# Mixing - Mixing Process Analysis Reaction rate is defined...

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1 Mixing: Process Analysis: Reaction rate is defined as v V dM dt r = 1 for a homogeneous reaction, where v r = reaction rate or velocity V = volume M = moles (not concentration) t = time. The number of moles in any volume is M CV = , where C = concentration in M/L V = liters. Then the reaction rate becomes ( ) v V dCV dt r = 1 Usually V is constant in aqueous environmental processes reaction, so v dC dt r = , which can be + or -. Reactions may only occur on the surface (heterogeneous ); then, v A dM dt r S = 1 where A S = surface area. For a reaction: rR pP v V dR dt rr ⟩= 1 v V dP dt rp 1 Since these reactants react on molar basis (concentration): r moles R need p moles P (molar basis): () −= 11 r dR dt p dP dt , which means concentration changes are always: v x dX dt r = 1 , where x = coefficient

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2 X = molar concentration. We have already seen vk C r = , which says the rate of reaction is proportional to the amount of C available to react (First Order). To solve for k: k v C r = , previously v V dM dt r = 1 , so k becomes k CV dM dt = 1 . This is only for first order reaction and k has units or time -1 . Let V= L C = mol L dM dt mol time = 11 1 CV dM dt mol L L mole time = So k = time -1 . Temperature Temperature will affect v r . From EES 4202 (Chemical Processes Control): kA e E RT = , where A = constant E = activation energy R = gas constant T = temperature in Kelvin And () ( ) ln ln E RT =− , which solves:
3 dk E RT E RT E RT dT E RT kk E RT E RT k k ET T RT T k k T T T T ln( ) ( ) ln( ) ln( ) ln( ) ln () =−− = == −= +  = ∫∫ 01 22 2 21 2 1 1 2 1 2 1 2 where E RT T 12 does not vary once T 2 T 1 are defined. Then, kn k k CT T or k k e CT T T T 2 1 2 1 =− = −− or = C' where C’ has been defined as 1.024 for many applications but is sufficient here to make point that a first order k may be determined if a k at one temperature is known and the other temperature is specified. Complete Mix Most reactions in Bio-Environmental Processes are irreversible and modeled as first order : R P v dR dt kt Solves e r kt R=R 0 Mass Balances are required for any process analysis as a f(t): IN = OUT + Changes where changes are typically growth, death, accumulation, etc.

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## This note was uploaded on 01/14/2012 for the course ENV 6015 taught by Professor Taylor during the Fall '11 term at University of Central Florida.

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Mixing - Mixing Process Analysis Reaction rate is defined...

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