It should be pointed out that industrial-scale chemical plant equipment cannot be built simply by enlarging the laboratory apparatus used in basic chemical research. Consider, for example, the case of a chemical reactor—that is, the apparatus used for chemical reactions. Although neither the type nor size of the reactor will affect the rate of the chemical reaction per se, they will affect the overall or apparent reaction rate, which involves effects of physical processes, such as heat and mass transfer and fluid mixing.

Thus, in the design and operation of plant-size reactors, the knowledge of such physical factors — which often is neglected by chemists — is important. Davis, a British pioneer in chemical engineering, described in his book, A Handbook of Chemical Engineering , , a variety of physical operations commonly used in chemical plants.

Little of the Massachusetts Institute of Technology MIT , where the instruction of chemical engineering was organized via unit operations. Since then, the scope of chemical engineering has been broadened to include not only unit operations but also chemical reaction engineering, chemical engineering thermodynamics, process control, transport phenomena, and other areas.

KGaA, Weinheim ISBN: 4 1 Introduction various plants which involve biological systems, if the differences in the physical properties of some materials are taken into account. Furthermore, chemical engineers are required to have some knowledge of biology when tackling problems that involve biological systems.

Today, the applications of chemical engineering are becoming broader to include not only bioprocesses but also various biological systems involving environmental technology and even some medical devices, such as artificial organs. However, this does not necessarily mean that engineers can solve everything theoretically, and quite often they use empirical rather than theoretical equations. Any equation — whether theoretical or empirical — which expresses some quantitative relationship must be dimensionally sound, as will be stated below.

In engineering calculations, a clear understanding of dimensions and units is very important. Dimensions are the basic concepts in expressing physical quantities. Dimensions used in chemical engineering are length L , mass M , time T , the amount of substance n and temperature y.

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Units are measures for dimensions. Scientists normally use the centimeter cm , gram g , second s , mole mol , and degree Centigrade 1C as the units for the length, mass, time, amount of substance, and temperature, respectively the CGS system. Whereas, the units often used by engineers are m, kg, h, kmol, and 1C. Traditionally, engineers have used kg as the units for both mass and force. However, this practice sometimes causes confusion, and to avoid this a designation of kg-force kgf is recommended.

Mass and weight are different entities: the weight of a body is the gravitational force acting on the body, that is, mass gravitational acceleration g. Strictly speaking, g — and hence weight — will vary slightly with locations and altitudes on the Earth. It would be much smaller in a space ship.

In recent engineering research papers, units with the International System of Units SI are generally used. The SI system is different from the CGS system often used by scientists, or from the conventional metric system used by engineers [4]. In the SI system, kg is used for mass only, and Newton N , which is the unit 1.

It is roughly the weight of an apple distributed over the area of one square meter. As it is generally too small as a unit for pressure, kPa kilopascal i. One bar, which is equal to 0. Although use of the SI units is preferred, we shall also use in this book the conventional metric units that are still widely used in engineering practice.

The English engineering unit system is also used in engineering practice, but we do not use it in this text book. Values of the conversion factors between various units that are used in practice are listed in the Appendix, at the back of this book. Empirical equations are often used in engineering calculations. Their values in the kcal, kg, and 1C units are different from those in the kJ, kg, and K units. Equations such as Equtation 1. The use of dimensional equations should preferably be avoided; hence, Equtation 1.

Thus, as long as the same units are used for cp and R and for T and Tc, respectively, the values of the ratios in the parentheses as well as the values of coefficients au and bu do not vary with the units used. Ratios such as those in the above parentheses are called dimensionless numbers groups , and equations involving only dimensionless numbers are called dimensionless equations. Dimensionless equations — some empirical and some with theoretical bases — are often used in chemical engineering calculations.

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Most dimensionless numbers are usually called by the names of the person s who first proposed or used such numbers. They are also often expressed by the first two letters of a name, beginning with a capital letter; for example, the well-known Reynolds number, the values of which determine conditions of flow laminar or turbulent is usually designated as Re, or sometimes as NRe. Most dimensionless numbers have some significance, usually ratios 5 6 1 Introduction of two physical quantities.

How known variables could be arranged in a dimensionless number in an empirical dimensionless equation can be determined by a mathematical procedure known as dimensional analysis, which will not be described in this text. Examples of some useful dimensionless equations or correlations will appear in the following chapters of the book. Example 1. What is the pressure p in SI units?

