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Page 1: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Chemical kineticsChemical kinetics

Page 2: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Kinetics and food deteriorationKinetics and food deterioration

• Objective– Prediction of change in quality as a function

of time and environmental conditions

See Labuza, T. P. 1984. Application of chemical kinetics todeterioration of food, J. Chemical Education,61, 348.

Page 3: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Kinetics and food deteriorationKinetics and food deterioration

• Why is this technique needed?– Evaluation of new ingredients– Setting of “use by” dates– To insure nutritional labeling compliance

Page 4: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Quality change predictionQuality change prediction

• To predict quality change you need to know– Major modes of quality loss– Factors controlling initial quality– Environmental conditions– Nature of the packaging material– Chemical kinetics

Page 5: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Common modes of Common modes of food deteriorationfood deterioration• Microbial decay

– pH, aw, redox potentials, etc.• Senesence

– Normal enzymatic reactions in post-harvest physiology of food stuffs

• Non-enzymatic browning– aw, pH, temperature, etc.

Page 6: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Common modes of Common modes of food deteriorationfood deterioration• Lipid oxidation

– Off flavor– Loss of solubility and biological value of

proteins– Bleaching of fat-soluble pigments

(carotenoids)– Loss of efficacy of fat soluble vitamins (A, D,

E, and K)

Page 7: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Common modes of Common modes of food deteriorationfood deterioration• Vitamin loss

– Hydrolysis– Light– Heat– Acid– Oxidation

• Vitamin C is most labile

Page 8: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Common modes of Common modes of food deteriorationfood deterioration• Color changes

– Loss of Mg from chlorophyll

• Enzymatic activity– PPO– Pectic enzymes– Lipase

Page 9: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Common modes of Common modes of food deteriorationfood deterioration• Sensory changes• Physical deterioration

– Decreased solubility of certain constituents– Mushiness– Freezing-thawing– Melting-recrystallization of fat– Bread staling

Page 10: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

General methodologyGeneral methodology

• Select the major mode of deterioration to study

• Measure some quality factor related to this mode

• Apply mathematical models to make predictions

Page 11: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Selecting what to measureSelecting what to measure

• In selecting what to measure, consider– Key labile ingredients– Characteristics of the packaging material– How the product will be shipped and stored

Page 12: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Selecting what to measureSelecting what to measure

– Relative humidity– Temperature– Susceptibility to light– If no chemical test exists, would a sensory

test work?

Page 13: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

KineticsKinetics

• aA + bB cC + dD

• kf = rate constant for the forward reaction

• kr = rate constant for the reverse reaction• Rate of loss of reactants:• -dA/dt = -dB/dt

kf

kr

Page 14: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

KineticsKinetics

• Rate of gain of products:• dC/dt = dD/dt• Further, rate of loss = rate of gain• -dA/dt =-dB/dt = dC/dt = dD/dt• Rate of reaction• rate= (rate constant)Π[reactants]n

Page 15: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

KineticsKinetics

• Net rate of loss of A:• -dA/dt = rate of loss - rate of reformation• -dA/dt = kf[A]a[B]b - kr[C]c[D]d

Rate of forward reaction

Rate of reverse reaction

Page 16: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

KineticsKinetics

– To simplify this equation, select conditions where the forward or reverse reaction predominates and/or one of the reactants is in such large concentration excess that it’s concentration doesn’t change over time.

Page 17: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

KineticsKinetics

• Thus, if kr <<< kf and [B] is large relative to [A] (so that B is effectively constant) then

• -dA/dt = kf’[A]a , where kf’ is the pseudo first order rate constant

• Assume for a given mode of food deterioration that the previous assumptions are true, then

Page 18: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

KineticsKinetics

• Loss of quality may be expressed as– -dQ/dt = kn[Q]n

• and gain in undesirable factors may be– +dUF/dt = kn[UF]n

• In these equations, kn is the pseudo first order rate constant, and n is the order of the reaction

Page 19: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Reaction order and integrationReaction order and integration

• -dQ/dt = kn[Q]n

• For n = 0• -dQ/dt = k0[Q]0 = k0

• -d[Q] = k0dt• d[Q] = -k0dt• ∫d[Q] = -k0∫dt• [Q] - [Q0] = -k0t• [Q] = -k0t + [Q0]

Page 20: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Reaction order and integrationReaction order and integration

• For n = 0, a plot of [Q] vs. time should yield a straight line

Q

time

[Q0]

Slope = -k0

Page 21: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Reaction order and integrationReaction order and integration

• For n = 1• -d[Q]/dt = k1[Q]1

• ∫d[Q]/[Q] = -k1∫dt• ln[Q] - ln[Q0] = -k1t• log [Q] = -(k1/2.3) t + log [Q0]

Page 22: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Reaction order and integrationReaction order and integration

• A plot of log [Q] vs. time should yield a straight line

Log [Q]

time

Log[Q0]

Slope = -k1/2.3

Page 23: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

HalfHalf--life (first order)life (first order)

• From ln[Q] - ln[Q0] = -k1t• ln([Q]/[Q0]) = -k1t, and• k1 = {-ln([Q]/[Q0])}/t• When [Q] has decreased to 1/2 of its

original value, we call this time the half-life of the reaction.

