5.111 Lecture Summary #19

5.111 Lecture Summary #19 CHEMICAL EQUILIBRIUM (Chapter 9 Section 9.0-9.9) Topics Nature of Chemical Equilibrium Meaning of K Relationship between Equilibrium Expressions External Effects on K 19.1 Chemical reactions reach a state of dynamic equilibrium in which the rates of forward and reverse reactions are equal and there is no net change in composition. Consider: N2(g) + 3H2(g) 2NH3(g) ∆G° = -32.90 kJ/mol conc time When the reaction mixture has not produced enough products to have reached equilibrium, the spontaneous direction of change is toward more products (∆Gforward reaction ___ 0). When excess products are present (ex. pure ammonia), the reverse reaction is spontaneous (∆Gforward reaction ______ 0). ∆G > 0 ∆G < 0 Free energy, G ∆G = 0 Pure reactants Pure products Progress of reaction 19.2 The reaction free energy (∆G) changes as the proportion of reactants and products change. To find out how ∆G changes with composition of reactants and products, we need to know how the molar free energy of each substance varies with its partial pressure (if gas), or with its concentration (if solute). ∆G = ∆G° + RT ln Q Where ∆G = reaction free energy at any definite, fixed composition of the reaction mixture. ∆G° = is the difference in molar free energy of the products and reactants in their standard states. R = universal gas constant, T = Temperature, and Q = reaction quotient For aA + bB cC + dD in gaseous phase !G = !G° + RT ln in solution (PC/Pref)c (PD/Pref)d !G = !G° + RT ln ([A]/Cref)a ([B]/Cref)b (PA/Pref)a (PB/Pref)b Q Pref = 1 bar ([C]/Cref)c ([D]/Cref)d Cref = 1 M and [C] in M Q Q = [C]c [D]d Q = PCc PDd [A]a [B]b PAa PBb At equilibrium ∆G = 0 and Q = K (the equilibrium constant), 0 = ∆G° + RT ln K ∆G° = -RT ln K K = is the equilibrium constant. It has the same form as Q, but only uses the amounts of products and reactants at equilibrium. K= [C]c [D]d PCc PDd PAa K = PBb eq. [A]a [B]b eq. ______ We can rewrite ∆G = ∆G° + RT ln Q as ∆G = -RT ln K + RT ln Q or ∆G = RT ln (Q/K) 19.3 Relationship between K and Q: If Q < K, ∆G is ___________ and the forward reaction will occur If Q > K, ∆G is ___________and the reverse reaction will occur Example: N2(g) + 3H2(g) 2NH3(g) If K=1.9 x 10-4 at 400°C, and PN2 = 5.5 bar PH2=2.2 bar PNH3 = 1.1 bar at 400°C, which direction will the reaction go? Q= WHAT DOES K TELL US? K tells us about the mixture of products and reactants at equilibrium, whether we can expect high or low concentration of products at equilibrium. when K > 1, __________ products when K < 1, _________ products For K >1 2NO2 N2O4 ∆G° = -4.76 kJ/mol and K = 6.84 at 298 K partial pressures Start with 1.000 bar of NO2 (reactant) and no N2O4 (product) so Q < K and ∆G < 0, and the reaction goes forward N2O4 NO2 time 19.4 2NO2 1.000 initial partial pressure (bar) change partial pressure equilibrium partial pressure N2O4 0 +X +X K= For K >1, more products at equilibrium. Large K results from very spontaneous reaction (very negative ∆G°) Relationship between ∆G° and the magnitude of K: rewrite ∆G° = -RT ln K as K = exp [-∆G° / RT] K is large if ∆G° is ??? Relationship among equilibrium expressions If the equilibrium constant for the overall reaction can be written as the sum of two or more chemical equations, the equilibrium constant for the overall reaction is the product of the equilibrium constant for the component reactions. 2P (g) + 3Cl2 (g) 2 PCl3 (g) K1 PCl3 (g) + Cl2 (g) PCl5 (g) K2 2P (g) + 5 Cl2 (g) 2PCl5 (g) K3 K3 = When a balanced equation is multiplied by a constant factor, K is raised to the power of that constant factor. 19.5 EXTERNAL EFFECTS ON K Principle of Le Châtelier: A system in equilibrium that is subjected to stress will react in a way that tends to minimize the effect of the stress. Le Châtelier's principle provides a way to predict qualitatively the direction of change of a system under an external perturbation. ADDING AND REMOVING REAGENTS N2(g) + 3H2(g) 2NH3(g) H2 molar conc add more H2 H2 add more NH3 N2 NH3 N2 NH3 time 1) ADDING MORE REACTANT If you are at equilibrium and then add more hydrogen, according to Le Châtelier's principle, the system will tend to minimize the increase in the number of hydrogen molecules. Reaction shifts to the right toward product. This can be explained in terms of Q and K. When reactants are added, Q falls below K momentarily, because the reactant concentration term appears in the denominator. Q = [products]/[reactants] K= {[products]/[reactant]} equilibrium With QK, reaction goes toward reactants (reaction proceeds in the reverse direction). 3) REMOVING PRODUCT What happens?