Chemical Kinetics in Bioprocessing - Lecture 14

Chemical Kinetics

Study of reaction rates and mechanisms.

Reaction Kinetics

Rate of conversion from reactants to products.

Irreversible Reaction

Reaction that proceeds in one direction only.

Rate of Reaction (Ri)

Change in mass or moles of species.

Consumption Rate

Rate at which reactants are used up.

Production Rate

Rate at which products are formed.

Mass Balance Equation

Equation representing mass conservation in reactions.

Volumetric Rate (r)

Rate of reaction per unit volume of reactor.

Specific Rate (r_specific)

Reaction rate per unit quantity of enzymes or biomass.

Collision Theory

Theory explaining how molecules react through collisions.

Collision Properties

Conditions required for effective molecular collisions.

Correct Orientation

Molecules must align properly to react.

Correct Speed

Molecules must collide with sufficient energy.

Bond Affinity

Tendency of atoms to form stable bonds.

Mass Change Rate

Rate of change in mass over time.

Concentration (C)

Amount of substance per unit volume.

Closed System

System where mass does not enter or leave.

Reference Species

Chosen species for calculating reaction rates.

Rate of Change

Speed at which a quantity changes.

Energy Transfer

Energy exchanged during molecular collisions.

Molecular Basis

Reference point for defining reaction rates.

Reaction Mechanism

Step-by-step sequence of elementary reactions.

Temporary Bonds

Short-lived bonds formed during reactions.

Collision Theory

Molecules must collide to react effectively.

Kinetic Energy (KE)

Energy of an object due to its motion.

KE Formula

KE = 1/2 mv², where v is velocity.

Energy Barrier

Minimum energy required for a reaction.

Threshold Energy

Energy must exceed ∆Eactivation to react.

Exothermic Reaction

Releases energy; Eproducts < Ereactants.

Endothermic Reaction

Absorbs energy; Eproducts > Ereactants.

Rate Constant (k)

Constant that relates reaction rate to concentrations.

Order of Reaction

Exponent indicating concentration's effect on rate.

Overall Order

Sum of individual orders in a reaction.

Arrhenius Equation

k = A e^(-Ea/RT), links k to activation energy.

Arrhenius Constant (A)

Frequency factor related to effective collisions.

Activation Energy (Ea)

Minimum energy needed for a reaction to occur.

Zero-Order Reaction

Rate independent of reactant concentration.

Zero-Order Rate Constant (k0)

Units: mol m³ s⁻¹, for zero-order reactions.

Enzyme Concentration

Affects zero-order reaction rates significantly.

First-Order Reaction

Rate depends on the concentration of one reactant.

First-Order Rate Equation

r = kA[C], where kA is first-order rate constant.

Integration of Zero-Order Kinetics

C - C0 = -k0t, relates concentration and time.

Serratia marcescens Example

Used to determine oxygen uptake rate constant.

Reaction Extent

Measure of how far a reaction proceeds.

Effective Collisions

Collisions with sufficient energy to cause reaction.

First-order rate constant (kA)

Constant for reactions with concentration dependence.

Dimension of kA

Measured in (Time)-1 or second-1.

Rate of reaction (rC)

Change in concentration over time, negative.

Differential rate equation

−dC/dt = kA * C.

Integration of rate equation

ln(C) - ln(C0) = -kA * t.

Concentration equation

C = C0 e^(-kA t).

Total Petroleum Hydrocarbons

Measured in mg kg-1 in soil samples.

Time measurement

Concentration data taken over 6 weeks.

Enzyme-catalyzed reaction

E + S ⇌ ES ⇌ E + P.

Enzyme-substrate complex (ES)

Intermediate formed during enzyme reactions.

Rate of reaction step 1

Rate1 = k1 [E] [S].

Rate of reaction step 2

Rate2 = k2 [ES].

Total volumetric rate (rS or rP)

Rate of substrate or product formation.

Vmax

Maximum rate of reaction at saturation.

Substrate concentration ([S])

Influences the rate of enzyme reactions.

Activation energy

Energy barrier lowered by enzyme presence.

Contaminant concentration estimation

Predict concentration after specific time period.

Initial concentration (C0)

Concentration at time t=0.

Exponential decay

Describes concentration decrease over time.

Mixed population treatment

Using bacteria and fungi for bioremediation.

Hydrocarbon degradation

Breakdown of petroleum compounds in soil.

Reaction kinetics

Study of rates of chemical processes.

Michaelis-Menten kinetics

Model for enzyme-catalyzed reaction rates.

Vmax

Maximum reaction velocity (mol l-1 min-1)

r

Rate of product formation (mol l-1 min-1)

[S]

Substrate concentration (mol m-3 or mol l-1)

Km

Michaelis constant (mol m-3)

kcat

Catalytic constant or turnover number

E

Enzyme in reaction (E + S → P)

S

Substrate in enzyme-catalyzed reaction

P

Product formed from substrate

Zero-order reaction

Reaction rate independent of substrate concentration

First-order reaction

Reaction rate directly proportional to substrate concentration

Lineweaver-Burk equation

Linear transformation of Michaelis-Menten equation

Eadie-Hofstee equation

Alternative method to determine Vmax and Km

Substrate saturation

Condition where [S] greatly exceeds Km

Enzyme concentration

Amount of enzyme present in reaction

Experimental data

Measured [S] and reaction rates for analysis

Trendline fitting

Graphical method to extract kinetic parameters

Half-maximal rate

Condition where reaction rate is Vmax/2

Catalytic efficiency

Ratio of kcat to Km, indicating enzyme efficiency

Rate constant

Characteristic constant for reaction speed

Reaction velocity

Speed of product formation in reaction

Substrate concentration units

Measured in mol l-1 or mol m-3

Michaelis-Menten model

Describes enzyme kinetics based on substrate concentration