Introduction to Chemical Engineering

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This section outlines the scope of chemical engineering and then covers the classification of reactions, the definition of reaction rate, the variables affecting it, order and molecularity, elementary and non-elementary reactions, the Arrhenius law and activation energy, and reaction equilibrium.

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Overview of Chemical Engineering • Chemical engineering is the branch of engineering concerned with the design, operation, control and optimisation of processes that transform raw materials into useful products by chemical, physical or biological change, at an economic scale and with acceptable safety and environmental impact. • The unit operations concept (Arthur D.

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Little, 1915) is its organising idea: however different two processes may appear, they are built from the same small set of physical steps — fluid flow, heat transfer, evaporation, distillation, absorption, extraction, drying, crystallisation, filtration, size reduction and mixing.

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Alongside these are the unit processes, the chemical conversions of 1.5 — oxidation, nitration, halogenation, hydrogenation, hydrolysis, polymerisation, alkylation, esterification and sulphonation. • The core disciplines of the subject, which are also the chapters of this paper: stoichiometry and material and energy balances; thermodynamics; fluid mechanics; heat and mass transfer; chemical reaction engineering; separation processes; process control; plant design and economics; and safety and environmental engineering. • Industrial relevance in Nepal: cement, sugar, paper, soap and detergent, vegetable ghee and edible oil refining, brewing and distilling, dairy processing, pharmaceuticals, plastics and PVC pipe, fertiliser handling, water and wastewater treatment, and herbal and essential oil extraction.

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Classification of Reactions Basis Classes Number of phases Homogeneous — reaction occurs in one phase throughout (most gas-phase and liquid-phase reactions); heterogeneous — at least two phases are involved and reaction occurs at the interface (gas-solid catalysis, combustion of coal, gas-liquid absorption with reaction) Catalyst Catalytic or non-catalytic Direction Irreversible (proceeds essentially to completion) or reversible (attains equilibrium with both reactants and products present) Thermal effect Exothermic (ΔH negative, heat released) or endothermic (ΔH positive, heat absorbed) Number of reactions Single — one stoichiometric equation and one rate expression suffices; multiple — series (consecutive, A → B → C), parallel (competing, A → B and A → C), or series-parallel.

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With multiple reactions, selectivity and yield become as important as conversion Mechanism Elementary — occurs in a single step exactly as written, so the rate law follows directly from the stoichiometry; non-elementary — the observed stoichiometry is the net result of several elementary steps, so the rate law must be determined experimentally and often contains fractional or negative orders Molecularity Unimolecular, bimolecular or termolecular — applies only to an elementary step; termolecular steps are rare because three-body collisions are improbable Rate of Reaction and the Variables Affecting It • The rate of reaction is defined as the change in the moles of a species per unit time per unit volume (for homogeneous reactions), or per unit mass or surface of catalyst (for heterogeneous ones): −rA = −(1/V)·dNA/dt, with the minus sign for a reactant being consumed.

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It is intensive, always positive as defined for consumption, and must be referred to a stated species, since the rates for different species are related by the stoichiometric coefficients: for aA + bB → cC, (−rA)/a = (−rB)/b = rC/c. • Variables affecting the rate: concentration (or partial pressure) of the reactants — the more crowded the molecules, the more frequent the collisions; temperature, by far the strongest variable, acting through the Arrhenius term below; pressure, significant for gas-phase reactions because it changes concentration; catalyst, which provides an alternative pathway of lower activation energy; the nature of the reactants and the bonds to be broken; surface area and degree of mixing in heterogeneous systems; light in photochemical reactions; and the presence of inhibitors or inert diluents. • Collision theory holds that molecules must collide with at least the activation energy and with the correct orientation, so only a small fraction of collisions are effective; transition state theory describes the reactants passing through a high-energy activated complex at the top of the energy barrier.

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Order, Molecularity and the Rate Law • The rate law expresses the rate as a function of concentrations, typically −rA = kCA αCB β.

