Chemical Equilibrium

# Chemical Equilibrium - BME100L:Topic4 FreeEnergyand...

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1 BME 100L: Topic 4 Free Energy and Chemical Equilibria Chemical Equilibria Basic concepts y Chemical potential y Standard states y Biochemist standard state y Equilibrium constant y Temperature dependence y Calculation of system composition

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2 Partial Derivatives V = V (P,T) V is a function of P & T OR constant) (P P nR dT dV = = For an ideal gas V = V(P, T) = nRT/P How does V change with T? constant) (T 1 Similarly, T V d nRT dV P nRT V P nR P = = = = V P = 1 P = 2 2 2 P V OR P nRT P nRT dP dV P dP dP T = = T P = 4 Chemical Potential For a mixture of n A moles A, n B moles B, etc. A n n P T A C B μ ... , , , n G (Chemical potential) μ A is the change in Gibbs free energy that occurs upon an infinitesimal change (dn A ) in the number of moles of A while ) in the number of moles of A while keeping T, P, and moles of all other components constant This is a compound’s chemical potential in a chemical reaction, just like the height of substance determines its potential energy in a gravitational field.
3 So far, we have dealt with pure substances , where G = G(T, P, n) Intuitively with a mixture G would also depend on composition Chemical Potential Intuitively, with a mixture, G would also depend on composition of the mixture: G = G(T, P, n 1 , n 2 , …, n k ) where n i is the mole number of component i . ,, ii i i Pn Tn i TPn GG G dG dT dP dn TP n ⎛⎞ ∂∂ =++ ⎜⎟ ⎝⎠ j i Chemical potential: ji i i G n μ For a pure substance: , i G G n = The chemical potential is equivalent to molar Gibbs free energy If we know the chemical potential ( i ) for each constituent species in a mixture, what’s the total Gibbs free energy? To address this question, let’s consider a hypothetic process where the mixture is generated from nothing. n 1 , n 2 , n 3 , … Almost nothing mixture Then the question becomes: what’s Δ G for this “creation” process? Since G is a state variable, it doesn’t matter which path we choose to accomplish the creation process. In particular, we can choose a path we add each species incrementally, where each increment is proportional to the species’ final mole number Thus the concentration of each increment is proportional to the species final mole number. Thus the concentration of each remains the same throughout the process. This way, the chemical potential of each component will also remain a constant! Therefore: ( ) 11 00 if ; where varies from 0 to 1 Thus: i i i dn n dx x dG dn n dx Gd G n d x nd x n μμ = == ⎡⎤ = = ⎢⎥ ⎣⎦ ∑∑ ∫∫ i Gn = For a mixture

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4 Ideal gas mixtures 21 2 1 () () l n (/) GP nRT P P = Recall the dependence of G on P for a pure ideal gas at a constant T 0 () ( 1 a tm ) l n ( ) 1atm ln( ) P GP G nRT P RT μμ −= =+ constant T: Thus, if we know G(P 1 ) , we can calculate G at any other pressure.
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## This note was uploaded on 04/21/2011 for the course BME 100 taught by Professor Yuan during the Spring '07 term at Duke.

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Chemical Equilibrium - BME100L:Topic4 FreeEnergyand...

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