Chemical Reaction Engineering

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This section covers the general mole balance equation and its reduction for batch and continuous reactors, an introduction to industrial reactors, mole balances written in terms of conversion, the application of the conversion equation to each reactor type, the calculation of reactors in series, and the definitions of space time and space velocity.

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The General Mole Balance Equation • For any species j in any system volume: in − out + generation = accumulation, or symbolically Fj0 − Fj + ∫rj dV = dNj/dt. • Every reactor design equation in the subject is a special case of this one statement.

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Setting the flow terms to zero gives the batch reactor; setting the accumulation term to zero gives the steady-state flow reactors; assuming perfect mixing removes the integral; assuming no radial gradients gives the plug-flow form. • Sign convention: rA is negative for a reactant being consumed, so the quantity −rA (the rate of disappearance of A) is positive and is what appears in the design equations.

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The rate of reaction is defined per unit volume for homogeneous reactions, per unit mass of catalyst (r′A) for fluid-solid catalytic reactions, and per unit surface area for surface reactions. • The rate law is an algebraic equation, not a differential one, and −rA is a function of concentration and temperature alone, independent of reactor type — a point worth holding on to, because it is what makes the same kinetics usable in every reactor.

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The Four Ideal Reactors Reactor Mode Mole balance Design equation Batch Unsteady, no flow in or out dNA/dt = rAV t = NA0∫0 X dX/(−rAV) Semi-batch One reactant charged, other fed continuously dNA/dt = FA0 + rAV Solved numerically CSTR (mixed flow) Steady, perfectly mixed FA0 − FA + rAV = 0 V = FA0X/(−rA)exit PFR (tubular) Steady, no axial mixing dFA/dV = rA V = FA0∫0 X dX/(−rA) PBR (packed bed) Steady, catalyst mass as the variable dFA/dW = r′A W = FA0∫0 X dX/(−r′A) • The key conceptual distinction: in a CSTR the rate is evaluated at the exit (lowest) concentration throughout the whole volume, because the contents are uniform; in a PFR the rate falls progressively along the length, so the average rate is higher.

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This is precisely why a PFR requires less volume than a CSTR for the same conversion with positive-order kinetics. • The one exception — autocatalytic reactions, in which a product accelerates the reaction: here the low initial rate makes a CSTR superior at low conversion, and the optimum arrangement is a CSTR followed by a PFR.

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Industrial Reactors • Stirred tanks, batch or continuous, dominate the fine chemical, pharmaceutical and polymer industries, where flexibility, small volumes and multiple products matter more than throughput. • Tubular reactors are used for gas-phase reactions at high throughput, such as thermal cracking and steam reforming. • Packed-bed (fixed-bed) reactors hold a stationary catalyst charge and are the standard for ammonia synthesis, sulphuric acid, hydrotreating and methanol; they give near plug flow but are hard to regenerate and may develop hot spots. • Fluidized-bed reactors give uniform temperature and continuous catalyst regeneration, at the price of attrition and back-mixing; fluid catalytic cracking is the classic example. • Trickle beds, bubble columns and slurry reactors handle three-phase gas-liquid-solid systems such as hydrogenation and hydrodesulphurisation.

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Conversion and the Design Equations • Conversion X = (moles of A reacted)/(moles of A fed) = (FA0 − FA)/FA0, defined always with respect to the limiting reactant. • The four design equations in conversion form are worth writing out until they are automatic: • Batch: t = NA0∫dX/(−rAV); for constant volume this is t = CA0∫dX/(−rA). • CSTR:

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V = FA0X/(−rA), with the rate evaluated at exit conditions — an algebraic equation, requiring no integration. • PFR:

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V = FA0∫0 X dX/(−rA). • PBR:

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W = FA0∫0 X dX/(−r′A), giving the mass of catalyst rather than a volume. • Levenspiel plot: plotting FA0/(−rA) against X makes the comparison visual — the PFR volume is the area under the curve and the CSTR volume is the area of the rectangle of height FA0/(−rA) at the exit conversion.

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The rectangle always exceeds the area for a curve that rises with X, which is the geometric statement of the PFR advantage.

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Reactors in Series • For reactors in series, the conversion is always cumulative — measured from the feed to the first reactor, never reset between stages.

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So for the ith CSTR in a chain, Vi = FA0(Xi − Xi−1)/(−rA)i. • N equal CSTRs in series approach plug-flow behaviour as N increases, and the total volume required falls steadily towards the PFR volume.

