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Unformatted text preview: The Temperature Dependence of K P BACKGROUND: The exact value of K P for a given reaction will depend on the experimental conditions. • It is useful to know what this dependency is so that we can control the point of equilibrium to suit the production requirements. QUESTION: How does K P depend on temperature? ANSWER: Lets take the temperature derivative! Starting from Eq. 4.211 we have dlog e ( K P ) d T = 1 R d Δ G reaction T 1 d T . (4.217) • We can derive an expression for the red term. ∂ GT 1 ∂ T ! P = ∂ G ∂ T P T 1 GT 2 (4.218) = S T T T + H + TS T 2 (4.219) = H T 2 , (4.220) which is known as the GibbsHelmholtz Equation . • So then Eq. 4.217 reads: dlog e ( K P ) d T = + Δ H reaction RT 2 , (4.221) which is called the van’t Hoff Equation . QUESTION: How do we use this to calculate K P ( T ) at a 4–67 nonstandard temperature T 6 = T ? ANSWER: ‹ calculate Δ G reaction and K P ( T ) using tabulated values of Δ G f . › integrate the van’t Hoff Equation by separation of the variables: dlog e ( K P )= Δ H reaction R T 2 d T (4.222) Z K p ( T ) K P ( T ) dlog e ( K P )= Z T T Δ H reaction R T 2 d T (4.223) log e ( K P ( T ) ) log e K p ( T ) = Δ H reaction R h T 1 i T T = Δ H reaction R h T 1 T 1 i , (4.224) where we have assumed that Δ H reaction is temperature independent. • Then we can express K p ( T ) at the higher temperature as a function of the K P ( T ) at standard conditions: log e ( K p ( T ) ) = log e K P ( T ) Δ H reaction R h T 1 T 1 i . (4.225) 4–68 EXAMPLE: (Engel et al.) Dissociation of Chlorine • We place Cl 2 in a temperature controlled chamber under pressure P . Some of the chlorine molecules will dissociate: Cl 2 ( g ) EGGGG GGGGC 2 Cl ( g ) (4.226) QUESTION:...
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This note was uploaded on 12/05/2010 for the course CHBE 251 taught by Professor Scotty during the Winter '09 term at UBC.
 Winter '09
 scotty
 Equilibrium

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