Properties which do not vary with the amount of mass of a substance — for example, temperature, pressure, surface tension, and mole fraction — are termed intensive properties. On the other hand, those properties which vary in proportion to the total mass of substances — for example, total volume, total mass, and heat capacity — are termed extensive properties. It should be noted, however, that some extensive properties become intensive properties, in case their specific values — that is, their values for unit mass or unit volume — are considered.

For example, specific heat i. Sometimes, capital letters and small letters are used for extensive and intensive properties, respectively. Measured values of intensive properties for common substances are available in various reference books [5]. Equilibrium is the end point of any spontaneous process, whether chemical or physical, in which the driving forces potentials for changes are balanced and there is no further tendency to change. Chemical equilibrium is the final state of a reaction at which no further changes in compositions occur at a given temperature and pressure.

As an example of a physical process, let us consider the absorption of a gas into a liquid. Equilibrium values do not vary with the experimental apparatus and procedure. The rate of a chemical or physical process is its rapidity — that is, the speed of spontaneous changes toward the equilibrium.

The rate of absorption of a gas into a liquid is how much of the gas is absorbed into the liquid per unit time. Such rates vary with the type and size of the apparatus, as well as its operating conditions. The rates of chemical or biochemical reactions in a homogeneous liquid phase depend on the concentrations of reactants, the temperature, the pressure, and the type and concentration of dissolved catalysts or enzymes.

However, in the cases of heterogeneous chemical or biochemical reactions using particles of catalyst, immobilized enzymes or microorganisms, or microorganisms suspended in a liquid medium, and with an oxygen supply from the gas phase in case of an aerobic fermentation, the overall or apparent reaction rate s or growth rate s of the microorganisms depend not only on chemical or biochemical factors but also on physical factors such as rates of transport of reactants outside or within the particles of catalyst or of immobilized enzymes or microorganisms.

Such physical factors vary with the size and shape of the suspended particles, and with the size and geometry of the reaction vessel, as well as with the operating conditions, such as the degree of mixing or the rate s of gas supply. The physical conditions in industrial plant equipment are often quite different from those in the laboratory apparatus used in basic research.

Let us consider, as an example, a case of aerobic fermentation. The maximum amount of oxygen that can be absorbed into the unit volume of a fermentation medium at given temperature and pressure i. On the other hand, the rates of oxygen absorption into the medium vary with the type and size of the fermentor, and also with its operating conditions, such as the agitator speeds and rates of oxygen supply.

To summarize, chemical and physical equilibria are independent of the configuration of apparatus, whereas overall or apparent rates of chemical, biochemical, or microbial processes in industrial plants are substantially dependent on the configurations and operating conditions of the apparatus used. A simple example is the heating of a liquid. If the amount of the fluid is rather small e.

However, when the amount of the liquid is fairly large e. Most unit operations can be carried out either batchwise or continuously, depending on the scale of operation. Most liquid-phase chemical and biochemical reactions, with or without catalysts or enzymes, can be carried out either batchwise or continuously. For example, if the production scale is not large, then a reaction to produce C from A and B, all of which are soluble in water, can be carried out batchwise in a stirred-tank reactor; that is, a tank equipped with a mechanical stirrer.

The reactants A and B are charged into the reactor at the start of the operation. Product C is subsequently produced from A and B as time goes on, and can be separated from the aqueous solution when its concentration has reached a predetermined value. When the production scale is large, the same reaction can be carried out continuously in the same type of reactor, or even with another type of reactor see Chapter 7.

In this case, the supplies of the reactants A and B and the withdrawal of the solution containing product C are performed continuously, all at constant rates. The washout of the catalyst or enzyme particles can be prevented by installing a filter mesh at the exit of the product solution. Except for the transient start-up and finish-up periods, all of the operating conditions such as temperature, stirrer speed, flow rates and the concentrations of the incoming and outgoing solutions, remain constant — that is, in the steady state.

Let us consider a system, which is separated from its surroundings by an imaginary boundary. It should be zero with a continuously operated reactor mentioned in the previous section. Q and W are both energy in transit and hence have the same dimension as energy. The total energy of the system includes the total internal energy E, potential energy PE , and kinetic energy KE. In normal chemical engineering calculations, changes in PE and KE can be neglected. The internal energy E is the intrinsic energy of a substance including chemical and thermal energy of molecules.

