Chemical Thermodynamics: Entropy, Free Energy and Equilibrium Chapter 16

Chemical Thermodynamics Science of interconversion of energy Heat into other forms of energy Amount of heat gained/released from a system Spontaneity of a reaction Gibbs free energy function Relationship between Gibbs Free Energy and chemical equilibrium

Spontaneous Processes Main objective Spontaneous Reaction- a reaction does occur under specific conditions Non-spontaneous Reaction- a reaction does not occur under specific conditions Main objective of thermodynamics is to be able to determine if a reaction will occur when reactants are brought together under certain conditions.

Spontaneous Processes A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0ºC and ice melts above 0ºC Heat flows from a hotter object to a colder object Iron exposed to oxygen and water forms rust

Spontaneous Processes Which is spontaneous? Be logical. When it comes down to reactions that cant be seen with the naked eye, we have to look at the properties of the reactions. Enthalpy, which is a measure of the heat in the system may be able to help determine the spontaneity of a reaction.

Spontaneous Processes Does a decrease in enthalpy mean a reaction proceeds spontaneously? Spontaneous reactions CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l) DH0 = -890.4 kJ H+ (aq) + OH- (aq) H2O (l) DH0 = -56.2 kJ The first two reactions have low enthalpy values and the second two have slighlty positive values. Cannot rely on enthalpy because it does not guarantee a correct prediction of spontaneity. It allows us to recognize that most exothermic reactions are spontaneous, and that most endothermic reactions are nonsponstaneous. It is not a guarantee. We have to look at another thermodynamic quantity to make an accurate prediction. This is entropy. H2O (s) H2O (l) DH0 = 6.01 kJ NH4NO3 (s) NH4+(aq) + NO3- (aq) DH0 = 25 kJ H2O

Entropy To predict spontaneity we need: Change in enthalpy Entropy Entropy- a measure of the randomness or disorder of a system. ↑ Disorder = ↑ Entropy

Entropy New Deck Order Shuffled Deck Order Probability Ordered state Disordered State To relate entropy to something in real life, think of a deck of cards. When you open a new deck of cards, it is in order from ace to kings and also in order of suits. This deck is highly ordered. When the deck is shuffled, the cards are in a new disrupted order. There are many ways to keep this deck out of order, but only one way for it to stay in its original order. It would be nearly impossible to shuffle the cards in a way to make them appear in their original order. One way to cenceptualize order is in terms of probability. A probable event is one that can happen in many different ways, whlie an improbable event is one that can only happen in one or a few ways. Ordered- low probability of occuring and a small entropy. Disordered- high probability and large entropy.

Entropy and Disorder Sf > Si DS > 0 If the change from initial to final results in an increase in randomness Sf > Si DS > 0 For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state Ssolid < Sliquid << Sgas

Entropy and Disorder To look at the changes in the entropy of the system, we are going to take a look at the changes in the ms of the systems. a.) increase in ms b/c liquid state has more chance for arrangement b.) increase in ms b/c vapor has more room for the molecules to reside in. c.) solute is being surrounded by solution and formation of ions leads to more particles and more chances for arrangement d.) heating increases the entropy b/c it causes the molecules to vibrate and the energies associated with the molecules increases. More molecules can vibrate and more molecules can exsist in higher energy states.

Entropy and Disorder How does the entropy of a system change for each of the following processes? (a) Forming sucrose crystals from a supersaturated solution Randomness decreases Entropy decreases (DS < 0) (b) Heating hydrogen gas from 600C to 800C Randomness increases Entropy increases (DS > 0)

Entropy and Disorder

Standard Entropy The standard entropy of reaction (DS0 ) is the entropy change for a reaction carried out at 1 atm and 250C. rxn Compare s.e. of h2o liquid and h2o gas. Explain.

The Second Law of Thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. Importance? DSuniv = DSsys + DSsurr > 0 Spontaneous process: First Law of Thermodynamics- Energy can be converted to one form or another, but it cannot be created or destroyed. The second law of thermodynamics explains to us the connection between entropy and the spontaneity of a reaction. The universe is made up of a system and its surroundings…..so the total entropy change in the universe = the sum of the entropy changes in the system plus the sum of the entropy changes in the surroundings. For a spontaneous process, the second law says that S univ must be greater than 0. system or surr. Can be negative, no restrictions. For an equilibrium process, the S univ = 0……. S system and S equilibrium must be equal in magnitude and opposite in sign. What does it mean if S univ. is negative? It means that the reaction is spontaneous, but in the opposite direction described. Equilibrium process: DSuniv = DSsys + DSsurr = 0

Entropy Changes in the System To calculate ΔSuniv, we need both ΔSsys ΔSsurr ΔSsys aA + bB cC + dD DS0 rxn nS0(products) = S mS0(reactants) - To calculate the entropy of a system, use the format from the equation above. The standard entropy of the system is equal to the sum of the standard entropy of the products - the sum of the standard entropy of the reactants. m and n represent the stoichiometric coefficients in the reaction. The standard entropy values for reactants and products are in appendix 3. All you have to do is look up the values and plug them into this equation with the proper coefficients.