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Here α and β are the orders with respect to A and B, and their sum n = α + β is the overall order. • The distinction between order and molecularity is one of the most frequently examined points in the whole paper: order is an experimentally determined quantity, obtained from the rate law, which may be zero, fractional or even negative and has no mechanistic meaning for a non-elementary reaction; molecularity is the number of molecules taking part in a single elementary step, is necessarily a small positive integer (1, 2 or rarely 3), and is a theoretical concept applying only to an elementary step.

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For an elementary reaction alone, the order equals the molecularity. • The rate constant k is independent of concentration but depends strongly on temperature.

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Its units depend on the overall order: for an n-th order reaction, k has units of (concentration)1−n·(time)−1 — so zero order: mol/L·s; first order: s−1; second order:

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Being asked to deduce the order from the units of k is a standard question. • Integrated rate laws for a constant-volume batch reactor: • Zero order:

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CA = CA0 − kt; a plot of CA against t is linear; t1/2 = CA0/2k, so the half-life is proportional to the initial concentration. • First order: ln(CA0/CA) = kt, or CA = CA0e−kt; a plot of ln CA against t is linear; t1/2 = 0.693/k, independent of the initial concentration — the characteristic test for first order, and the same relation as radioactive decay. • Second order (single reactant):

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1/CA − 1/CA0 = kt; a plot of 1/CA against t is linear; t1/2 = 1/(kCA0), inversely proportional to the initial concentration. • Methods of determining the order: the integral method (assume an order, plot the corresponding function and test for linearity — good for simple orders); the differential method (plot ln(−rA) against ln CA; the slope is the order — suitable for fractional orders); the half-life method, using t1/2 ∝ CA0 1−n; and the method of excess (isolation), in which all but one reactant is present in large excess so that the reaction becomes pseudo-first-order in the remaining one.

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Arrhenius Law and Activation Energy • The Arrhenius equation is the central relation of kinetics: k = A·e−Ea/RT, where A is the frequency (pre-exponential) factor, Ea the activation energy, R the gas constant and T the absolute temperature. • Logarithmic form: ln k = ln A − Ea/(R·T).

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A plot of ln k against 1/T — the Arrhenius plot — is therefore a straight line of slope −Ea/R and intercept ln A, which is how Ea is measured.

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Between two temperatures, ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂). • Activation energy is the minimum energy that colliding molecules must possess for reaction to occur — the height of the energy barrier between reactants and products.

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A high activation energy means a strongly temperature-sensitive reaction; a rough working rule is that many reactions roughly double or treble their rate for a 10 °C rise near room temperature.

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Note that activation energy is not related to the heat of reaction: ΔH is the difference in energy between reactants and products, whereas Ea is the height of the barrier between them, and Ea,forward − Ea,reverse = ΔH. • Catalysis: a catalyst provides an alternative reaction pathway of lower activation energy, thereby increasing the rate.

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The essential points, all examinable: it is not consumed in the overall reaction; it speeds the forward and reverse reactions equally, so it shortens the time to reach equilibrium but does NOT shift the equilibrium position or change ΔG, ΔH or K; and it does not make a thermodynamically impossible reaction occur.

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Catalysts may be homogeneous (same phase, such as an acid in solution), heterogeneous (a solid in contact with gas or liquid, as in ammonia synthesis or catalytic cracking) or biological (enzymes), and they may be deactivated by poisoning, fouling, sintering or coking.

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Reversible Reactions and Equilibrium • In a reversible reaction, products re-form reactants, and the system approaches a dynamic equilibrium in which the forward and reverse rates are equal and the composition ceases to change, although both reactions continue. • The equilibrium constant for aA + bB ⇌ cC + dD is Kc = [C]c[D]d/([A]a[B]b), with Kp = Kc(RT)Δn, where Δn is the change in the number of moles of gas.

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At equilibrium K = kforward/kreverse, which connects kinetics to thermodynamics, and ΔG° = −RT ln K. • The van 't Hoff equation, d(ln K)/dT = ΔH°/(RT²), shows that K increases with temperature for an endothermic reaction and decreases for an exothermic one. • Le Chatelier's principle: a system at equilibrium subjected to a change responds so as to partly offset that change.