Although absolute values of E are unknown, DE, difference from its base values, for example, from those at 01C and 1 atm, are often available or can be calculated. Enthalpy h, a compound thermodynamic function defined by Equation 1. For a steady-state flow system, again neglecting changes in the potential and kinetic energies, the energy balance per unit time is given by Equation 1. The density and specific heat of milk are 1. Solution Applying Equation 1. Further Reading 1. It then falls freely to the ground. The acceleration of gravity is 9. Calculate a the potential energy of the weight relative to the ground; b the velocity and kinetic energy of the weight just before it strikes the ground.

How much water will be required in the case where the exit water temperature is 30 1C? The heat of vaporization of ethanol at 1 atm, References 1 Aiba, S. Further Reading 1 Hougen, O. Thus, knowledge of the engineering principles of such physical processes is important in the design and operation of bioprocess plants.

Although this chapter is intended mainly for non-chemical engineers who are unfamiliar with such engineering principles, it might also be useful to chemical engineering students at the start of their careers. When a fluid flows through a conduit, its pressure drops due to friction as a result of transfer of momentum, as will be shown later. The driving forces, or driving potentials, for transport phenomena are: i the temperature difference for heat transfer; ii the concentration or partial pressure difference for mass transfer; and iii the difference in momentum for momentum transfer.

When the driving force becomes negligible, then the transport phenomenon will ceases to occur, and the system will reach equilibrium. It should be mentioned here that, in living systems the transport of mass sometimes takes place apparently against the concentration gradient. Active transport in biological systems is beyond the scope of this book. Transport phenomena can take place between phases, as well as within one phase. Let us begin with the simpler case of transport phenomena within one phase, in connection with the definitions of transport properties.

Heat transfer within a homogeneous solid or a perfectly stagnant fluid in the absence of convection and radiation takes place solely by conduction. Values of thermal conductivity generally increase with increasing temperature. Except in the case of equimolar counter-diffusion of A and B, the diffusion of A would result in the movement of the mixture as a whole. However, in the usual case where the concentration of A is small, the value of DAB is practically equal to the value defined with reference to the fixed coordinates.

Values of diffusivity in gas mixtures at normal temperature and atmospheric pressure are in the approximate range of 0. Values of the liquid-phase diffusivity in dilute solutions are in the approximate range of 0. Both, gas-phase and liquid-phase diffusivities can be estimated by various empirical correlations available in reference books. There exists a conspicuous analogy between heat transfer and mass transfer.

Hence, Equation 2. There are two distinct regimes or modes of fluid flow. In the first regime, when all fluid elements flow only in one direction, and with no velocity components in any other direction, the flow is called laminar, streamline, or viscous flow. In the second regime, the fluid flow is turbulent, with random movements of the fluid elements or clusters of molecules occurring, but the flow as a whole is in one general direction. Incidentally, such random movements of fluid elements or clusters of molecules should not be confused with the random motion of individual molecules that causes molecular diffusion and heat conduction discussed in the previous sections, and also the momentum transport in laminar flow discussed below.

Figure 2. If both plates move at constant but different velocities, with the top plate A at a faster velocity than the bottom plate B, a straight velocity profile such as shown in the figure will be established when steady conditions have been reached. This is due to the friction between the fluid layers parallel to the plates, and also between the plates and the adjacent fluid layers. In other words, a faster-moving fluid layer tends to pull the adjacent slower-moving fluid layer, and the latter tends to resist it. Thus, momentum is transferred from the faster-moving fluid layer to the adjacent slower-moving fluid layer.

Therefore, a force must be applied to maintain the velocity gradient; such force per unit area parallel to the fluid layers t Pa is called the shear stress. The proportionality constant m Pa s is called molecular viscosity or simply viscosity, which is an intensive property.

From Equation 2. A comparison of Equations 2. A fluid with viscosity which is independent of shear rates is called a Newtonian fluid. On a shear stress—shear rate diagram, such as Figure 2. All gases, and most common liquids of low molecular weight e. It is worth remembering that the viscosity of water at 20 1C is 0. Liquid viscosity decreases with increasing temperature, whereas gas viscosity increases with increasing temperature. The viscosities of liquids and gases generally increase with pressure, with gas and liquid viscosities being estimated by a variety of equations and correlations available in reference books.

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, these are categorized into pseudoplastic, and dilatant, and Bingham plastic fluids see Figure 2. The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is Figure 2.

