increase the temperature. • …we allow gas to expand against a vacuum. • …we mix gases, liquids, or otherwise make solutions of most types.
Problem • Predict whether entropy increases, decreases, or we’re uncertain for the following processes or reactions: Answers: a) decreases b) increases c) uncertain d) increases
Evaluating entropy and entropy changes • Phase transitions – In phase transitions the heat change does occur reversibly, so we can use the formula • DSrev = qrev / T • to calculate the entropy change. In this case the heat is the enthalpy of the phase transition and the temperature is the transition temperature • DS = DHtr / Ttr
Evaluating entropy and entropy changes • Phase transitions – For water going from ice (solid) to liquid, DHfus = 6.02 kJmol-1 at the melting point (transition temp.) of 273.15 K (0 C) • DSfus = DHfus / Tmp • DSfus = 6.02 kJmol-1 / 273.15 K • DSfus = 22.0 JK-1mol-1