KINETICS OF CHEMICAL REACTIONS

1
KINETICS OF CHEMICAL REACTIONS
2
Kinetics

• Rate of reaction
• Time dependency of a reaction
• relation between concentration and time

3
Kinetics of a chemical reaction

• kf
• aA bB cC dD
• kb
• 6 unknowns, need to simplify

4

• Ass
• If
• B gtgt A
• B not limiting
• kb ltlt kf

5

• Apply in practice not theoretically true.
• Assumptions
• Backward reaction is negligible
• Other reaction species are not limiting
• Reaction conditions are constant pH, T, aw,
  redox potential, concentration of other species
• Therefore, k is a pseudo rate constant particular
  for a given food system.

6
Reaction order

• n 0 A Ao kt
• B Bo kt
• n 1 ln A/Ao - kt
• A Ao e-kt B Bo
  ekt

7
(No Transcript)
8
(No Transcript)
9
Units are different, cannot compare.
10
Half-life time for decrease in quality by
50 If n 1
11
Order determination

• Method of differentiation

ln dA dt
slopen
lnA
12

• 2. Method of integration
• Assume order n 0 or 1 or 2
• Integrate rate equation, plot equation
• Evaluate the fit of linear line

13

• 3. When n ? 1

14
Microbial growth
N number of microorganisms kG growth rate
constant
15
G time for one doubling DG time for 1 log cycle
increase in number of microorganisms G is
determined from the log phase of growth
16

• Accurate data ? accurate k ? need to measure over
  50 change in reactant species.
• but in foods 20-30 change is enough for quality
  degradation, can use simple zero order kinetics
• s std. dev.
• mean value.

17

• Reaction order for some common reactions in foods
• n 0 enzymatic degradation, lipid oxidation, NEB
  
• n 1 microbial growth, rancidity
• n 2 vitamin C loss
• For shelf life study
• Need to determine
• Criteria to be measured
• Environmental conditions affect the reaction
  rates
• T, RH

18
Temperature effect

• Activation energy
• Arrhenius relation
• ko Arrhenius equation constant
• Ea Activation energy (cal/mol) excess energy
  barrier to over come
• R universal gas constant (1.9872 cal/mol K)
• T absolute temperature, K

19

• Important points
• Mode of deterioration changes with temperature
• Need to have more than two temperatures to obtain
  reliable results
•  
• Activation energies for some degradation
  reactions (kcal/mol)
• Hydrolysis 10-20
• Lipid oxidation 15-25
• NEB 20-40
• Enzymatic or microbial degradation 50-150

20
Temperature effect

• Q10 value
• measure of sensitivity to temperature

21

• Q10
• 1.5-2 sensory quality loss in canned foods
• 1.5-3 rancidity
• 4-10 browning
• 20-40 quality loss for frozen fruits and
  vegetables

22

• Deviations from Arrhenius relation
•  
• change in moisture
• change in physical state, phase change, ice or
  glass formation
• change in mode of deterioration with T
  increase
• partitioning of reactants between two phases,
  such as concentration of reactants upon
  freezing
• temperature history effects

23

• Tg considerations
• gt Tg rubbery state
• slope of Arrhenius plot changes, William, Landel
  and Ferry (WLF) equation applies which
  empirically models T dependence of mechanical and
  dielectric relaxations with in the rubbery state.

24

• In diffusioncontrolled systems
• where diffusion is free volume dependent, WLF
  equation is needed to express reaction rate
  constants as a function of T

25
kref rate constant at Tref gt Tg C1, C2
system-dependent coefficients. C1 -17.44 C2
51.6 for Tref Tg for various polymers 10-100?C
above Tg viscosity-dependent changes in food
quality (crystallization, textural changes) fit
WLF model.
26

• But chemical reactions may be kinetically and/or
  diffusion limited.
• Effective reaction rate constant k/(1k/?D)
• D Diffusion coefficient
• ? constant, independent of T
• k Arrhenius-type T dependence constant
• D follows Arrhenius equation with a change in
  slope at Tg, or follows WLF equation in the
  rubbery state and especially in the range
  10-100?C above Tg,
• k/?D defines relative influence of k and D.
• If k/?D lt 0.1 Arrhenius equation can be used for
  modeling T dependency.
• Slope changes in Arrhenius plot at Tg with either
  constant slope above Tg or with a gradually
  changing slope.
• WLF equation is appropriate at 10-100?C above Tg.
  
• For complex food systems involving multiple
  reaction steps and phases, either model can be
  used for controlled-temperature functions like
  sine, square wave T fluctuations to verify the
  shelf life model.

27
Variable temperature storage

• Zero order
• sum of losses (rate constant x time interval at
  the average temperature Ti for a given time
  period ?t).

28
(No Transcript)
29
Fraction of shelf life consumed
fr 1 - fc fr ts (1 - fc) ts remaining time
at temperature Ts
30
Variable temperature storage

• 1st order

31
Temperature effects

• Fluctuating temperatures
• sine wave
• square wave

32
aw and temperature

• Clasius-Clapeyron equation describes temperature
  dependence of aw

33
BET equation

• Brunauer-Emmett-Teller equation
• Sorption isotherm moisture content vs aw
• can determine monolayer value (m1)
• valid for aw 0 - 0.5

34
GAB equation

• valid for aw 0 - 0.9
• wider range than BET equation
• can determine monolayer value
• There are other sorption isotherm models
• Need to find which fits for food using
  experimental data

35
Moisture gain or loss

• Can estimate changes in moisture in packaged
  foods
• k/x permeability of the package

36
Kinetics of enzymatic reactions

• Michaelis-Menten equation
• k1 k2
• E S ES E P
• k2

37
Kinetics of enzymatic reactions

• Vmax Maximum velocity when enzyme is saturated
  with substrate
• Km Substrate concentration at half maximum
  velocity, (k-1 k2) / k1

38
Linear regression

• To estimate changes in a quality index with time
• Need to fit experimental data to equations and
  calculate equation parameters
• Can convert equations to linear form
• Use statistics for fitting data to equations
• accurate estimates of the parameters

39
Linear regression

• Relation of a dependent variable y with an
  independent variable x
• y bo b1x
• bo , b1 parameters to estimate
• y a quality index
• x time
• Assumptions
• 1. Data are normally distributed
• 2. Constant variance
• 3. Independence of error
• 4. Linear relation

40
Linear regression
Minimize sum of squares of error
41
Linear regression

• More data more accurate prediction
• df degree of freedom, depend on number of data,
  more data more df
• lose 1 df to estimate 1 parameter
• confidence level (1-?) 90, 95, 99

42
Linear regression

• t?/2 a test statistic, student t value at a
  given confidence level
• If n 3 df 1 t?/2 at 95 12.71
• If min n 8 df 6 t?/2 2.45

43
Linear regression

• Confidence interval for a parameter estimate
• change in the parameter estimate

44
Linear regression

• Correlation Coefficient (R2)
• Proportion of variability in y explained by the
  linear relation
• Total variability in y
• variability explained by linear relation
  residuals
• R2 lt 1

45
Linear regression

• Strength of a linear relation
• 1. Small confidence intervals for parameter
  estimates
• 2. High Correlation Coefficient (R2) 1
• If R2 is small
• 1. no relation between x and y
• 2. relation not linear, use nonlinear equations