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For a first-order reaction in N equal CSTRs, CAN/CA0 = 1/(1 + kτi)N, where τi is the space time of one tank. • Ordering of unequal reactors: for a reaction whose rate falls steeply with conversion, the best sequence is generally the arrangement that keeps the rate as high as possible for as long as possible, which for a normal n-th order reaction means PFR first, then CSTR, and for an autocatalytic reaction the reverse. • A PFR is equivalent to an infinite number of infinitesimally small CSTRs in series — the standard conceptual link between the two ideal models.

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Space Time and Space Velocity • Space time τ = V/v₀, the time required to process one reactor volume of feed measured at the entrance conditions.

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Its units are time, and it is the natural measure of reactor size per unit throughput. • Space velocity SV = v₀/V = 1/τ, in reciprocal time.

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Two industrial variants are defined on different bases and are commonly confused:

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LHSV (liquid hourly space velocity) uses the liquid volumetric feed rate measured at 60-70 °F, while GHSV (gas hourly space velocity) uses the gas feed rate measured at standard temperature and pressure. • The distinction that matters: space time equals the mean residence time only when the volumetric flow rate is constant throughout the reactor — true for essentially all liquid-phase reactions but false for a gas-phase reaction in which the number of moles changes, or where there is a large temperature or pressure change.

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In those cases the actual residence time must be found from the varying volumetric flow. • For a variable-density gas reaction, v = v₀(1 + εX)(P₀/P)(T/T₀), where ε = yA0δ and δ is the change in total moles per mole of A reacted.

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An expanding reaction (ε positive) reduces the residence time and hence the conversion below what constant-density analysis would predict.

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This section covers the expression and interpretation of rate laws, reaction rate constants, the design structure for isothermal reactors, the design of batch reactors, of single CSTRs and CSTRs in series, and of tubular reactors, together with pressure drop in reactors and the application of software to reactor design.

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Rate Laws • A power-law rate expression takes the form −rA = k CA αCB β, where α and β are the orders with respect to A and B and α + β is the overall order. • The essential warning: reaction order is determined experimentally and is not in general equal to the stoichiometric coefficient.

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The two coincide only for an elementary reaction, one that proceeds in a single step exactly as written.

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Molecularity, by contrast, is always a small positive integer and applies only to an elementary step, whereas order may be fractional, zero or even negative. • Elementary reactions are identifiable by the rate law matching the stoichiometry; a reversible elementary reaction must have a rate law consistent with the equilibrium constant at equilibrium, which is the thermodynamic consistency requirement.

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Order Rate law Integrated form (constant volume batch) Half-life Units of k Zero −rA = k CA = CA0 − kt CA0/2k mol/(m³·s) First −rA = kCA ln(CA0/CA) = kt 0.693/k s−1 Second −rA = kCA² 1/CA − 1/CA0 = kt 1/(kCA0) m³/(mol·s) n-th (n ≠ 1) −rA = kCA n CA 1−n − CA0 1−n = (n−1)kt ∝ CA0 1−n varies • The half-life test is the quickest way to recognise order: t1/2 is independent of initial concentration only for a first-order reaction; it is proportional to CA0 for zero order and inversely proportional to CA0 for second order.

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Radioactive decay is first order, which is why its half-life is a fixed constant. • Units of the rate constant are a reliable order indicator: for an n-th order reaction, k has units of (concentration)1−n(time)−1.

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The Rate Constant and Temperature • Arrhenius equation: k = A exp(−Ea/RT), with A the frequency or pre-exponential factor and Ea the activation energy, the minimum energy the colliding molecules must possess. • Plotting ln k against 1/T gives a straight line of slope −Ea/R and intercept ln A.

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Between two temperatures, ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂).

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This is the single most examined calculation in the chapter. • A high activation energy makes the rate very temperature sensitive; a low activation energy makes it relatively insensitive.

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The common rule of thumb that the rate roughly doubles for every 10 °C rise near room temperature corresponds to an activation energy of about 50 kJ/mol. • A catalyst lowers the activation energy of both forward and reverse reactions by the same amount, increasing both rates and leaving the equilibrium constant untouched.

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Stoichiometry • Stoichiometric tables express every species concentration in terms of the single variable X. • For a constant-volume (liquid-phase or constant-density gas) system:

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CA = CA0(1 − X) and CB = CA0(ΘB − (b/a)X), where ΘB = FB0/FA0. • For a variable-volume gas-phase system:

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CA = CA0(1 − X)/(1 + εX) × (P/P₀)(T₀/T), with ε = yA0δ. • The effect of expansion: when ε is positive the mixture expands, concentrations fall faster than conversion alone would suggest and the reaction slows; when ε is negative the mixture contracts and the reaction is accelerated.

