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Modelling Kinetic Reactions in PHREEQC‐2
Modelling Kinetic Reactions in PHREEQC‐2
Equilibrium or kinetic reactions?
• When a reaction is reversible and the rate is fast compared to residence time equilibrium descriptionq p
• When a reaction is irreversible, OR it’s reaction rate is slower than the residence time kinetic description
• Partial Equilibrium ‐ system where some reactions q yfast, others are slow – sound familiar?hybrid kinetic and equilibrium reactions
Time Scales
Reactions and Kinetics
• Elementary reactions are those that represent the EXACT reaction, there are NO steps between productEXACT reaction, there are NO steps between product and reactant in between what is represented.
• Overall reactions represent the beginning reactants and final products, but do NOT include one or more steps in between.
FeS2 + 3.5 O2 + H2O Fe2+ + 2 SO42‐ + 2 H+
2 NaAlSi3O8 + 9 H2O + 2 H+
Al Si O (OH) + 2 Na+ + 4 H SiOAl2Si2O5(OH)4 + 2 Na+ + 4 H4SiO4
Rate Law
• For any reaction: A B• We can write the general rate law:
nAkdtAd
)()(
dt
Order of reaction
Rate Constant
Rate = change in concentration of A with time, t Concentration of A
Reaction Order
• Reaction order is tied to the reaction ONLY for l t tielementary reactions
• The molecularity of an elementary reaction is determined by the number of reacting species: mostly uni‐ or bi‐molecular reactions
• Overall reactions need not have integral reaction orders (fractional orders are common – fitting parameters)
Some Common Rate Laws
Reaction Rate Law Integrated Units for kOrder Rate Law Rate Law Units for k
Ad ][0 A=A0‐kt mol/cm3 s
Ad ][
kdtAd
][
1 ln A=lnA0‐kt s‐1kAdtAd
][
2 cm3/mol sktAA
0
112][
kAdtAd
0dt
• Zeroth orderZeroth order Rate is constant with concentration
• First & second orderRate changes as a f ti ffunction of concentration
Zero Order
kAd
][
kdt
• Rate independent of reactant or product concentrations.Di l i f i l• Dissolution of quartz is an example:
SiO2(qtz) + 2 H2O H4SiO4(aq)
log k‐ (s‐1) = 0.707 – 2598/T
First Order
kAdtAd
][
• Rate is dependent on concentration of a reactant or product.
dt
product.• Pyrite oxidation, sulfate reduction are examples
Second Order
• Rate is dependent on two reactants or products
• Fe2+ oxidation:Fe2+ + ¼ O2 + H+ Fe3+ + ½ H2O
2][
][ 22
OPFekdtFed
dt
Consecutive (Chain) Reactions
A B CA B Ck1 k2
][AdReaction sequence: (k1≈k2) ][
][][
1
Bd
AkdtAd
( 1 2)
][
][][][
21 BkAkdtBd
][][
2 BkdtCd
Bacterial Growth and Decay
XCC
vv eaorg XCKCK
vveaeaorgorg
m max
vYt
Xmx
growth
Xvt
Xt
decaydecay
tX
tX
tXt
decaygrowth
ttt
Toluene Biodegradation
SHNOHCHCO
HOHSONHHC
22753
224487
15.414.030.6
86.158.215.414.0
SHNOHCHCO 22753 15.414.030.6
mgrowth vt
X14.0
