Chemical Processes. Transport Processes in the Environment. Transport Processes. Advection. Advection. t 1 t 2

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1 hemical Processes by Stefan Trapp (taken from course 4) Transport Processes in the Environment a definition of our nomenklatura Transport Processes Only 3 types of transport processes exist ) by advection ) by molecular diffusion 3) by dispersion Advection: movement in x-direction Diffusion: random movement of molecules in x,y,zdirection Dispersion: random movement with medium in x,y,z-direction. Advection ovement with flow in x-direction Advection Flow in/out a well-mixed compartment gives a linear differential equation.8.4 t t t Effect of advection alone inflow dm/ = + Q * in units: mg/d = m 3 /d x mg/m 3 mixing gives dm Qin Q outflow dm/ = - Q * Q Q in I / V k V V units: = mg/m 3, t = d, Q = m 3 /d, V = m 3, I = mg/d, k = /d

2 Diffusion - between compartments = st Fick s Law - across boundaries = st Fick s Law Fick's st Law of Diffusion ixing between two "well-mixed compartments" separated by a boundary (film, layer) of thickness Dx - within a medium (water, air) = nd Fick s Law (not our topic today) Dx dm D ( ) Dx Fick s st Law of Diffusion the Equation The diffusion coefficient D ass flux Area * oefficient = * oncentration gradient per time Diffusion length dm D ( ) Dx kg/s = m *(m s - m - ) * kg m -3 ok! A D ( ) V Dx D is a function of viscosity, temperature and molecule size D is much faster in gases than in liquids D (oxygen in water) =.78 x -4 m d - at standard conditions D (H O in air) =. m d - (about times faster) m mass (kg) A = Area (m ) D = Diffusion coefficient (m /s) Dx = diffusion length D= - = oncentration gradient Di D j j i Estimation of an unknown diffusion coefficient Permeability P dm D D P D Dx P is Permeability, unit is m / s so it is a velocity (synonym exchange velocity; conductivity; conductance: mass transfer coefficient) /P = r = resistance (s/m) Resistances in series r total = r + r r n Resistances in parallel P total = g + g g n From Fick s st Law of Diffusion to rate k dm D D Dx with = m/v Units: A D k V Dx D A D D V Dx A = m ; V = m 3 ; A/V = m - = depth of the water D = m s - ; /Dx = m - m m -3 m s - m - = s - = rate k s (rates always have the unit per time )

3 Partition coefficient K = oncentration ratio in phase equilibrium Diffusion between two different phases Diffusion stops when concentration ratio is at equilibrium K ij = i / j K is partition coefficent (kg/m 3 to kg/m 3 = m 3 :m 3 ) is equilibrium concentration (kg/m 3 ) i and j are indices of phases K AW Partition coefficient between Air and Water K OW Partition coefficient between Octanol and Water K O Partition coefficient between Organic arbon and Water Dx dm D ( / K ) Gradient = when *K = Dx Partition coefficient K is endpoint of diffusion Reaction Processes Reaction Processes We consider the reaction B + A where (mg/l) is our target compound. We wish to know the rate by which vanishes. Reaction Type : Zero order Reaction Type : Zero order - in each time interval, the same number of white molecules react - the reaction velocity is constant const. K unit of rate K: mg L - d const. K This is called "zero order" because K Examples: alcohol in blood; many (biological) reactions at high dose 3

4 Reaction Type : First order Reaction Type : First order - the more white molecules, the more molecules react - the reaction velocity is proportional to unit of rate k: d - This is called "first order" because Exponential decay Examples: most chemical reactions, radio-active decay Reaction Type 3: Second order - the more white molecules, the more molecules react - the more black molecules B, the more molecules react - the reaction velocity is proportional to and B * B unit of rate k*: mg - L d - This is called "second order" because, if B = then * * k Reaction Type 3: Second order * B Similar to exponential decay, but stops when B gets low Examples: some chemical reactions B Pseudo-first order Often, in the nd order reaction, one reaction partner is known or quasi-constant. * B with B = constant or known or controlled where k k * B This is a pseudo-first order" reaction, because a second order reaction is handled as a first order. Enzymatic Reaction We consider the reaction E + E A where (mg/l) is our target compound, E is enzyme. We wish to know the rate by which vanishes. 4

5 Substrate (mg/l) Substrate (mg/l) The amount of enzymes is fixed, thus If E << then E is limiting (case ) and the reaction rate is constant const. K If E >> then is limiting, and case applies (proportional to ) 3 Overall, this gives v v K "ichaelis-enten enzyme kinetics" etabolism kinetics by enzymes ichaelis-enten kinetics dm v v K (kg) is the mass of the enzymes or of the organism. where v is the reaction velocity (mg L - s - ) and K is the half-saturation constant (mg L - ) ichaelis-enten enzyme kinetics K v K "first order", exponential v K K v "zero order", linear Questions? low 4 6 (d) (d) high 5