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Hence raising the temperature favours the endothermic direction; raising the pressure favours the side with fewer moles of gas; adding a reactant or removing a product drives the reaction forward; and adding an inert gas at constant volume has no effect, while at constant pressure it shifts the equilibrium towards the side with more moles.

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This is the reasoning behind the operating conditions of every industrial reversible process — the Haber ammonia synthesis at high pressure and moderate temperature being the classic illustration of the compromise between equilibrium yield (favoured by low temperature) and rate (favoured by high temperature).

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This section covers the ideal gas law, real gases and their equations of state, compressibility charts, real gas mixtures, phase diagrams and the phase rule, and vapour-liquid equilibrium in single- and multi-component systems.

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Ideal Gases • The ideal gas law, PV = nRT, combines Boyle's, Charles's and Avogadro's laws.

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It rests on the assumptions that molecules occupy negligible volume and exert no intermolecular forces, and it is therefore accurate at low pressure and high temperature, where molecules are far apart. • Values of R worth memorising:

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8.314 J/mol·K = 8.314 kPa·m³/kmol·K = 0.08206 L·atm/mol·K = 1.987 cal/mol·K.

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At standard conditions (0 °C, 1 atm) one kmol occupies 22.414 m³, and at NTP (25 °C, 1 atm) 24.45 m³ — figures used constantly in material balance work. • Partial pressure and Dalton's law: in an ideal gas mixture the total pressure is the sum of the partial pressures, and pi = yiP, where yi is the mole fraction.

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Amagat's law states the corresponding result for volumes, so that for an ideal gas the mole fraction, the volume fraction and the pressure fraction are numerically equal — the reason gas analyses may be quoted interchangeably by volume or by mole.

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Real Gases and Equations of State • Real gases deviate from ideality because molecules do occupy volume and do attract one another.

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The deviations are large at high pressure and near the critical point or the condensation line. • The compressibility factor is the simplest measure:

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Z = PV/(nRT), so that Z = 1 for an ideal gas.

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Z below 1 indicates that attractive forces dominate (the gas is more compressible than ideal), and Z above 1 that molecular volume dominates, which is the case at high pressure. • The law of corresponding states and the generalised compressibility chart: defining the reduced properties Tr = T/Tc, Pr = P/Pc, it is found that Z is very nearly the same function of Tr and Pr for all gases.

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A single chart therefore serves for every gas, and this is the standard practical method: look up Tc and Pc, compute the reduced properties, read Z from the chart and use PV = ZnRT.

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Kay's rule extends this to mixtures by using pseudo-critical properties, Tpc = Σ yiTci and Ppc = Σ yiPci.

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Equation of state Form and features Ideal gas PV = nRT — simplest, accurate only at low P and high T van der Waals (P + a/Vm²)(Vm − b) = RT, where a corrects for intermolecular attraction and b for the finite volume of the molecules; the first and most instructive real-gas equation, and it predicts the critical point, but it is only moderately accurate Redlich-Kwong, Soave-RK and Peng-Robinson Two- and three-parameter cubic equations of state with a temperature-dependent attraction term; far more accurate, especially for vapour-liquid equilibrium, and the equations actually used in process simulators Virial equation Z = 1 + B/Vm + C/Vm² + …, a power series with a sound theoretical basis; the second virial coefficient B accounts for two-body interactions, and truncation after two terms is accurate at moderate pressure Compressibility chart A graphical method rather than an equation; quick, general and adequate for most engineering calculations Phase Diagrams and the Phase Rule • Gibbs phase rule:

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F = C − P + 2, where F is the number of degrees of freedom (the number of intensive variables that may be independently fixed), C the number of components and P the number of phases in equilibrium.