In general, the shear stress t can be represented by Equation 2. Values of n are smaller than 1 for pseudoplastic fluids, and greater than 1 for dilatant fluids. The apparent viscosity ma Pa s , which is defined by Equation 2. Fermentation broths — that is, fermentation media containing microorganisms — often behave as non-Newtonian liquids, and in many cases their apparent viscosities vary with time, notably during the course of the fermentation.

Fluids that show elasticity to some extent are termed viscoelastic fluids, and some polymer solutions demonstrate such behavior. Elasticity is the tendency of a substance or body to return to its original form, after the applied stress that caused a strain i. The elastic modulus Pa is the ratio of the applied stress Pa to strain —. The relaxation time s of a viscoelastic fluid is defined as the ratio of its viscosity Pa s to its elastic modulus.

Example 2. Solution Taking the logarithms of Equation 2. Thus, this CMC solution is pseudoplastic. Incidentally, plotting data on a log—log paper i. Whether a fluid flow becomes laminar or turbulent depends on the value of a dimensionless number called the Reynolds number, Re. For a flow through a conduit with a circular cross-section i. Under steady conditions, the flow of fluid through a straight round tube is laminar, when Re is less than approximately However, when Re is higher than , the flow becomes turbulent.

In the transition range between these two Re values the flow is unstable; that is, a laminar flow exists in a very smooth tube, but only small disturbances will cause a transition to turbulent flow. This holds true also for the fluid flow through a conduit with a noncircular cross-section, if the equivalent diameter defined later is used in place of d in Equation 2.

However, fluid flow outside a tube bundle, whether perpendicular or oblique to the tubes, becomes turbulent at much smaller Re , in which case the outer diameter of tubes and fluid velocity, whether perpendicular or oblique to the tubes, are substituted for d and v in Equation 2. Equation 2. The principle of the capillary tube viscometer is based on this relationship. Solution Differentiation of Equation 2.

The velocity at the tube wall is zero, and the fluid near the wall moves in laminar flow, even though the flow of the main body of fluid is turbulent. The thin layer near the wall in which the flow is laminar is called the laminar sublayer or laminar film, while the main body of fluid where turbulence always prevails is called the turbulent core. The intermediate zone between the laminar sublayer and the turbulent core is called the buffer layer, where the motion of fluid may be either laminar or turbulent at any given instant.

With a relatively long tube, the above statement holds for most of the tube length, except for the entrance region. A certain length of tube is required for the laminar sublayer to develop fully. Velocity distributions in turbulent flow through a straight, round tube vary with the flow rate or the Reynolds number. With increasing flow rates, the velocity distribution becomes flatter and the laminar sublayer thinner. Dimensionless empirical equations involving viscosity and density are available which correlate the local fluid velocities in the turbulent core, buffer layer, and the laminar sublayer as functions of the distance from the tube axis.

The ratio of the average velocity over the entire tube cross-section to the maximum local velocity at the tube axis is approximately 0. It can be seen from comparison of Equations 2. A similar statement holds for momentum transfer. The temperature gradient in the laminar sublayer is linear and steep, because heat transfer across the laminar sublayer is solely by conduction, and the thermal conductivities of fluids are much smaller those of metals. The temperature gradient in the turbulent core is much smaller, as heat transfer occurs mainly by convection — that is, by mixing of the gross fluid elements.

The gradient becomes smaller with increasing distance from the wall due to increasing turbulence. The temperature gradient in the buffer region between the laminar sublayer and the turbulent core is smaller than in the laminar sublayer, but greater than in the turbulent core, and becomes smaller with increasing distance from the wall.

Conduction and convection are comparable in the buffer region. It should be noted that no distinct demarcations exist between the laminar sublayer and the buffer region, nor between the turbulent core and the buffer region. What has been said above also holds for solid—fluid mass transfer. The concentration gradients for mass transfer from a solid phase to a fluid in turbulent flow should be analogous to the temperature gradients, such as shown in Figure 2.

When representing rates of transfer of heat, mass, and momentum by eddy activity, the concepts of eddy thermal conductivity, eddy diffusivity, and eddy viscosity are sometimes useful. Extending the concepts of heat conduction, molecular diffusion, and molecular viscosity to include the transfer mechanisms by eddy activity, one can use Equations 2. It should be noted that these are not properties of fluid or system, because their values vary with the intensity of turbulence which depends on flow velocity, geometry of flow channel, and other factors.