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Feeding an inert diluent lowers yA0 and therefore damps the expansion effect.

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Isothermal Reactor Design:

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The Algorithm • The standard procedure, which should be followed in this order every time: • 1.

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Mole balance — write the design equation for the reactor type. • 2.

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Rate law — write −rA as a function of concentration. • 3.

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Stoichiometry — express each concentration in terms of X. • 4.

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Combine — substitute to obtain a single equation in X. • 5.

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Evaluate — integrate analytically where possible, otherwise numerically by Simpson's rule or software. • Useful closed-form results that recur constantly: for a first-order liquid-phase reaction in a CSTR, X = kτ/(1 + kτ), and in a PFR, X = 1 − exp(−kτ).

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Comparing these two expressions at the same kτ demonstrates the PFR advantage numerically.

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Pressure Drop in Reactors • Pressure drop is irrelevant to liquid-phase reactions but can dominate gas-phase packed beds, because concentration is proportional to pressure, so a falling pressure lowers the rate. • The Ergun equation governs the drop through the bed.

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In reactor design it is usually written in the compact form dp/dW = −α(T/T₀)(FT/FT0)/2p, where p = P/P₀ and α lumps the bed properties. • Consequences for design: pressure drop reduces conversion in a reaction with ε ≥ 0, and the effect is worse for higher-order reactions.

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It is reduced by using larger catalyst particles, a shorter and wider bed, or a lower mass flux — but larger particles worsen internal diffusion limitation, so the choice of particle size is a trade-off between pressure drop and effectiveness factor. • Software — Polymath, MATLAB, Aspen Plus and COMSOL — is used to integrate the coupled mole, energy and pressure-drop balances that have no analytical solution.

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The examination expects awareness of the role rather than the syntax.

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This section covers the algorithm for data analysis, the determination of rate-law parameters by the differential and integral methods, the method of initial rates and differential reactors, the evaluation of laboratory reactors, yield and selectivity in multiple reactions, maximizing the desired product in series reactions, and the algorithm for the solution of complex reactions.

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Methods of Analysing Rate Data Method Procedure Strengths and limitations Integral method Assume an order, integrate, plot the linearised form and test for a straight line Simple and robust with scattered data; trial and error; works only for simple integer orders Differential method Differentiate the concentration-time data, then plot ln(−rA) against ln CA; slope gives order Handles fractional and complicated orders directly; amplifies scatter through differentiation Method of initial rates Measure the initial rate for several initial concentrations Avoids interference from products and reverse reaction; requires many separate runs Half-life method Measure how the half-life varies with initial concentration Quick order determination; needs accurate long-run data Method of excess Flood the system with all reactants but one, so the rate depends on one species only Reduces a multi-reactant rate law to a pseudo-order; requires large excesses Differential reactor Very small conversion across a thin catalyst bed, so the rate is essentially constant Gives the rate directly at a known composition; needs precise analysis of small differences • In the differential method, the slope of ln(−rA) against ln CA is the order and the intercept is ln k.

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The derivative −dCA/dt is obtained by graphical differentiation, finite differences or polynomial fitting, the last being preferred because it smooths noise. • In the method of excess, if B is in large excess then CB is essentially constant and −rA = k′CA α with k′ = kCB0 β; the order in B is then found by a second set of runs with A in excess.

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The observed k′ is called a pseudo-rate constant and the kinetics pseudo-first-order if α is one. • The differential reactor is the standard laboratory device for catalytic kinetics: because conversion is kept below a few per cent, the concentration is nearly uniform and the measured conversion gives the rate directly as −r′A = FA0X/W. • Laboratory reactor choice: a batch reactor suits slow liquid-phase reactions and gives a full concentration-time curve from one run; a differential reactor suits catalytic kinetics; a CSTR (Berty or recycle) reactor gives the rate directly at steady state with no integration needed at all, which is why recycle reactors are favoured for catalyst testing; and an integral reactor is closest to the industrial unit but hardest to interpret.

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Yield and Selectivity • Parallel (competing) reactions:

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A → D (desired) and A → U (undesired). • Series (consecutive) reactions:

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A → B → C, where B is usually the desired product. • Independent and complex reactions combine both features. • Instantaneous selectivity SD/U = rD/rU, the ratio of the rates at a point; overall selectivity S̃ = FD/FU, the ratio of the molar flows leaving. • Instantaneous yield YD = rD/(−rA); overall yield = moles of D formed / moles of A consumed.