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The 2 accounts for temperature and pressure; if one of these is fixed the rule becomes F = C − P + 1, and with r independent chemical reactions the component count is reduced, C = (number of species) − r. • Application to a single-component (one-component) system, such as water: with one phase, F = 1 − 1 + 2 = 2, so temperature and pressure may both be varied independently (an area on the diagram); with two phases in equilibrium, F = 1, so fixing the temperature fixes the pressure (a line — the vapour pressure curve, fusion curve or sublimation curve); and with three phases, F = 0, an invariant point — the triple point, which for water is at 0.01 °C and 0.611 kPa. • Features of a P-T diagram: the sublimation, fusion and vaporisation curves meeting at the triple point; the critical point, at which the vaporisation curve ends and the liquid and vapour become indistinguishable — above the critical temperature no amount of pressure will liquefy the gas (for water, 374 °C and 22.1 MPa); and the supercritical region beyond it, exploited in supercritical fluid extraction.

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Water is anomalous in that its fusion curve has a negative slope, because ice is less dense than liquid water. • The Clausius-Clapeyron equation relates vapour pressure to temperature: ln(P₂/P₁) = −(ΔHvap/R)(1/T₂ − 1/T₁), so a plot of ln P against 1/T is linear with slope −ΔHvap/R; the Antoine equation, log P = A − B/(T + C), is its practical correlation form.

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Vapour-Liquid Equilibrium • Raoult's law describes an ideal solution: pi = xi·Pi sat — the partial pressure of a component above the liquid equals its mole fraction in the liquid times its pure-component vapour pressure.

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Combined with Dalton's law this gives the fundamental VLE relation yiP = xiPi sat, and hence the relative volatility α = (yA/xA)/(yB/xB) = PA sat/PB sat, which measures how easily two components can be separated by distillation — the larger α is, the easier the separation, and at α = 1 separation by ordinary distillation is impossible. • Henry's law applies to a dilute solute, typically a sparingly soluble gas: pi = H·xi, and it is the basis of gas absorption calculations. • Deviations from ideality are expressed by the activity coefficient γ, giving yiP = γixiPi sat.

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Positive deviations (γ > 1) arise when unlike molecules repel and may produce a minimum-boiling azeotrope — ethanol and water at 95.6 % ethanol is the classic example, and the reason absolute alcohol cannot be made by simple distillation; negative deviations (γ < 1) may produce a maximum-boiling azeotrope, as with nitric acid and water.

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An azeotrope is a mixture whose vapour has the same composition as the liquid, so it boils at constant temperature and cannot be separated by ordinary distillation, requiring instead azeotropic, extractive or pressure-swing distillation or a membrane process. • Diagrams used: the T-x-y diagram at constant pressure, whose upper curve is the dew point (saturated vapour) line and lower curve the bubble point (saturated liquid) line, with a two-phase region between them across which tie-lines are drawn and the lever rule gives the relative amounts of the phases; the P-x-y diagram at constant temperature; and the x-y equilibrium diagram, on which the McCabe-Thiele construction for distillation is performed. • Two-component gas/single-component liquid systems — a condensable vapour in a non-condensable carrier gas, as in humidification and drying — are described by relative saturation (relative humidity) = p/Psat, absolute (molal) saturation, dew point (the temperature at which condensation begins on cooling at constant pressure) and the psychrometric (humidity) chart.

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Multicomponent VLE is handled by K-values, Ki = yi/xi, with bubble point when Σ Kixi = 1, dew point when Σ yi/Ki = 1, and flash calculations performed with the Rachford-Rice equation.

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This section covers the principle of material balances, balances without chemical reaction, stoichiometry and reaction terminology, species and element balances, combustion calculations, and recycle, bypass and purge systems.

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The General Balance Equation • Material balances are applications of the law of conservation of mass, and the general statement, which must be written out before any problem is attempted, is: • INPUT − OUTPUT + GENERATION − CONSUMPTION = ACCUMULATION • Simplifications: at steady state the accumulation term is zero; without chemical reaction the generation and consumption terms are zero, so the balance reduces to INPUT = OUTPUT; and for a batch process input and output are zero, leaving generation − consumption = accumulation.

