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PFRPFR
dt
dNdVrFF AA
V
AA 0
Steady state
This is the integral form. Often the differential form is more useful. Take the derivative with respect to volume of each term.
Rate of ReactionRate of Reaction
rate = amount/(time x “volume”)rate = amount/(time x “volume”)
amount [=] mol, gamount [=] mol, g
time [=] s, min, htime [=] s, min, h
““volume” [=] L (dmvolume” [=] L (dm33), kg cat, m), kg cat, m22 cat cat
rrAA = mol/s/L = mol/s/L
rrAA’ = mol/s/g’ = mol/s/g
rrAA” = mol/s/m” = mol/s/m22
Generic ReactionGeneric ReactionaA + bB aA + bB cC + dD cC + dD
Elementary (irreversible) Elementary (irreversible)
-r-rAA = k C = k CAAaa C CBB
bb
Elementary (reversible) Elementary (reversible)
-r-rAA = k = kff C CAAaa C CBB
b b – k– krr C CCCcc C CDD
dd
Generic ReactionGeneric ReactionaA + bB aA + bB cC + dD cC + dD
11stst Order -r Order -rA A = k C= k CAA
22ndnd Order -r Order -rAA = k C = k CAA22
Power Law -rPower Law -rAA = C = CAA C CBB
Complex -rComplex -rA A = k= k11 C CAA/(1+k/(1+k2 2 CCAA))
So how do we know? So how do we know?
Experiment!Experiment!
Generic ReactionGeneric ReactionaA + bB aA + bB cC + dD cC + dD
Assume experiment shows reaction is Assume experiment shows reaction is elementary and irreversible: elementary and irreversible:
-r-rAA = k C = k CAAaa C CBB
bb
Now, rewrite the stoichiometric equation:Now, rewrite the stoichiometric equation:
A + (b/a)B A + (b/a)B (c/a)C + (d/a)D (c/a)C + (d/a)D
What is rate law?What is rate law?
So what about the rate So what about the rate constant?constant?
Arrhenius EquationArrhenius Equation
k = A exp(-Ea/RT)k = A exp(-Ea/RT)
ln k = ln A – ln k = ln A – Ea/RTEa/RT
m = -Ea/RT
Y = b + mX
Y = ln k
X = 1/T
Firefly Flashing Firefly Flashing FrequencyFrequency
T (T (ooC)C) 2121 2525 3030
FlasheFlashes/ mins/ min
9.09.0 12.1612.16 16.216.2