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Yield is referenced to the reactant consumed and selectivity to the competing product — confusing the two is a standard examination trap.

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Maximising the Desired Product • For parallel reactions, form the selectivity ratio: if rD/rU = (kD/kU)CA α₁−α₂, then: • If α₁ > α₂ (desired reaction of higher order), keep CA high — use a batch or PFR, no diluent, high pressure for gases, low conversion. • If α₁ < α₂ (desired reaction of lower order), keep CA low — use a CSTR, a diluent, low pressure, high conversion, or a semi-batch reactor with slow addition of A. • With two reactants, a semi-batch or side-feed (membrane) reactor allows one concentration to be kept high and the other low simultaneously, which is the key to many selectivity problems. • Temperature is the other lever: if the desired reaction has the higher activation energy, use a high temperature; if lower, use a low temperature, because the ratio of rate constants varies as exp[−(ED − EU)/RT]. • For series reactions A → B → C, the concentration of B passes through a maximum.

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For first-order steps in a batch reactor or PFR, the optimum time is topt = ln(k₂/k₁)/(k₂ − k₁), and the maximum yield of B is higher in a PFR than in a CSTR.

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Over-reaction is the danger: running longer than topt destroys B.

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If k₂ is much larger than k₁, B is consumed almost as fast as it forms and little can ever be recovered.

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Algorithm for Complex Reactions • Where several reactions occur together the procedure generalises: number the reactions, write the net rate of formation of each species as the algebraic sum of its rates in every reaction (rj = Σ rij), relate the rates within each reaction by its own stoichiometry, write a mole balance for every species rather than a single conversion, and solve the resulting set of coupled equations numerically. • Conversion is not a useful variable for multiple reactions — the balances are written in terms of molar flow rates or concentrations of each species instead.

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This is an important conceptual point and is asked directly.

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This section covers the pseudo-steady-state hypothesis, the search for a mechanism, chain reactions and reaction pathways, enzymatic reaction fundamentals with inhibition and bioreactors, and the derivation and application of the energy balance to adiabatic reactors, non-adiabatic tubular reactors, equilibrium reactors and non-adiabatic CSTRs.

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The Pseudo-Steady-State Hypothesis • Most reactions proceed through active intermediates — free radicals, ions, enzyme complexes or excited molecules — that are highly reactive and present in very small concentrations. • The pseudo-steady-state hypothesis (PSSH) sets the net rate of formation of each active intermediate equal to zero, because it is consumed as fast as it is produced.

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This converts a set of differential equations into algebraic ones that can be solved for the intermediate concentration and eliminated, yielding a rate law in terms of stable species only. • The PSSH is the standard route from a postulated mechanism to an observable rate law, and it explains why many overall reactions show fractional or pressure-dependent orders. • Searching for a mechanism: the accepted procedure is to postulate a set of elementary steps, apply the PSSH to every intermediate, derive the rate law, and compare its form with the experimental data.

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A mechanism can be disproved by data but never finally proved; agreement makes it plausible, no more.

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A species appearing in the denominator of the rate law usually appears as a reactant in a reverse step, and a species in the numerator as a reactant in a forward step — a useful diagnostic.

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Chain Reactions • A chain reaction proceeds through four kinds of step: initiation (generation of radicals, often by thermal or photochemical bond breaking), propagation (a radical reacts to give a product and another radical, so the chain continues), chain transfer (the radical centre moves to another molecule) and termination (two radicals combine and the chain ends). • Chain length is the number of propagation cycles per initiation event and may be enormous; this is why a trace of initiator can convert a large mass of monomer. • Branching chain reactions, in which one radical generates more than one, are the basis of explosions: hydrogen-oxygen and hydrocarbon combustion show explosion limits where branching overtakes termination. • Inhibitors and antioxidants work by scavenging radicals and terminating chains, which is why they are effective in very small quantities.

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Enzyme Kinetics • Enzymes are protein catalysts of extraordinary specificity and activity, operating under mild conditions of temperature and pH.

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The lock-and-key and the more accurate induced-fit models describe substrate binding at the active site. • Michaelis-Menten mechanism:

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Applying the PSSH to the complex ES gives the Michaelis-Menten equation −rS = VmaxCS/(KM + CS). • Interpretation, which is examined directly:

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Vmax = kcatEt is the maximum rate at saturating substrate and is proportional to total enzyme;

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KM, the Michaelis constant, is the substrate concentration at which the rate is half of Vmax, and a low KM indicates a high affinity of enzyme for substrate. • Limiting behaviour: at CS ≪ KM the kinetics are first order in substrate; at CS ≫ KM they are zero order and the enzyme is saturated. • Lineweaver-Burk plot of 1/(−rS) against 1/CS is linear with slope KM/Vmax and intercept 1/Vmax, and is the classical way of extracting the parameters; the Eadie-Hofstee and Hanes-Woolf plots are statistically better alternatives.

