chemical%20equilibria

chemical%20equilibria - Chemical Equilibria Basic concepts...

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Chemical Equilibria Basic concepts • Chemical potential • Standard states – Biochemist standard state • Equilibrium constant – Temperature dependence – Calculation of system composition
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So far, we have dealt with pure substances , where G = G(T, P, n) 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 ji i i Pn Tn i TPn GG G dG dT dP dn TP n ⎛⎞ ∂∂ =++ ⎜⎟ ⎝⎠ i i G n µ Chemical potential: The chemical potential is equivalent to molar Gibbs free energy , i G G n = For a pure substance:
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If we know the chemical potential ( µ 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 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 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: ii i i i dn n dx x dG dn n dx Gd G n d x nd x n µµ = == ⎡⎤ = = ⎢⎥ ⎣⎦ ∑∑ ∫∫ For a mixture i Gn =
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Ideal gas mixtures Recall the dependence of G on P for a pure ideal gas at a constant T: 21 2 1 () l n ( /) GP nRT P P = 0 ( 1 a tm ) l n ( ) 1atm ln( ) P G P RT µµ −= =+ Thus, if we know G(P 1 ) , we can calculate G at any other pressure. Typically, we use 1atm as the standard reference state. For an arbitrary pressure P, we have: This can be extended to an ideal gas (A) in a mixture. Now, the pressure for the gas is its partial pressure. 0 ln( ) A AA P RT Reference state
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Example: calculating G for the mixing of two ideal gases n A , P, T n B , P, T n A ,n B , P, T Constant P, T G mix State 1 State 2 00 (1) ( l n) 1atm AA BB Gn n PP nR T T µ µµ = + ⎛⎞ =+ ++ ⎜⎟ ⎝⎠ (2) ( ln ) ( ) AB Gn R T n R T Before mixing (2) ln ln ln ln 0 mix GG G P P nRT P P x x ∆= − =+< After mixing Thus Implication: Spontaneous process
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Application to chemical reactions Consider a typical chemical reaction a A + b B Æ c C+ d D At constant T, P, for a small change in the system composition ii i dG dn µ = where i indicates A, B, C, or D A special aspect is that dn A , dn B , etc are correlated, based on the stoichiometry of the reaction. They are all related to the extent of reaction ( α ). C AB D dn dn dn dn d ab c d α −= −== ≡ The unit of α is mole, or α [=] mole Thus () (per mole of reaction) = A B C D i ABC D dG dn a b c d d G dG abcd d µµ == + +→ =− + + Note: dG/d α depends on the system composition because each µ i depends on system composition
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Key points 1. We can judge possibility of a process at constant T, P, by the sign of
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chemical%20equilibria - Chemical Equilibria Basic concepts...

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