Entropy Changes in the System

Entropy Changes in the System When gases are produced (or consumed) If a reaction produces more gas molecules than it consumes, DS0 > 0. If the total number of gas molecules diminishes, DS0 < 0. If there is no net change in the total number of gas molecules, then DS0 may be positive or negative BUT DS0 will be a small number.

Entropy Changes in the System

Entropy Changes in the Surroundings These photos demonstrate the change in entropy of surroundings. If a system is exothermic, it is giving off heat to its surroundings. If the surroundings gain heat, that means there are now more molecules present. Since there are more molecules present after the distribution of heat, there are also more possible microstates. An increase in microstates = an increase in entropy. The second photo is of an endothermic reaction. The surroundings are giving off heat and the heat is being absorbed by the system. If the surroundings loose heat, then it is also losing molecules. A decrease in molecules leads to a decrease in microstates, therefore a decrease in entropy. Now how would the temperature of the surroundings affect the entropy? If the surroundings are already at a high temperature, then an exothermic reaction would not result in a large increase in entropy. (molecules are already excited and moving about, so adding a few more does not affect the surroundings much.) If the temperature of the surroundings are very low, then the transfer of heat to the surroundings would lead to a large increase in entropy. Coughing in Restaurant vs. Coughing in Library

Entropy Changes in the Surroundings ΔSsurr = -ΔHsys T Using the information from Example 18.2, determine whether or not the reaction is spontaneous. N2(g) + 3H2(g) → 2 NH3(g) ΔHºrxn = -92.6 kJ/mol ΔSsys = -199 J/K ∙ mol ΔSsurr = -(-92.6 x 1000) J/mol 298 K ΔSsurr = 311 J/mol ΔSuniv = ΔSsys + ΔSsurr ΔSuniv = -199 J/K ∙ mol + 311 J/mol ΔSUNIV = 112 J/K ∙ mol If the s universe is positive, the reaction is spontaneous.

The Third Law of Thermodynamics and Absolute Entropy Third Law of Thermodynamics- the entropy of a perfect crystalline substance is zero at the absolute zero of temperature.

Gibbs Free Energy Predicts the direction of a spontaneous reaction. Uses properties of the system to calculate. For a constant pressure-temperature process: DG = DHsys -TDSsys DG < 0 The reaction is spontaneous in the forward direction. DG > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction. DG = 0 The reaction is at equilibrium.

Standard Free-Energy Changes The standard free-energy of reaction (DG0 ) is the free-energy change for a reaction when it occurs under standard-state conditions. rxn Standard free energy of formation (DG0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. f DG0 rxn nDG0 (products) f = S mDG0 (reactants) -

Standard Free-Energy Changes

Factors Affecting ΔG

Free Energy and Chemical Equilibrium DG = DG0 + RT lnQ R is the gas constant (8.314 J/K•mol) T is the absolute temperature (K) Q is the reaction quotient Delta G is mainly influenced by G0. If G0 is very negative, G will be too. When this happens, the reaction favors the formation of products. According to le chatlier’s principle, RT lnQ will then slowly become positive and equal in magnitude to G. This will cause the reaction to move to equilibrium. This also happens when G is very positive. lnQ will cause the reaction to move towards equilibrium again. K= equilibrium constant At Equilibrium DG = 0 Q = K 0 = DG0 + RT lnK DG0 = - RT lnK

Free Energy and Chemical Equilibrium

Free Energy and Chemical Equilibrium

Free Energy and Chemical Equilibrium

Thermodynamics of a Rubber Band a.) rubber band unstretched. Highly disordered….large # of microstates. High entropy. b.) Stretched rubber band. More ordered. Less # of microstates. Low entropy. When the rubber band is stretched, you can feel a warming effect. Than means that the stretching is nonspontaneous and that the opposite reaction is spontaneous. If you let go of the rubber band, it will automatically fall back into its original form and the band will become cool.