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Inhibition type Binds to Effect on Vmax Effect on apparent KM Overcome by excess substrate? Competitive Free enzyme, at the active site Unchanged Increased Yes Uncompetitive Enzyme-substrate complex only Decreased Decreased No Non-competitive (mixed) Both enzyme and complex, away from the active site Decreased Unchanged No Substrate inhibition A second substrate molecule binds Rate passes through a maximum with CS — No — excess makes it worse Bioreactors and Cell Growth • Cell growth follows the phases lag, exponential, stationary and death.

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The Monod equation μ = μmaxCS/(KS + CS) describes the specific growth rate and has exactly the same hyperbolic form as Michaelis-Menten. • Chemostat: a CSTR for cells operating at steady state.

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A material balance on cells gives the central result μ = D, where D = v₀/V is the dilution rate — that is, the cells grow at exactly the rate at which they are washed out. • Washout occurs when the dilution rate exceeds the maximum specific growth rate, because the culture can no longer keep pace; the productivity of a chemostat is maximised just below the washout point. • Yield coefficients such as YX/S (mass of cells per mass of substrate) and YP/S link growth, substrate consumption and product formation.

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Energy Balances for Non-isothermal Reactors • The steady-state energy balance for a flow reactor is Q̇ − Ẇs − FA0Σ ΘiCpi(T − T₀) − ΔHrxnFA0X = 0.

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Combined with the mole balance it gives two coupled equations in X and T that must be solved together. • Adiabatic operation (Q̇ = 0) gives the simple and heavily examined result T = T₀ + (−ΔHrxn)X/(Σ ΘiCpi) — a straight line relating temperature to conversion, called the energy balance line.

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For an exothermic reaction the temperature rises linearly with conversion; the adiabatic temperature rise at complete conversion is a key safety figure. • Equilibrium (reversible) reactions: for an exothermic reversible reaction the equilibrium conversion falls as temperature rises, while the adiabatic energy balance line rises.

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The intersection of the two curves is the adiabatic equilibrium conversion, and to exceed it the reaction must be run in stages with interstage cooling — exactly the arrangement used in sulphur dioxide oxidation and ammonia synthesis. • Non-adiabatic tubular reactors add a heat-exchange term, dT/dV = [Ua(Ta − T) + (−ΔHrxn)(−rA)]/(FA0ΣΘiCpi), which must be integrated numerically along with the mole balance. • Hot spots and parametric sensitivity: in an exothermic packed-bed reactor with wall cooling, the temperature may rise sharply at some point along the bed.

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Near the runaway boundary, a very small change in coolant temperature or feed composition produces a disproportionately large change in the peak temperature — the phenomenon of parametric sensitivity, which is a central safety concern. • Non-adiabatic CSTR and multiple steady states: plotting the heat generated G(T), an S-shaped curve, against the heat removed R(T), a straight line, may give one or three intersections.

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Where there are three, the upper and lower are stable and the middle one is unstable; which is reached depends on the start-up path, and the sudden jump between branches as a parameter is varied is called ignition-extinction hysteresis.

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This section covers catalysts and the steps in a catalytic reaction, reaction mechanisms and the synthesis of a rate law, heterogeneous data analysis, chemical vapour deposition and catalyst deactivation, the effects of external and internal diffusion on heterogeneous reactions, and the characterization, measurement and use of residence time distributions in reactor modelling.

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Catalysts and Catalytic Reaction Steps • A catalyst provides an alternative reaction path of lower activation energy, increasing the rate of both the forward and reverse reactions equally and leaving the equilibrium position unchanged.

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Its industrial value lies as much in selectivity as in speed. • Catalyst structure: an active component (often a metal) dispersed on a high-area support or carrier (alumina, silica, carbon, zeolite), with promoters added to enhance activity or stability.

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Typical surface areas run from 100 to over 1000 m²/g, nearly all of it inside the pores. • The seven steps of a heterogeneous catalytic reaction, in order — a certainty in the examination: • 1.

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External diffusion of reactant from the bulk fluid to the outer surface. • 2.

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Internal diffusion through the pores to the active site. • 3.

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Adsorption of the reactant on the site. • 4.

