Chapter 16 Spontaneity entropy and free energy Spontaneous

Chapter 16 Spontaneity, entropy and free energy

Spontaneous l. A reaction that will occur without outside intervention. l We can’t determine how fast. l We need both thermodynamics and kinetics to describe a reaction completely. l Thermodynamics compares initial and final states. l Kinetics describes pathway between.

Thermodynamics l 1 st Law- the energy of the universe is constant. l Keeps track of thermodynamics doesn’t correctly predict spontaneity. l Entropy (S) is disorder or randomness l 2 nd Law the entropy of the universe increases.

Entropy l Defined in terms of probability. l Substances take the arrangement that is most likely. l The most likely is the most random. l Calculate the number of arrangements for a system.

l 2 possible arrangements l 50 % chance of finding the left empty

l 4 possible arrangements l 25% chance of finding the left empty l 50 % chance of them being evenly dispersed

l 4 possible arrangements l 8% chance of finding the left empty l 50 % chance of them being evenly dispersed

Gases l Gases completely fill their chamber because there are many more ways to do that than to leave half empty. l. Ssolid <Sliquid <<Sgas l there are many more ways for the molecules to be arranged as a liquid than a solid. l Gases have a huge number of positions possible.

l Solutions Entropy form because there are many more possible arrangements of dissolved pieces than if they stay separate. l 2 nd Law l DSuniv = DSsys + DSsurr l If DSuniv is positive the process is spontaneous. l If DSuniv is negative the process is spontaneous in the opposite direction.

exothermic processes DSsurr is positive. l For endothermic processes DSsurr is negative. l Consider this process H 2 O(l)® H 2 O(g) l DSsys is positive l DSsurr is negative l DSuniv depends on temperature. l For

Temperature and Spontaneity l Entropy changes in the surroundings are determined by the heat flow. l An exothermic process is favored because by giving up heat the entropy of the surroundings increases. l The size of DSsurr depends on temperature l DSsurr = -DH/T

DSsys DSsurr DSuniv + + - ? At High temp. - + ? At Low temp. Spontaneous? Yes No, Reverse

Gibb's Free Energy l G=H-TS l Never used this way. l DG=DH-TDS at constant temperature l Divide by -T l -DG/T = -DH/T-DS l -DG/T = DSsurr + DS l -DG/T = DSuniv l If DG is negative at constant T and P, the Process is spontaneous.

Let’s Check the reaction H 2 O(s) ® H 2 O(l) l DSº = 22. 1 J/K mol DHº =6030 J/mol l Calculate DG at 10ºC and -10ºC l Look at the equation DG=DH-TDS l Spontaneity can be predicted from the sign of DH and DS. l For

DG=DH-TDS Spontaneous? DS DH + - At all Temperatures + At high temperatures, “entropy driven” - At low temperatures, “enthalpy driven” + Not at any temperature, Reverse is spontaneous + -

Third Law of Thermo l The entropy of a pure crystal at 0 K is 0. l Gives us a starting point. l All others must be>0. l Standard Entropies Sº ( at 298 K and 1 atm) of substances are listed. l Products - reactants to find DSº (a state function). l More complex molecules higher Sº.

Free Energy in Reactions l DGº = standard free energy change. l Free energy change that will occur if reactants in their standard state turn to products in their standard state. l Can’t be measured directly, can be calculated from other measurements. l DGº=DHº-TDSº l Use Hess’s Law with known reactions.

Free Energy in Reactions are tables of DGºf. l Products-reactants because it is a state function. l The standard free energy of formation for any element in its standard state is 0. l Remember- Spontaneity tells us nothing about rate. l There

DG=DH-TDS Spontaneous? DS DH + - At all Temperatures + At high temperatures, “entropy driven” - At low temperatures, “enthalpy driven” + Not at any temperature, Reverse is spontaneous + -

Third Law of Thermo l The entropy of a pure crystal at 0 K is 0. l Gives us a starting point. l All others must be>0. l Standard Entropies Sº ( at 298 K and 1 atm) of substances are listed. l Products - reactants to find DSº (a state function) l More complex molecules higher Sº.

Free Energy in Reactions l DGº = standard free energy change. l Free energy change that will occur if reactants in their standard state turn to products in their standard state. l Can’t be measured directly, can be calculated from other measurements. l DGº=DHº-TDSº l Use Hess’s Law with known reactions.

Free Energy in Reactions are tables of DGºf l Products-reactants because it is a state function. l The standard free energy of formation for any element in its standard state is 0. l Remember- Spontaneity tells us nothing about rate. l There

Free energy and Pressure l DG = DGº +RTln(Q) where Q is the reaction quotients (P of the products /P of the reactants). l CO(g) + 2 H 2(g) ® CH 3 OH(l) l Would the reaction be spontaneous at 25ºC with the H 2 pressure of 5. 0 atm and the CO pressure of 3. 0 atm? l DGºf CH 3 OH(l) = -166 k. J l DGºf CO(g) = -137 k. J DGºf H 2(g) = 0 k. J

How far? l DG tells us spontaneity at current conditions. When will it stop? l It will go to the lowest possible free energy which may be an equilibrium. l At equilibrium DG = 0, Q = K l DGº = -RTln. K

DGº =0 <0 >0 K =1 >0 <0

Temperature dependence of K l DGº= -RTln. K = DHº - TDSº l ln(K) = DHº/R(1/T)+ DSº/R l A straight line of ln. K vs 1/T

Free energy And Work l Free energy is that energy free to do work. l The maximum amount of work possible at a given temperature and pressure. l Never really achieved because some of the free energy is changed to heat during a change, so it can’t be used to do work.