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A quote of the week (or camel of the week): Minds are like parachutes – they only function when open Thomas Dewar Physical Chemistry EPM/04 1 Entropy and reaction spontaneity Back to the II law ot thermodynamics A spontaneous change is accompanied by an increase in the total entropy of the system and its surroundings. ∆stot = ∆ssys + ∆ssur = ∆ssys − ∆h Tsur ∆stot > 0 ∆stot = 0 ∆stot < 0 spontaneous equilibrium externally driven Physical Chemistry EPM/04 2 Gibbs free energy ∆Stot = ∆S − ∆H T − T∆Stot = ∆H − T∆S ∆G = ∆H − T ∆S ∆G < 0 ∆G = 0 ∆G > 0 spontaneous equilibrium externally driven forced spontaneous in reversed direction Physical Chemistry EPM/04 3 Gibbs free energy (2) reaction ∆S spontaneous exothermic >0 always exothermic ≤0 |T∆S|<|∆H| endothermic >0 |T∆S|>|∆H| endothermic ≤0 never ∆G = ∆H − T ∆S Physical Chemistry EPM/04 4 Gibbs free energy (3) The standard reaction free energy ∆G0 is the difference between the free energies of formation of the products and the reactants (all in their standard states). n n i =1 i =1 ∆Gr0, 298 = ∑ ni ∆Gi0, f , pr , 298 − ∑ ni ∆Gi0, f ,re , 298 The standard free energy of formation, ∆G0f , of a compound is the standard reaction free energy per mole for its synthesis from elements in their most stable forms. Standard free energies of elements in their most stable forms are equal to zero at 298K. Physical Chemistry EPM/04 5 Gibbs free energy (4) Physical Chemistry EPM/04 6 Gibbs free energy (5) Physical Chemistry EPM/04 7 Gibbs free energy (6) Physical Chemistry EPM/04 8 Chemical equilibrium ∆G = ∆G 0 + RT ln Q For reaction: aA + bB + ... = mM + nN + ... reaction quotient Q is defined as: Q= aMm ⋅ aNn a Aa ⋅ aBb where: a means activity of the reactant or product indicated. Physical Chemistry EPM/04 9 Chemical equilibrium (2) Q= aMm ⋅ aNn a Aa ⋅ aBb Activity: • for liquids and solids in pure form a=1 • for gases ai=Pi/P0 • for solutions ai=fi·ci, where c is concentration and f is activity coefficient. For perfect solutions f=1. For real solutions f→1 when c→0. Standard state for compounds in solutions is when a=1. Physical Chemistry EPM/04 10 Chemical equilibrium (3) ∆G = ∆G 0 + RT ln Q At equilibrium: ∆G 0 = − RT ln K ∆G = 0 K = Qeq = m n aeqM ⋅ aeqN a b aeqA ⋅ aeqB K is known as the reaction equilibrium constant. It is reaction specific and depends on temperature only. (Guldberg–Waage law). Physical Chemistry EPM/04 11 Chemical equilibrium (4) ∆G = ∆G 0 + RT ln Q At standard conditions: Q = 1; ln Q = 0 ∆G = ∆G 0 One can say, that the reaction quotient term in the top equation represents the deviation in Gibbs free energy from the standard state. Standard Gibbs free energy is reaction characteristic, while the second term depends on composition of the reaction mixture. Physical Chemistry EPM/04 12 Conclusions from the Guldberg-Waage law K = Qeq = m n aeqM ⋅ aeqN a b aeqA ⋅ aeqB If, in the reaction mixture of a reaction at equilibrium, one increases activities (concentrations, pressures) of the reactants, the reaction will move to the right (toward products), reducing the denominator and increasing the numerator to maintain the constancy of K; If one increases activities of the products of the reaction being at equilibrium, the reaction will move to the left. If one reduces activities of the reactants ... If one reduces activities of the products ... Physical Chemistry EPM/04 13 Le Chatelier principle If a system, containing a chemical reaction at equilibrium, is subject to an external factor (P, T) disrupting this equilibrium, the system reacts in a way leading to minimalization of this external factor. Temperature: increase in temperature shifts the equilibrium of exothermic reaction to the left, while that of endothermic reactions – to the right. Pressure can influence state of equlibrium only in reactions leading to change in number of moles of gaseous substances. Physical Chemistry EPM/04 14 Le Chatelier principle (2) Influence of pressure upon a dissociation in the gas phase: A 2B The principle says: in reactions leding to increase in number of moles of gaseous substances, increase in pressure shifts the equilibrium to the left, while decrease – to the right. initial state, Pi external change, P2>Pi Physical Chemistry EPM/04 system response, P2>Pf>Pi 15