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Surface reaction. • 5.

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Desorption of the product from the site. • 6.

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Internal diffusion of product out through the pores. • 7.

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External diffusion of product to the bulk fluid. • The slowest step controls the overall rate, and identifying it is the object of heterogeneous data analysis.

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Adsorption and Rate-Law Synthesis • Physisorption involves weak van der Waals forces, a low heat of adsorption (under about 40 kJ/mol), is multilayer, non-specific and fully reversible, and occurs at low temperature.

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Chemisorption involves chemical bonding, a high heat of adsorption (80-400 kJ/mol), is monolayer, highly specific and often irreversible, and is the form responsible for catalysis. • Langmuir isotherm: θ = KP/(1 + KP), derived assuming a uniform surface, monolayer coverage, no interaction between adsorbed molecules and dynamic equilibrium between adsorption and desorption.

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The BET isotherm extends this to multilayer adsorption and is the standard method for measuring catalyst surface area, using nitrogen at 77 K. • Langmuir-Hinshelwood mechanism: both reactants adsorb on the surface and react there; this is the commoner case.

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Eley-Rideal mechanism: one reactant adsorbs and reacts directly with the other from the gas phase. • Synthesising a rate law: postulate which step is rate limiting, write equilibrium expressions for the remaining steps, and assemble the result.

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The characteristic form is rate = (kinetic term × driving force)/(adsorption term), with the adsorption term raised to a power equal to the number of sites involved.

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A product appearing in the denominator indicates that it is adsorbed and inhibiting the reaction, which is a very common interpretive question.

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External and Internal Diffusion • External (film) diffusion control is recognised by a strong dependence of the rate on fluid velocity — raising the velocity thins the film and raises the rate — and by a low apparent activation energy of only a few kJ/mol, since diffusion is weakly temperature dependent. • Internal (pore) diffusion is characterised by the Thiele modulus φ, essentially the ratio of the reaction rate to the diffusion rate, and by the effectiveness factor η = actual rate / rate with no diffusion resistance. • The two limits: for a small Thiele modulus (φ ≪ 1) the reaction is slow relative to diffusion, the pellet is uniform in concentration and η approaches 1 — the reaction is kinetically controlled.

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For a large Thiele modulus (φ ≫ 1) diffusion cannot keep up, reaction is confined to a thin outer shell, and η ≈ 1/φ, falling inversely with particle size. • Diagnostics for internal diffusion limitation: the apparent reaction order shifts towards (n + 1)/2, so a true first-order reaction still appears first order but a true second-order reaction appears 1.5 order; and the apparent activation energy falls to about half the true value.

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These two signatures are asked about repeatedly. • Remedies: smaller particles, or egg-shell catalysts with the active material only near the outer surface — but smaller particles increase pressure drop, giving the trade-off already noted in 4.2.

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Catalyst Deactivation and CVD Mechanism Cause Reversible ? Countermeasure Sintering (ageing) Loss of active surface area by crystallite growth at high temperature No Limit temperature; use thermally stable supports and promoters Coking / fouling Carbonaceous deposit blocking pores and sites Yes Burn off in air or steam; add hydrogen to the feed Poisoning Strong chemisorption of an impurity such as sulphur, lead or arsenic Often not Purify the feed; use guard beds and sacrificial layers Volatilisation / attrition Loss of active species or physical breakdown No Change formulation or operating conditions • Decay laws express the activity a(t), and deactivation may be independent of concentration, or linear or exponential in time.

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The reactor is then designed to compensate by raising the temperature progressively, using a moving or fluidized bed for continuous regeneration, or by the straight-through transport reactor used in catalytic cracking. • Chemical vapour deposition (CVD) deposits a solid film from gaseous precursors on a heated substrate, and is analysed with exactly the same surface-kinetics machinery: adsorption, surface reaction, desorption and diffusion through a boundary layer.

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It is central to semiconductor manufacture; the deposition rate is surface-reaction controlled at low temperature and mass-transfer controlled at high temperature, and the low-temperature regime is preferred because it gives better film uniformity.

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Residence Time Distribution • Real reactors deviate from the ideal models through channelling, dead zones, short-circuiting (bypassing), internal recirculation and stagnant regions.