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A total mass balance is always valid even with reaction, because mass is conserved; a total mole balance is not, unless the number of moles happens to be unchanged — a distinction that is examined repeatedly. • Types of balance: total mass, total moles, individual species (with generation terms if the species reacts) and individual elements (never generated or consumed, so always input = output).

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An inert or tie substance — a species that enters and leaves unchanged and appears in only one stream — is the single most useful device in material balance work, since it links the streams directly. • Systematic procedure:

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(1) draw and label a flowsheet with every stream and all known quantities and compositions;

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(2) choose a convenient basis of calculation — 100 kg or 100 kmol of a feed, or one hour of operation;

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(3) define the system boundary;

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(4) count the unknowns and the independent equations available;

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(5) write the balances, starting with any tie component and with the species giving the simplest equation;

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(7) check by an independent overall balance. • Degrees of freedom analysis:

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DOF = number of unknowns − number of independent equations.

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If DOF = 0 the problem is exactly determined and can be solved; if positive it is underspecified and more data are needed; if negative it is overspecified and the data may be inconsistent.

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Stoichiometry and Terminology for Reacting Systems • Stoichiometry is the quantitative relationship between reacting species, fixed by the balanced chemical equation.

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The following definitions must be known exactly: • Limiting reactant: the reactant present in the smallest stoichiometric amount, which would be completely consumed first and which therefore determines the maximum possible extent of reaction.

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It is identified by dividing the moles fed of each reactant by its stoichiometric coefficient and taking the smallest result. • Excess reactant: any reactant present in more than the stoichiometric amount.

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Percentage excess = (moles fed − moles theoretically required by the limiting reactant) / (moles theoretically required) × 100 — note that the denominator is the theoretical requirement, not the amount fed, a common source of error. • Conversion = (moles of reactant consumed)/(moles of reactant fed), usually referred to the limiting reactant. • Yield = (moles of desired product formed)/(moles that would have formed if the limiting reactant were completely converted to that product). • Selectivity = (moles of desired product)/(moles of undesired product) — the crucial quantity when multiple reactions occur. • Extent of reaction ξ: defined by ni = ni0 + νiξ, where νi is the stoichiometric coefficient (positive for products, negative for reactants).

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It is the most economical way of handling reacting balances because a single variable describes the whole reaction. • Two equivalent methods for a reacting system: species (molecular) balances, which need generation and consumption terms, and element balances, in which atoms of each element are conserved so that input = output with no generation term at all.

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Element balances are usually the simpler choice when the reactions are numerous or not fully known — as in combustion.

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Combustion Calculations • Combustion is the commonest reacting balance in practice and has its own vocabulary. • Theoretical (stoichiometric) air is the exact quantity required for complete combustion of all the fuel to CO₂, H₂O and SO₂; excess air is the amount supplied above that, always based on complete combustion, regardless of how much of the fuel actually burns completely. • Composition of air is taken as 21 % O₂ and 79 % N₂ by mole (volume), giving the constantly used ratio 79/21 = 3.76 moles of nitrogen per mole of oxygen and an average molecular weight of 29.

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Nitrogen is the classic tie component in combustion problems, since it passes through unchanged. • Flue gas analysis: an Orsat analysis reports the composition on a dry basis, water having been condensed out, so the distinction between wet and dry basis must be watched carefully; conversion between the two is a standard examination step. • Complete combustion gives CO₂; incomplete combustion gives CO, which indicates insufficient air or poor mixing and represents both an efficiency loss and a serious safety hazard.

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Useful stoichiometry:

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CH₄ + 2O₂ → CO₂ + 2H₂O;

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CnHm + (n + m/4)O₂ → nCO₂ + (m/2)H₂O.

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Recycle, Bypass and Purge • Recycle returns part of a downstream stream to the process inlet.

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Its purposes are to increase the overall conversion of an expensive reactant, recover and reuse catalyst or solvent, improve control of temperature by dilution, and reduce waste. • The essential analytical point, and the source of most examination marks, is the distinction between two conversions: single-pass (once-through) conversion is based on what enters the reactor itself, while overall conversion is based on the fresh feed entering the whole process.