This is usually impossible, however, because the thickness of the 2. Thus, a common engineering practice is to use the film or individual coefficient of heat transfer, h, which is defined by Equation 2. The bulk mixing-cup temperature tb, which is shown in Figure 2. The temperature of a fluid emerging from a heat transfer device is the bulk temperature at the exit of the device.

If the temperature profile were known, as in Figure 2. It should be noted that the effective film thickness Dyf is a fictive concept for convenience. This is thicker than the true thickness of the laminar sublayer. From Equations 2. Also, h values can be increased by decreasing the effective thickness of the laminar film Dyf by increasing fluid velocity along the interface.

Various correlations for predicting film coefficients of heat transfer are provided in Chapter 5. The film individual coefficients of mass transfer can be defined similarly to the film coefficient of heat transfer. Few different driving potentials are used today to define the film coefficients of mass transfer. However, using kL and kGp of different dimensions is not very convenient. Conversion between kGp and kGc is easy, as can be seen from Example 2. By applying the effective film thickness concept, we obtain Equation 2.

From operating data, the air-side film coefficient of heat transfer was determined as Estimate the effective thickness of the air film. The heat conductivity of air at 50 1C is 0. Solution From Equation 2. Further Reading 2. The vapor pressure of water at 20 1C is The diffusivity of water vapor in air at the air film temperature is 0. Estimate the effective thickness of the air film above the water surface. Calculate the heat flux and estimate the effective thickness of the water film.

The thermal conductivity of water at 50 1C is 0. Further Reading 1 Bennett, C. Knowledge concerning changes in the compositions of reactants and products, as well as their rates of utilization and production under given conditions, is essential when determining the size of a reactor. With a bioprocess involving biochemical reactions, for example, the formation and disappearance terms in Equation 1. It is important, therefore, that we have some knowledge of the rates of those enzyme-catalyzed biochemical reactions that are involved in the growth of microorganisms, and are utilized for various bioprocesses.

Reactions with particles of catalysts, or of immobilized enzymes and aerobic fermentation with oxygen supply, represent examples of reactions in heterogeneous phases. In this chapter, we will provide the fundamental concepts of chemical and biochemical kinetics, that are important for understanding the mechanisms of bioreactions, and also for the design and operation of bioreactors.

First, we shall discuss general chemical kinetics in a homogeneous phase, and then apply its principles to enzymatic reactions in homogeneous and heterogeneous systems. In Equation 3.

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The rate ri is negative, in case i is a reactant. Several factors, such as temperature, pressure, the concentrations of the reactants, and also the existence of a catalyst, affect the rate of a chemical reaction. In some cases, what appears to be one reaction may in fact involve several reaction steps in series or in parallel, one of which may be rate limiting.

Its value for a given reaction varies with temperature and the properties of the fluid in which the reaction occurs, but is independent of the concentrations of A and B. The dimension of the rate constant varies with the order of a reaction. Equation 3. P This type of reaction for which the rate equation can be written according to the stoichiometry is called an elementary reaction.

Rate equations for such cases can easily be derived. Many reactions, however, are nonelementary, and consist of a series of elementary reactions. In such cases, we must assume all possible combinations of elementary reactions in order to determine one mechanism which is consistent with the experimental kinetic data. Usually, we can measure only the concentrations of the initial reactants and final products, since measurements of the concentrations of intermediate reactions in series are difficult.

Thus, rate equations can be derived under assumptions that rates of change in the concentrations of those intermediates are approximately zero steady-state approximation. An example of such treatment applied to an enzymatic reaction will be shown in Section 3. The frequency factor and the rate constant k should be of the same unit. The frequency factor is related to the number of collisions of reactant molecules, and is slightly affected by temperature in actual reactions.

The activation energy is the minimum excess energy which the reactant molecules should possess for a reaction to occur. From Equation 3. Figure 3. Strictly, the Arrhenius equation is valid only for elementary reactions. Apparent activation energies can be obtained for nonelementary reactions.

From experimental data, the reaction kinetics can be analyzed either by the integration method or by the differential method:. In the integration method, an assumed rate equation is integrated and mathematically manipulated to obtain a best straight line plot to fit the experimental data of concentrations against time. Each of these methods has both merits and demerits. For example, the integration method can easily be used to test several well-known specific mechanisms.

In more complicated cases the differential method may be useful, but this requires more data points.

