Thermodynamics 2: Gibbs Free Energy and Equilibrium Reading: Moore chapter 18, sections 18.6-18.11 Questions for Review and Thought: 62, 69, 71, 73, 78, 83, 99, 102. Key Concepts and skills: definitions of Gibbs Free Energy (ΔG), Equilibrium constant (K eq ), Reaction Quotient (Q), Standard State Gibbs Free Energy (ΔG ) Review the methods of calculation of ΔG, the prediction of reaction spontaneity from the sign of ΔG, Prediction of the effect of temperature on reaction direction, the relation between ΔG and the equilibrium constant (K) and reaction quotient (Q). Understand the following concepts: 1.) the relation between ΔG and work; 2.) how coupling reactions can make practical use of Gibbs energy work, and 3.) the distinction between thermodynamic stability and kinetic stability. Lecture Topics: Review: Prediction of reaction spontaneity: ΔS universe >0 reaction spontaneous in forward direction ΔS universe =0 reaction at equilibrium (a reversible process) ΔS universe <0 reaction spontaneous in the reverse direction Useful to define reaction spontaneity by considering properties of the system only: New parameter: ΔG system = -TΔS universe Thus, ΔG system = ΔH system -TΔS system Under standard state conditions, ΔG system = ΔH system -TΔS system (1 atm pressure or 1M concentrations) Definitions The Gibbs Free Energy (G) of a substance measures a molecule s inherent likelihood or potential to undergo a change or reaction. In general, at constant T and P, when ΔG system < 0, the process/reaction is spontaneous in the forward direction when ΔG system = 0, the process/reaction is in equilibrium/ reversible when ΔG system > 0, the process/reaction is spontaneous in the reverse direction The Gibbs energy of a substance depends on its temperature, pressure, phase, and concentration. Gibbs energy changes for chemical reactions are often compared under a welldefined set of standard-state conditions (ΔG rxtn ): 1 atm gases and solutes at 1M concentation. ΔG rxtn values are computed using tabulated ΔG f values for all reactants and products: ΔG rctn = Σ[(moles of product)* ΔG f product ] - Σ[(moles of reactant)* ΔG f reactant]
as for ΔH f, ΔG f = 0 for an element in its standard state. Chemical equations can be added together, with their ΔG f values combined. Effect of Temperature on ΔG Values of ΔG rxn calculated from Appendix J are accurate only at 298 K. Values of ΔG rxn can be estimated for reactions at other temperatures and at P=1atm using ΔG = ΔH -TΔS and tables of standard entropies and enthalpies of formation. The estimates will be close to the true values if it is assumed ΔH and ΔS are not strongly dependent on T. The value of ΔG depends strongly on T. There exists a special temperature T * defined by: T* = ΔH / ΔS at which ΔG =0 If both ΔH and ΔS are positive, the reaction will be spontaneous at temperatures higher than T If both ΔH and ΔS are negative, the reaction will be spontaneous at temperatures lower than T. Effects of Concentration on ΔG(for non-standard conditions) For the reaction: a A + b B > cc + dd where Q= [A] a [B] b /[C] c [D] d From the empirical study of the effects of concentration on G, it has been found that ΔG = ΔG + RT ln Q For standard conditions (concentrations of all reactants and products 1mol/L or 1 atm) Q=1 and ΔG = ΔG. When ΔG=0, the reaction is at equilibrium (there is no tendency for the reaction to occur in either the forward or revese direction), thus ΔG = -RT ln K where K is the thermodynamic equilibrium constant for the reaction at a specific temperature T: d Q (at equilibrium) =K=[A] eqa [B] eqb /[C] eqc [D] eq = e -ΔG /RT Combining the above equations gives the simple result: ΔG = RT lnq/k When Q>K, ΔG>0, forward reaction is non-spontaneous When Q<K, ΔG<0, forward reaction is spontaneous When Q=K, ΔG=0, the reaction is at equilibrium. (Dependence of K on temperature: Since -RT ln K= ΔG =ΔH -TΔS ; lnk = -ΔH /RT+ΔS /R A plot of K vs. 1/T gives straight line with slope = -ΔH /R and intercept ΔS /R Furthermore: lnk 2 /K 1 = -ΔH /R [1/T 2 1/T 1 ] ) ΔG and Work; Coupling reactions For ΔG >0, ΔG represents the minimum amount of work that must be done to force a reactant-favored process to produce products. For ΔG <0, ΔG represents the maximum amount of useful work that can be done by a product-favoring system on its surroundings. Example: C 8 H 18 (l)+ 25/2 O 2 (g) > 8 CO 2 (g) + 9 H 2 O (l) ΔG = -5295 kj Part of the Free energy given off in this combustion powers the motion of the automobile
The useful work can also be used to drive a reactant-favored process in the reverse product-favored direction. Example: Coupling processes for the reduction of iron ore: 2Al(s) + 3/2O 2 (g) > Al 2 O 3 (s) ΔG = -1582 kj Fe 2 O 3 (s) > 2 Fe(s) + 3/2O 2 (g) ΔG = 742 kj Net: 2Al (s) + Fe 2 O 3 (s) > 2 Fe(s) + Al 2 O 3 (s) ΔG = -840 kj (a favored reaction) Thermodynamic/Kinetic stability E a1 E a2 Consider the following process : P1 < SM > P2 Where for SM >P1 ΔG= -50kJ/mol And SM > P2 ΔG= -150kJ/mol E a1 <E a2 A Chemical process at low temperature is under kinetic control if it leads preferentially to the less thermodynamically stable product P1 The same chemical process at high temperature is under thermodynamic control if it leads preferentially to the more thermodynamically stable product P2.
