Zero and First-Order Rate Reactions

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Zero and First-Order Rate Reactions

• Samir Kumar Khanal, Ph.D.
• Department of Civil, Construction and
  Environmental Engineering
• Iowa State University

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Question!! Assume you are a process engineer
(biological), newly recruited by P G. In your
first week of job, you have been assigned to
assist in the design of a bioreactor for growing
edible fungi on synthetic growth medium to
produce light-weight protein diet for astronauts.
How are you going to design? Specifically what
data do you need?
Call your professor?
Ask the senior engineer?
Surf the internet?
Consult BSE 482 lecture notes
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Before you start designing a bioreactor
(fermentor), you must have clear understanding of
the followings
How fast the fungi are able to convert the
organics into protein? That is bioconversion rate
or reaction rate or kinetics. (C2-C1)/(t2-t1)
dC/dt
When is the reaction going to be over? t
Which bioreactor configuration would be ideal?
Suspended growthAttached growth
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At the end of this class, you should be able to

• define biochemical kinetics, reaction rate and
  order
• derive the rate of a reaction in terms of the
• appearance of products or disappearance of
  reactants
• describe the basic factors that influence the
  rate
• of a reaction
• integrate the rate laws for 0, and 1st order
  reactions
• determine the rates and orders of the
  biochemical
• reactions
• explain the practical significance of reaction
  rate and
• order

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Reaction Rates

• Definition
• change in concentration of a reactant or product
  with time

• The rate will be negative (-) for reactants
• The rate will be positive () for products

Reactants mostly pollutants (we want to get rid
of), e.g. nitrate, phosphate, organics,
pesticides, etc. Products mostly value-added
commodities (we want to produce), e.g. protein,
lactic acid, enzymes, nisin, yeast, etc.
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• Determination of biological reaction rate 
• (A) The rate of decrease in concentration
• of a reactant, or
• (B) The rate of increase in concentration
• of the products.
•  
• The basic requirements are
• A good thermostat as rates change
• with temperature
• 2. An accurate timing device (stopwatch)
• 3. A method of determining the
• concentration of reactant or product.

• Determined by measuring the
• concentration of a reactant or
• product as a function of time
• during the course of a
• biological reaction

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• Factors affecting the speed or rate of a
  biological reaction
• Concentration
• Temperature
• Presence of a macro/micro-nutrients
• Physical state of reactants

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Effect of Concentration on Reaction Rate
n reaction order usually an integer (e.g. 0, 1,
2)
The order of a reaction refers to the powers to
which concentration are raised
A second-order reaction is one in which the
rate of reaction is directly proportional to the
square of the concentration.
A zero-order reaction is one in which the rate
of reaction is independent of concentration.
A first-order reaction is one in which the rate
of reaction is directly proportional to
concentration.
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What does reaction order tell us??
Relationship between rate and concentration! How
the amount of compound speeds up or retards the
reaction rate!
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Zero-Order Reactions
k rate constant
?
For zero-order reaction, n 0
Negative means, C decreases with time
unit of k is mass volume-1 time-1
If C increases with time (for product
formation)
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Graphical representation of zero-order reaction
?
Zero-order reactions not very common in
biological engineering
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Some examples of zero-order reactions

• Biodegradation of 2,4-D (2,4-Dichlorophenoxyaceti
  c acid)
• Ammonia oxidation to nitrite
• Biodegradation of aromatic hydrocarbons in
  compost
• Phenol degradation by methanogens

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First-Order Reactions
k rate constant
?
For first-order reaction, n 1
Negative means, C decreases with time
?
unit of k is time-1
Which is similar to a straight line equation
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Graphical representation of first-order reaction
First-order reactions very common in biological
engineering
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Some examples of first-order reactions

• Degradation of chlorinated compounds
• Microbial growth (bacteria/fungi)
• Oxidation of organic matter

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Comparisons of zero and first-order reactions
Zero-Order
First-Order

• How the reaction changes with time.
• 2. What about change in slope (k)?
• 3. What is the unit of k in each case?
• 4. What is the effect of concentration?

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Example An engineering student was interested
in the biodegradation of atrazine in an aqueous
environment, its reaction rate and order. She
went to the lab and conducted a series of batch
tests in shaker flasks at 25oC using an enriched
microbial culture of Pseudomonas. During her
experiments, she collected data every alternative
day. The data are shown in the table below.
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Zero-order C Co- kt
First-order ln (C) ln (Co)- kt y
2.9871- 0.0519x
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Effect of temperature on biological reaction rate
The effect of temperature on reaction rate is
given by the Arrhenius equation
EA activated energy, J/mol R Universal gas
constant 8.31J/mol-K T Temperature in Kelvin
(oC 273) A Constant (not significantly
affected by small temp. change
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What happens if you increase the temperature by
10C from, say, 20C to 30C (293 K to 303 K)?
Let's assume an activation energy, EA of 50,000 J
mol-1. gas constant,
R, is 8.31 J K-1 mol-1. 
At 30C (303 K), the fraction is  
At 20C (293 K), the value of the fraction 
Rule of thumb Rate of a reaction doubles for
every 10 degree rise
in temperature
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For biological reactions, this role will hold
more or less true up to a certain optimum
temperature
kT2
Activities of mesophilic methanogens at different
temperature
Temperature correction for rate constant
? temperature-activity coefficient 1.034 1.08