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The residence time distribution (RTD) characterises this quantitatively. • Measurement uses a tracer, injected either as a pulse, which gives the E(t) curve directly after normalisation, or as a step, which gives the cumulative F(t) curve, the two being related by E(t) = dF(t)/dt. • Properties: ∫E(t)dt = 1; the mean residence time tm = ∫tE(t)dt; and the variance σ² = ∫(t − tm)²E(t)dt, which measures the spread. • The two ideal limits, which must be known: for a PFR, E(t) is a spike at t = τ and σ² = 0; for a single CSTR, E(t) = (1/τ)exp(−t/τ), an exponential decay, and σ² = τ². • Diagnosis from the curve: an early sharp peak indicates bypassing or channelling; a long tail indicates dead zones or stagnant regions; a mean residence time less than V/v₀ indicates dead volume; and multiple peaks indicate internal recirculation or parallel paths. • Models: the tanks-in-series model characterises non-ideality by N = τ²/σ², with N = 1 a single CSTR and N → ∞ a PFR; the dispersion model uses the vessel dispersion number D/uL, with zero for plug flow and infinity for perfect mixing. • The limitation that is asked about: the RTD alone does not determine conversion except for first-order reactions.

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For other orders, the degree of micromixing matters too, and the RTD only bounds the answer between the complete segregation and maximum mixedness models.

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This section covers the basics of microbiology, the chemicals of life — lipids, sugars and polysaccharides, nucleotides through to RNA and DNA, amino acids, peptides and proteins, and hybrid biochemicals — together with the kinetics of enzyme-catalysed reactions, metabolic stoichiometry and energetics, and molecular genetics and control systems.

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Basics of Microbiology Group Cell type Key features Industrial relevance Bacteria Prokaryotic No nucleus or membrane-bound organelles;

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0.5-5 μm; rapid growth; binary fission Amino acids, antibiotics, enzymes, recombinant proteins (E. coli) Yeasts Eukaryotic Single-celled fungi, 5-10 μm; budding; facultative anaerobes Ethanol, baking, brewing, heterologous protein expression Moulds (filamentous fungi) Eukaryotic Grow as hyphae forming a mycelium; aerobic Penicillin, citric acid, industrial enzymes Algae Eukaryotic Photosynthetic; need light and CO₂ Biofuels, pigments, food supplements Viruses Acellular Obligate intracellular parasites; a nucleic acid in a protein coat Vaccines, gene-therapy vectors, bacteriophage contamination • Prokaryotic versus eukaryotic is the central distinction: prokaryotes lack a membrane-bound nucleus and organelles and carry a single circular chromosome; eukaryotes have a true nucleus, mitochondria and linear chromosomes.

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Bacteria are prokaryotic; yeasts, moulds, algae, plant and animal cells are eukaryotic. • Gram staining divides bacteria by cell-wall structure:

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Gram-positive cells have a thick peptidoglycan layer and stain purple;

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Gram-negative cells have a thin layer plus an outer lipopolysaccharide membrane and stain pink. • Sterilisation is essential for most fermentations, usually by steam at 121 °C for 15-20 minutes for media and equipment, and by filtration through 0.2 μm membranes for heat-sensitive liquids and for air.

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The Chemicals of Life • Carbohydrates: monosaccharides (glucose, fructose, galactose — all C₆H₁₂O₆ and isomers of one another), disaccharides (sucrose = glucose + fructose, lactose = glucose + galactose, maltose = glucose + glucose) and polysaccharides (starch and glycogen as energy stores, cellulose and chitin as structural materials).

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Starch and cellulose are both glucose polymers and differ only in the linkage — α-1,4 in starch, β-1,4 in cellulose — which is why humans can digest starch but not cellulose. • Lipids are defined by solubility rather than structure: fats and oils (triglycerides), phospholipids, steroids and waxes.

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Phospholipids, being amphipathic, form the bilayer of every cell membrane.

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Lipids are the most energy dense of the food groups, at about 38 kJ/g against 17 kJ/g for carbohydrate and protein. • Amino acids, peptides and proteins: there are 20 standard amino acids, each with an amino group, a carboxyl group, a hydrogen and a distinguishing side chain (R) on the same α-carbon.

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They join by peptide (amide) bonds formed with the loss of water.

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Protein structure is described at four levels — primary (the sequence), secondary (α-helix and β-sheet, held by hydrogen bonds), tertiary (the overall three-dimensional fold) and quaternary (the assembly of several subunits).

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Denaturation by heat, extreme pH or solvents destroys the higher-order structure while leaving the primary sequence intact, and it is why enzymes lose activity above a modest temperature. • Nucleotides, RNA and DNA: a nucleotide comprises a phosphate group, a five-carbon sugar and a nitrogenous base.

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DNA has deoxyribose and the bases A, T, G and C, and is double-stranded in a helix;

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RNA has ribose, uses U in place of T, and is normally single-stranded.