Problems Set #4 1. Decide if each of the following statements are true or false. If false, correct the statement to make it a valid assertion: (a) Reactions with a positive ΔH rxn and a positive ΔS rxn can never be spontaneous (b) At absolute zero (0 K) an endothermic reaction is never spontaneous (c) A reaction with a negative Gibbs energy change is predicted to be spontaneous with a rapid transformation of reactants to products (d) The entropy of a substance increases from the liquid to the vapor state (e) When ΔG is positive for a reaction, the reaction cannot take place. 2. The oxidation of SO 2 (g) is too slow at 298K to be useful in the manufacture of sulfuric acid, so the process is conducted at an elevated temperature (973K) to produce product at a faster rate: 2 SO 2 (g) + O 2 (g) <-> 2SO 3 (g) (a) Given one mole of each of the starting materials and sufficient time, at what temperature would you obtain the greater amount of SO 3 (g), 298K or 973K? Use thermodynamic data from Appendix J in support of your answer. (b) What is the equilibrium constant for the reaction at 298K and at 973K, assuming a temperature-independent enthalpy and entropy of reaction? (c) In experiments to determine the effect of temperature on reaction spontaneity, sealed containers are filled with 0.50 atm SO 2, 0.010 atm O 2, and 0.20 atm SO 3 and kept at 298K and 973K, respectively. By calculating ΔG system at each temperature, determine in which direction the reaction will proceed to reach equilibrium at each temperature 3. At 25 C and 1 atm, the following reactions are NOT spontaneous in the forward direction. Indicate whether an INCREASE, a DECREASE, or NOT POSSIBLE CHANGE IN TEMPERATURE will make the forward reaction spontaneous at constant T and P. (a) Br 2 (liq) Br 2 (g) (b) 2 NO 2 (g) N 2 O 4 (g) (c) CdS(s) Cd(s) + S(s) 4. One promising method of making coal a cleaner fuel involves the conversion of coal to methane. One such scheme follows: (1) C (s) + H 2 O (g) CO(g) + H 2 (g) (2) CO (g) + H 2 O (g) CO 2 (g) + H 2 (g) (3) CO (g) + 3 H 2 (g) CH 4 (g) + H 2 O (g) (a) For each of the three reactions, calculate ΔH, ΔS, and ΔG at 298K and 1atm. (b) Over what temperature ranges will each of these reactions be spontaneous? (c) Write the equation for the overall reaction, with the net equation consuming the intermediate CO (you need to carry out step 1 twice for this to occur) (d) What is the Enthalpy and Gibbs Free Energy change for the overall (net) reaction? Is this reaction spontaneous at 298K? If not, over what temperature range will it be spontaneous. Do you think this will be a practical process?
5. For the melting of one mole of ice at 10 C and 1 atm, what is the sign of each quantity below? Assume that the density of ice is less than that of liquid water at 10 C. Provide a brief explanation of your responses. >0 =0 <0 Can t tell ΔE ΔV ΔT ΔP q w ΔS sys ΔS surr ΔH sys ΔS universe ΔG sys Remember: q p =ΔH sys, and w irrev =-P ext ΔV Note the enthalpy of fusion (melting) of water is 6 kj/mol Bonus: 6. For the dimerization reaction 2NO 2 (g) N 2 O 4 (g), use the data below to graphically determine ΔH rxtn and ΔS rxtn (assume that both ΔH rxtn and ΔS rxtn are temperature independent): T (K) 282.2 293.2 298.2 306.2 325.2 333.2 343.2 K eq 33.2 13.1 8.79 4.77 1.26 0.751 0.408