# 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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Zero and First-Order Rate Reactions Samir Kumar Khanal, Ph.D. Department of Civil, Construction and Environmental Engineering Iowa State University

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? Ask the senior engineer? Call your professor? Surf the internet? Consult BSE 482: lecture notes

Before you start designing a bioreactor (fermentor), you must have clear understanding of the followings: When is the reaction going to be over? “t” How fast the fungi are able to convert the organics into protein? That is bioconversion rate or reaction rate or kinetics. (C 2 -C 1) /(t 2 -t 1 ) = dC/dt Which bioreactor configuration would be ideal? Suspended growth Attached growth

 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 1 st order reactions  determine the rates and orders of the biochemical reactions  explain the practical significance of reaction rate and order At the end of this class, you should be able to

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.

Determined by measuring the concentration of a reactant or product as a function of time during the course of a biological reaction Concentration mg/L C2 C1 C1 C2 t1 t2 -dC/dt= (C1-C2)/(t2-t1) C2 C1 t1 t2 dC/dt= (C2-C1)/(t2-t1) 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: 1.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.

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

Effect of Concentration on Reaction Rate n = reaction order usually an integer (e.g. 0, 1, 2) ln (conc.) ln (rate) Zero order n = 0 1 st order n =1 1 1 2 nd order n =2 1 2 The order of a reaction refers to the powers to which concentration are raised “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.” “A second-order reaction is one in which the rate of reaction is directly proportional to the square of the concentration.”

What does reaction order tell us?? Relationship between rate and concentration! How the amount of compound speeds up or retards the reaction rate!

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)

Graphical representation of zero-order reaction  Time C C0C0 Slope = -k Reaction rate (slope) remains constant Zero-order reactions: not very common in biological engineering

Some examples of zero-order reactions  Biodegradation of 2,4-D (2,4-Dichlorophenoxyacetic acid)  Ammonia oxidation to nitrite  Biodegradation of aromatic hydrocarbons in compost  Phenol degradation by methanogens

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

Graphical representation of first-order reaction C C0C0 ln C ln C 0 First-order reactions: very common in biological engineering

Some examples of first-order reactions  Degradation of chlorinated compounds  Microbial growth (bacteria/fungi)  Oxidation of organic matter

Comparisons of zero and first-order reactions Zero-Order First-Order 1.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?

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 25 o C using an enriched microbial culture of Pseudomonas. During her experiments, she collected data every alternative day. The data are shown in the table below. Time, days Atrazine, mg/Lln (C) 0182.890 5152.708 12112.398 226.81.917 314.21.435 402.60.956 501.50.405 60 0.8 - 0.223 Time, days Atrazine, mg/Lln (C) 0182.890 5152.708 12112.398 226.81.917 314.21.435 402.60.956 501.50.405 60 0.8 - 0.223

Zero-order C = C o - kt First-order ln (C) = ln (C o )- kt y = 2.9871- 0.0519x

Effect of temperature on biological reaction rate The effect of temperature on reaction rate is given by the Arrhenius equation: E A = activated energy, J/mol R = Universal gas constant 8.31J/mol-K T = Temperature in Kelvin = ( o C + 273) A = Constant (not significantly affected by small temp. change

What happens if you increase the temperature by 10°C from, say, 20°C to 30°C (293 K to 303 K)? Let's assume an activation energy, E A of 50,000 J mol -1. gas constant, R, is 8.31 J K -1 mol -1. At 30°C (303 K), the fraction is: At 20°C (293 K), the value of the fraction: Rule of thumb: Rate of a reaction doubles for every 10 degree rise in temperature

For biological reactions, this role will hold more or less true up to a certain optimum temperature Activities of mesophilic methanogens at different temperature Temperature correction for rate constant  : temperature-activity coefficient: 1.034 – 1.08 kT2kT2

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