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Base pairing is A with T (two hydrogen bonds) and G with C (three), which is why GC-rich DNA has a higher melting temperature.

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ATP is the universal energy currency of the cell. • Hybrid biochemicals combine classes: glycoproteins and proteoglycans (sugar plus protein, important in cell recognition and in the quality of therapeutic proteins), lipoproteins (lipid transport in blood, LDL and HDL) and glycolipids (membrane surface markers).

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Enzyme Kinetics in the Biochemical Context • Enzymes are classified into six principal groups: oxidoreductases (electron transfer), transferases (group transfer), hydrolases (hydrolysis), lyases (non-hydrolytic bond cleavage), isomerases (rearrangement) and ligases (bond formation with ATP). • Activity depends sharply on temperature and pH: the rate rises with temperature until denaturation sets in, giving a distinct optimum, typically 30-45 °C for most industrial enzymes, and each enzyme has a characteristic optimum pH — about 2 for pepsin and 8 for trypsin. • Immobilised enzymes, attached by adsorption, covalent bonding, entrapment, encapsulation or cross-linking, allow reuse, continuous operation and easy separation from the product, and often improve stability — but introduce diffusion resistance, so the observed kinetics are affected in exactly the way described for heterogeneous catalysts in 4.5, with an effectiveness factor below one and an apparent KM that is higher than the intrinsic value. • The Michaelis-Menten equation, its parameters and the inhibition patterns set out in 4.4 apply unchanged here, and are examined in either context.

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Metabolic Stoichiometry and Energetics • Catabolism breaks substrates down and releases energy, captured as ATP; anabolism builds cell material and consumes energy.

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Together they make up metabolism. • Glycolysis converts one mole of glucose to two of pyruvate with a net gain of 2 ATP and 2 NADH, and occurs in the cytoplasm without oxygen. • Aerobic respiration continues through the tricarboxylic acid (Krebs) cycle and the electron transport chain, yielding in total about 30-32 ATP per glucose — the figure formerly quoted as 36-38. • Anaerobic fermentation yields only the 2 ATP of glycolysis, the pyruvate being reduced to ethanol and CO₂ by yeast, or to lactic acid by lactic acid bacteria and by muscle.

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Ethanol fermentation from glucose:

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C₆H₁₂O₆ → 2 C₂H₅OH + 2 CO₂, with a theoretical yield of 51.1 per cent ethanol by mass — a figure worth remembering. • The Pasteur effect is the suppression of fermentation by oxygen; the Crabtree effect is the opposite phenomenon, in which high glucose concentration causes yeast to ferment even when oxygen is present, which is a real constraint in baker's yeast production and is handled by fed-batch operation with controlled glucose feeding. • Elemental balances on C, H, O and N, together with a degree-of-reduction balance, are the standard tools for writing a stoichiometric equation for growth.

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The respiratory quotient, RQ = moles CO₂ produced / moles O₂ consumed, is measured on-line and is widely used to infer the metabolic state of a fermentation.

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Molecular Genetics and Control • The central dogma:

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DNA → (transcription) → RNA → (translation) → protein, with replication copying DNA.

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Reverse transcription, from RNA to DNA, is the exception exploited by retroviruses and by laboratory cDNA synthesis. • The genetic code is read in triplets (codons); it is degenerate, since most amino acids have several codons, but unambiguous.

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AUG is the start codon and also codes for methionine;

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UAA, UAG and UGA are stop codons.

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Three types of RNA participate: mRNA carries the message, tRNA brings the amino acids, and rRNA forms the ribosome. • Gene regulation in bacteria is classically described by the operon model of Jacob and Monod.

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The lac operon is inducible — normally off, and switched on by lactose, which inactivates the repressor; the trp operon is repressible — normally on, and switched off when tryptophan accumulates.

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This inducible-versus-repressible contrast is a standard examination question. • Recombinant DNA technology: a gene is cut with restriction endonucleases, joined into a plasmid vector with DNA ligase, and transformed into a host such as E. coli or yeast, which then expresses the protein.

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Selection markers, usually antibiotic resistance, identify successful transformants.

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Industrially important products made this way include insulin, human growth hormone, interferons and a wide range of enzymes. • Plasmid instability — segregational loss of the plasmid, or the slower growth of plasmid-bearing cells — is the central engineering problem of recombinant fermentation, since unproductive cells eventually outgrow productive ones; it is countered by selection pressure and by using tightly regulated, inducible promoters so that the product is made only after growth is complete.