Chapter 18 Entropy, Free Energy, and Equilibrium Overview: Spontaneity and Entropy Entropy and Probability Second Law of Thermodynamics Free Energy and Equilibrium

Spontaneous Processes A spontaneous process is one that does occur under the given set of conditions. If a reaction does not occur under a given set of conditions, it is said to be non-spontaneous.

Some types of spontaneous processes: Phase transitions (melting, freezing) Mixing and dissolving of solutes into solution Expansion of gases into an evacuated bulb Heat transfer from hot to cold objects Movement towards chemical equilibrium Spontaneous Processes

Everyday Examples: Water freezes spontaneously below 0 o C and melts spontaneously above 0 o 1 atm A lump of sugar spontaneously dissolves in a cup of coffee, but dissolved sugar does not spontaneously reappear in its original form Expansion of a gas in an evacuated bulb is a spontaneous process. The gathering of all gas molecules into one location is not spontaneous Heat flow from a hotter object to a colder one is spontaneous, but the reverse never happens spontaneously Iron exposed to water and oxygen forms rust, but rust does not spontaneously change to iron

Spontaneous Process What makes a process spontaneous? Often, but not always, a system that is spontaneous tries to minimize its energy. A spontaneous system always maximizes its ENTROPY. Entropy usually increases when a pure liquid or solid dissolves in a solvent

Entropy (S) Entropy (S) is a direct measure of the randomness or disorder of a system At disorder increases, Entropy increases Entropy can also be related to probability Probable state after valve is opened Before valve is opened Gas expands to fill both bulbs equally

Order of Entropy (S) For all substances, the particles in the solid state are more ordered than those in the liquid state, which are both more ordered than those in the gaseous state. S solid < S liquid << S gas

Absolute Entropy and Units Unlike Enthalpy or Energy, it is possible to determine the absolute entropy of a substance Standard entropy is the absolute entropy of a substance at 1atm and 25 o C Entropy is measured in J/K or J/K. Mol Entropies of elements and compounds are all positive (S o > 0)

Entropy as a state function Like energy and enthalpy, entropy is a state function. ∆S = S f – S i If the change results in an increase in randomness, then S f > S i State functions are properties that are determined by the state of the system.

Second Law of Thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in and equilibrium process. Spontaneous: ∆S univ = ∆S sys + ∆S surr >0 Equilibrium: ∆S univ = ∆S sys + ∆S surr =0 For any spontaneous process, ∆S univ must be greater than zero. ∆S sys or ∆S surr may be negative, as long as the sum of the two is positive. If the process is not spontaneous in the direction described, then it is spontaneous in the opposite direction.

Entropy Changes in the System Entropy change (∆S) in the system aA + bB → cC + dD ∆S° standard entropy of reaction ∆S°rxn = sum of S° for products - sum of S° for reactants ∆S°rxn = ∑ S°(products) - ∑ S°(reactants) General Rules: If a reaction produces more gas molecules in the products than there were as reactants, S° > 0 If total moles of gas molecules decreases, S° < 0 No net change in the number of gas molecules, S° = 0

Entropy Changes in Surroundings ∆S surr = -∆H sys / T This assumes that both the system and the surroundings are at temperature T A thermite reaction, which produces tremendous heat, but is not thermodynamically favored at STP

Mr. Gibbs and His Free Energy “Free energy” does not mean “without cost”. Rather, it means “energy available to do work” The Sign and Value of the free energy will determine the spontaneity of a reaction. Diamond, which is Thermodynamically favored to graphite, but not Kinetically favored

More Mr. Gibbs Free energy is used to express the spontaneity of a reaction more directly. G = H – TS, where all quantities pertain to the system. The change in free energy in a constant temp. process can be expressed by: ∆G = ∆H - T∆S If ∆G is negative, then the reaction must be spontaneous.

Standard Free-Energy Changes Standard free energy of reaction is the free energy change for a reaction when it occurs under standard state conditions, when reactants in their standard states are converted to products in their standard states. ∆G° = ∑ ∆G°f (products) - ∑ ∆G°f (reactants) If both ∆H and ∆S are positive, ∆G will be negative only when T∆S is greater than ∆H If ∆H is negative, and ∆S is negative, ∆G will always be positive, regardless of temperature If∆H is neg. and ∆S is positive, then ∆G will be negative always If ∆H is negative and ∆S is negative, ∆G will be negative only when T∆S is smaller than ∆H

Temp and Chemical Reactions Ball park estimates of when a reaction becomes spontaneous Procedure: find ∆H° and ∆S° at 25 °C set ∆H - T∆S = 0 solve for T, estimated temperature at which reaction becomes spontaneous

Phase Transitions ∆G = 0 at the temperature of a phase transition thus, ∆H - T∆S = 0 so ∆S = ∆H / T Example: ∆S ice →water = ∆H / T ∆H = 6010 J/mole molar heat of fusion of water T = 273 freezing point of water is 0 °C ∆S ice →water = 6010 J/mole. 273 K = 22.0 J/mole.K (entropy increase) ∆S water → ice = J/mole.K (entropy decrease)

Free Energy and Chemical Equilibrium Once a reaction starts, standard state conditions no longer exist for the products or the reactants. For any chemical system: ∆G = ∆G° + (RT) ln Q If ∆G is not zero, then the system is not at equilibrium and it will spontaneously shift toward the equilibrium state At equilibrium: ∆G = 0 and Q = K ∆G° = - RT ln K When K is very small or large, may be difficult to measure the concentration of a reactant or product, so it is easier to find ∆G° and calculate K.