Page 24: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

HalfHalf--life (first order)life (first order)

• Then k1 = {-ln[50/100]}/t 1/2

• t 1/2 = 0.693/k1

• This is a general result for any first order reaction and we will have occasion to use this equation in a later problem.

Page 25: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Reaction order and integrationReaction order and integration

• We won’t do this but integration for n = 2 would indicate that plotting 1/[Q] vs. time would give a straight line.

Page 26: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Kinetic approach to accelerating Kinetic approach to accelerating shelf life deteriorationshelf life deterioration

• Concentration acceleration

• Moisture or relative humidity acceleration

• Temperature acceleration– This is usually done

Page 27: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

The Arrhenius equationThe Arrhenius equation

• The Arrhenius equation describes the effect of temperature on chemical reaction rate

• k = k0e -E/RT

– where k = rate constant, k0 = pre-exponential factor, E = activation energy, R = gas constant (8.3 J/deg K), and T = the absolute temperature in degrees Kelvin

Page 28: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

The Arrhenius equationThe Arrhenius equation

• Take the natural logarithm of the Arrhenius equation

• ln k = -(Ea/R)(1/T) + ln0k

Page 29: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

The The ArrheniusArrhenius equationequation

• Thus we can find k at several higher temperatures (accelerated shelf lifestudy) than the one in which we are interested. Then, plot ln k vs. 1/T to get a straight line which you can extrapolate to lower temperatures.

Page 30: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

The Arrhenius equationThe Arrhenius equation

ln k

1/T (reciprocal degrees K)

Plot for an accelerated shelf lifestudy

Page 31: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Case studyCase studyAsceptic packaged simulated orange drink product

Use by: ???????

Simulatedorange drinkproduct How do I establish my

“use by” date?

Page 32: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

• On the label of my asceptic packaged orange drink product it states that each serving provides 100% of the DV for vitamin C. I know that vitamin C is the most labile constituent of my product, therefore I can use it as a marker

• DV = 60 mg

Page 33: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

• Number of servings per package = 6• Total minimum vitamin C needed in

package at time of consumption = 360 mg• To account for breakdown, I add enough

vitamin C to make the total at manufacture = 720 mg

• Question: How do I determine my “use by” date?

Page 34: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

• Answer: Do an accelerated shelf life study. Measure k at 50, 60, and 70 degrees C (323, 333, and 343oK). Do an Arrhenius plot.

Page 35: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

ln k

1/T (reciprocal degrees K)

343 K333 K

323 K

Page 36: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

• Extrapolate to storage temperature, in this case 25 degrees C (298oK).

Page 37: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

ln k

1/T (reciprocal degrees K)

343 K333 K

323 K

298 K

Page 38: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

• At 25 C (298 oK), k1 = 3.1 x 10-3 days-1

• My maximum allowable loss occurs when the [vitamin C] reaches one-half of its initial level, that is, at the half-life for vitamin C under these conditions.

Page 39: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

• t 1/2= 0.693/k1=0.693/(3.1 x 10-3)• t 1/2 = 224 days

• So if my simulated orange drink product is packaged today then it’s use by date is November 4, 2005.

Page 40: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 1Treatment 1

Use by: Nov. 4, 2005

Simulatedorange drinkproduct

Page 41: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 2Treatment 2

• Same problem as treatment 1• We know from our kinetic experiments

that vitamin C degradation is a first order reaction. Thus,

Page 42: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 2Treatment 2

• ln [vitamin C] - ln [vitamin C]0 = -k1t• The vitamin C concentration at

consumption (time = t) must be 60 mg/serving.

Page 43: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 2Treatment 2

• My accelerated shelf life study tells me that k1 = 3.1 x 10-3 days-1. Thus,

• ln [60] - ln [vitamin C]0 = (3.1 x 10-3)t• I will specify a shelf life (or t) of 30 days.• Then, 4.1 - ln [vitamin C]0 = -0.093• ln [vitamin C]0 = 4.193

Page 44: Chemical kinetics - Purdue University · See Labuza, T. P. 1984. Application of chemical kinetics to deterioration of food, J. Chemical Education,61, 348. Kinetics and food deterioration

Treatment 2Treatment 2

• [vitamin C]0 = 66 mg/serving• So the total vitamin C needed per

package for a 30 day shelf life is 396 mg (storage at 25 degrees C/298oK)