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Analysis by the integration method can generally be summarized as follows. The rate equation for a reactant A is usually given as a function of the concentrations of reactants. Plotting the left-hand side of Equation 3. If experimental data points fit this straight line well, then the assumed specific mechanism can be considered valid for the system examined. If not, another mechanism could be assumed.

The heat sterilization of microorganisms and heat inactivation of enzymes are examples of first-order reactions. Example 3. Calculate the inactivation constants of a-amylase at each temperature. The heat inactivation of many enzymes follows such patterns. Enzyme reactions may involve uni-, bi-, or tri-molecule reactants and products. An analysis of the reaction kinetics of such complicated enzyme reactions, however, is beyond the scope of this chapter, and the reader is referred elsewhere [1] or to other reference books.

Here, we shall treat only the simplest enzyme-catalyzed reaction — that is, an irreversible, uni-molecular reaction. Enzyme-catalyzed hydrolysis and isomerization reactions are examples of this type of reaction mechanism. In this case, the kinetics can be analyzed by the following two different approaches, which lead to similar expressions. It is assumed that the aforementioned first reaction is reversible and very fast, reaches equilibrium instantly, and that the rate of the product formation is determined by the rate of the second reaction, which is slower and proportional to the concentration of the intermediate.

For the first reaction at equilibrium the rate of the forward reaction should be equal to that of the reverse reaction, as stated in Section 3. Thus, a small value of Km indicates a strong interaction between the substrate and the enzyme. An example of the relationship between the reaction rate and the substrate concentration given by Equation 3.

Here, the reaction rate is roughly proportional to the substrate concentration at low substrate concentrations, and is asymptotic to the maximum rate Vmax at high substrate concentrations. The reaction rate is one-half of Vmax at the substrate concentration equal to Km.

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It is usually difficult to express the enzyme concentration in molar units, because of difficulties in determining the enzyme purity. The definition of an enzyme unit is arbitrary, but one unit is generally defined as the amount of enzyme which produces 1 mmol of the product in 1 minute at the optimal temperature, pH, and substrate concentration. Several types of plots for this purpose have been proposed. Although the Lineweaver—Burk plot is widely used to evaluate the kinetic parameters of enzyme reactions, its accuracy is affected greatly by the accuracy of data at low substrate concentrations.

This plot is suitable for regression by the method of least-squares. Results with a wide range of substrate concentrations can be compactly plotted when using this method, although the measured values of rp appear in both coordinates. In the case of more complicated reactions, additional kinetic parameters must be evaluated, but plots similar to that for Equation 3. The initial reaction rates were obtained as shown in Table 3. Determine the kinetic parameters of this enzyme reaction. Table 3. The straight line was obtained by the method of least-squares.

From the figure, the values of Km and Vmax were determined as 2. Enzyme inhibitors combine, either reversibly or irreversibly, with enzymes and cause a decrease in enzyme activity. Effectors control enzyme reactions by combining with the regulatory site s of enzymes. There are several mechanisms of reversible inhibition and for the control of enzyme reactions. Competitive Inhibition An inhibitor competes with a substrate for the binding site of an enzyme.

As an enzyme—inhibitor complex does not contribute to product formation, it decreases the rate of product formation. Many competitive inhibitors have steric structures similar to substrates, and are referred to as substrate analogues. Product inhibition is another example of such an inhibition mechanism of an enzyme reactions, and is due to a structural similarity between the substrate and 39 40 3 Chemical and Biochemical Kinetics Figure 3.

From Equations 3. At high substrate concentrations, the reaction rates approach the maximum reaction rate, because a large amount of the substrate decreases the effect of the inhibitor. Rearrangement of Equation 3. Other Reversible Inhibition Mechanisms In noncompetitive inhibition, an inhibitor is considered to combine with both an enzyme and the enzyme—substrate complex.

Then, the following rate equation can be obtained by the Figure 3. The hydrolysis rates obtained are listed in Table 3. Determine the inhibition mechanism and the kinetic parameters Km, Vmax, KI of this enzyme reaction. This Lineweaver—Burk plot shows that the mechanism is competitive inhibition.

From the line for the data without the inhibitor, Km and Vmax are obtained as 0. From the slopes of the lines, KI is evaluated as 0. P are obtained at different temperatures, as listed in Table P3. Calculate the frequency factor and the activation energy for this reaction. Find the rate equation and calculate the rate constant for the reaction, using the integration method.

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