Equilibrium Constants Lecture 8 The Equilibrium Constant • Consider the reaction aA + bB = cC + dD • The Free Energy change of reaction is: ∆G = cµc + dµd – aµa – bµb • At equilibrium: ∆ G = ån i µi = 0 • Expanding the right side ån µ + RT ån ln a = 0 i o i i i ån i µi + RT ln Õi a = 0 • or • We define the right term as the equilibrium constant: ni o i K = ln Õ ani i i Free Energy and the Equilibrium Constant o n n µ + RT ln a åi i Õ =0 i i i • Since: o n µ å i = ∆ Gr o i • then • and ∆ Gro - RT lnK = 0 o r ∆ G = -RT lnK • Note of caution: our thermodynamic parameters are additive, but because of the exponential relation between the equilibrium constant and free energy, equilibrium constants are multiplicative. Manipulating Equilibrium Constants • Suppose we want to know the equilibrium constant for a reaction that can be written as the sum of two reactions, o e.g., we can sum Feaq3+ + e+ Fe(OH )2+ aq + H o to yield + Fe(OH )2+ aq + e + H 2+ Feaq Feaq3+ + H 2O 2+ Feaq + H 2O o The equilibrium constant of the net reaction would be the product of the equilibrium constants of the individual reactions. • For this reason and because equilibrium constants can be very large or very small numbers, it is often convenient to work with logs of equilibrium constants: pK = - log K o (we can then sum the pK’s). Apparent Equilibrium Constants and Distribution Coefficient • In practice, other kinds of equilibrium constants are used based on concentrations rather than activities. • Distribution Coefficient K = Õ Xni D i • Apparent Equilibrium K appConstant = Õ min i K app = K eq Kl = K eq n l Õ i i Other Forms • A ‘solubility constant’ is an equilibrium constant. For aq example: aNa aClaq K= + - aNaCls o Since the activity of NaCl in halite = 1, then aq aq K SP = aNa a + Cl - • Henry’s Law constants for describing solubility of gases in solution (e.g., CO2 in water). o Since Pi = hiXi hi = Pi Xi Law of Mass Action • Important to remember our equation K = Õ ani i i describes the equilibrium condition. At non-equilibrium conditions it is called the reaction quotient, Q. • Written for the reaction H2CO3 = HCO3- + H+ K= aHCO- aH + 3 aH 2CO3 • We can see that addition of H+ will drive the reaction to the left. • “Changing the concentration of one species in a reaction in a system at equilibrium will cause a reaction in a direction that minimizes that change”. Le Chatelier’s Principle • We can generalize this to pressure and temperature: dG = VdP - SdT • An increase in pressure will drive a reaction in a direction such as to decrease volume • An increase in temperature will drive a reaction in a direction such as to increase entropy. • “When perturbed, a system reacts to minimize the effects of perturbation.” Temperature and Pressure Dependence • Since ∆G˚ = ∆H˚ - T∆S˚ and ∆G˚ = -RT ln K then ∆ H ro ∆ Sro ln K = + RT R • Temperature and pressure dependencies found by taking derivatives of this equation with respect to T and P. Oxidation and Reduction Oxidation refers to processes in which atoms gain or loss electrons, e.g., Fe2+ Fe3+ Valence and Redox • We define valence as the charge an atom acquires when it is dissolved in solution. • Conventions o o o o Valence of all elements in pure form is 0. Sum of valences much equal actual charge of species Valence of hydrogen is +1 except in metal hydrides when it is -1 Valence of O is -2 except in peroxides when it is -1. • Elements generally function as either electron donors or acceptors. o Metals in 0 valence state are electron donors (become positively charged) o Oxygen is the most common electron acceptor (hence the term oxidation) • Redox o A reduced state can be thought of as one is which the availability of electrons is high o An oxidized state is one in which the availability of electrons is low.