Spontaneity, Entropy and Free Energy Chapter 17 Spontaneity, Entropy and Free Energy

Class Objectives To understand the following introductory terms concerning Thermodynamics. Spontaneity Entropy Disorder and Living Systems Phases Entropy Calculations Gibbs Free Energy Laws of Thermodynamics

Spontaneous A reaction that will occur without outside intervention. We can’t determine how fast. We need both thermodynamics and kinetics to describe a reaction completely. Thermodynamics compares initial and final states. Kinetics describes pathway between. TO SUMMARIZE – Spontaneity has nothing to do with the speed of a rxn.

Spontaneous Reactions The rusting of iron is spontaneous, however it is a relatively slow reaction. Diamond will turn into graphite but the time frame is hundreds of millions of years, but since it does happen on its own, it is said to be spontaneous. The melting of ice is spontaneous at temperatures above 0 ˚C. ( So this is a clue that temperature will factor into all of this.)

Thermodynamics 1st Law - The energy of the universe is constant. In other words the Law of Conservation of Energy. Keeps track of thermodynamics, though it doesn’t correctly predict spontaneity. Entropy (S) is disorder or randomness. 2nd Law of Thermodynamics states that the entropy of the universe increases.

Entropy Defined in terms of probability. Substances take the arrangement that is most likely. The most likely is the most random. This is another way of saying that disorder of a system increases. Calculate the number of arrangements for a system.

Entropy and Disorder When you buy a deck of cards, it is ordered by suit and number. After the deck is shuffled, this ordering no longer exists. We understand that there is a very low probability that the cards can be shuffled and somehow manage to regain their original order but we never expect it to happen.

Entropy and Living Systems It is worth noting that living things are also subject to the Second Law of Thermodynamics. If an apple is picked from the tree and just left there to be observed, we would see that it would start to decay into simpler substances. Water vapor and Carbon Dioxide being just two of them.

Entropy and Living Systems However, living systems grow less random, our bodies have an organized assembly of organs and tissues. This organization only continues as long as there is a supply of energy being consumed. Once energy is no longer added, the 2nd Law of Thermodynamics applies. We will need to remember this for a few upcoming topics.

2 possible arrangements 50 % chance of finding the left empty

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

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

Spontaneity Imagine that you have just flipped a coin 5 times. You would not be too surprised if we got 4 heads and 1 tail. However, if we flipped a coin 5 million times and got a head 4 million times, we would be extremely surprised. We inherently know the math principle called “The Law of Large Numbers”

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

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

For exothermic processes DSsurr is positive. For endothermic processes DSsurr is negative. Consider this process H2O (l) ® H2O (g) DSsys is positive DSsurr is negative DSuniv depends on temperature.

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

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

Gibbs' Free Energy G = H - TS Never used this way. D G = DH – T DS at constant temp. We can algebraically manipulate to get - DG / T = DSuniv If DG is negative at constant T and P, the Process is spontaneous.

Let’s Check For the reaction H2O (s) ® H2O (l) D Sº = 22.1 J / K mol D Hº = 6030 J / mol Calculate DG at 10 ºC and -10 ºC Look at the equation DG = DH –T DS

Solved Problems Calculate DG at 10 ºC and -10 ºC For 10 ºC D G = DH – T DS  6030 – [ 283 x 22.1 ] D G = - 224.3 J The value is negative For -10 ºC D G = DH – T DS  6030 – [ 263 x 22.1 ] D G = + 217.7 J The value is positive

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

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

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

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

Free Energy in Reactions What we have seen and worked with so far deals with systems in their standard states, such as all pressures being 1 atm. We need to be able to calculate the Free Energy of a System ( Δ G) when it isn’t at standard states. Since the conditions are important, we would expect to see Temperature and Concentration included in the calculations.

Free Energy and Pressure DG = DGº +RT ln (Q) where Q is the reaction quotients (P of the products /P of the reactants). CO (g) + 2 H2 (g) ® CH3OH (l) Is the reaction spontaneous at 25 ºC with the H2 pressure of 5.0 atm and the CO pressure of 3.0 atm ? D Gºf CH3OH(l) = - 166 kJ D Gºf CO(g) = -137 kJ DGºf H2(g) = 0 kJ

Solved Problem DG = DGº +RT ln (Q) CO (g) + 2 H2 (g) ® CH3OH (l) Is the reaction spontaneous at 25 ºC with the H2 pressure of 5.0 atm and the CO pressure of 3.0 atm ? (DGº = - 29 kJ according Prod. – Reac.) DG = (-29 kJ) +[ (8.314)(298) ln (1/((52)(3)))] DG = - 39.7 kJ This is more negative than the original. The reaction is more spontaneous than under the original conditions.

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

DGº K =0 =1 <0 >0 >0 <0

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

Free energy And Work Free energy is that energy free to do work. The maximum amount of work possible at a given temperature and pressure. 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.