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Because unconverted material is returned, the overall conversion is always higher than the single-pass conversion and may approach 100 %. • Balances may be written around four different envelopes, and choosing the right one is the whole skill: the overall process (in which the recycle stream does not appear at all, and which is therefore the place to start); the mixing point where fresh feed meets recycle; the reactor alone; and the separator. • Bypass diverts part of a stream around a unit and recombines it afterwards, which is done to control the extent of processing and hence the final composition or temperature — as in blending dried and undried air to reach a required humidity. • Purge is a small stream deliberately withdrawn from a recycle loop.

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Its necessity is a favourite question: if an inert or an impurity enters with the fresh feed but is not removed in the product, it will accumulate continuously in the recycle loop until the process is inoperable; a purge bleeds it off and establishes a steady state.

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At steady state, the rate at which the inert enters in the fresh feed equals the rate at which it leaves in the purge.

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The design compromise is that a larger purge keeps the inert concentration low but wastes more valuable reactant — the situation in ammonia synthesis, where argon and methane accumulate in the loop.

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This section covers the terminology of energy balances, the forms of energy included, balances with and without chemical reaction, the standard heat of formation, heat of reaction and heat of combustion, and the combination of sensible heat with heat of reaction.

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Terminology and the General Energy Balance • Energy balances are applications of the first law of thermodynamics — energy is conserved.

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The general statement mirrors the material balance:

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INPUT − OUTPUT + GENERATION = ACCUMULATION, and at steady state the accumulation vanishes. • Terminology: the system is the region under study, separated by its boundary from the surroundings; it is open (flow, with mass crossing the boundary), closed (no mass crossing) or isolated (neither mass nor energy).

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Q is heat and W is work, and the sign convention (which must be stated) is that heat added to the system and work done by the system are positive.

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State functions (U, H, S, G, T, P, V) depend only on the state and not on the path; path functions (Q and W) depend on how the change is carried out.

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Processes may be isothermal, isobaric, isochoric (constant volume) or adiabatic (Q = 0). • Forms of energy to be included: internal energy U (the molecular kinetic and potential energy); kinetic energy mu²/2 and potential energy mgz, both of which are usually negligible in chemical process calculations compared with enthalpy changes, except in nozzles, turbines and tall columns; heat Q; work W, including flow (PV) work; and enthalpy H = U + PV, which combines internal energy with flow work and is therefore the natural variable for flow systems. • Forms of the balance: for a closed system, ΔU = Q − W; for an open steady-flow system, ΔH + ΔKE + ΔPE = Q − Ws, where Ws is shaft work — and with the usual simplifications this reduces to Q = ΔH for a steady-flow process with no shaft work, which is the equation used in almost every heat exchanger, heater, cooler and reactor calculation.

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Energy Balances Without Reaction:

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Sensible and Latent Heat • When no reaction occurs, the enthalpy change of a stream is made up of sensible heat (a change of temperature) and latent heat (a change of phase). • Sensible heat: ΔH = ∫ Cp dT, or ΔH = m·Cp·ΔT when the heat capacity may be treated as constant.

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Cp is usually expressed as a polynomial, Cp = a + bT + cT² + dT³, and for gases Cp − Cv = R, with Cp = (5/2)R for a monatomic and (7/2)R for a diatomic ideal gas.

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For liquids and solids the two heat capacities are nearly equal. • Latent heat is the enthalpy change at constant temperature accompanying a phase change — heat of vaporisation, fusion or sublimation.

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For water the figures worth remembering are latent heat of vaporisation ≈ 2,257 kJ/kg at 100 °C, latent heat of fusion ≈ 334 kJ/kg and specific heat ≈ 4.18 kJ/kg·K. • Reference state: because only changes in enthalpy have meaning, a reference state must be chosen and stated (commonly 25 °C and 1 atm, or the inlet condition), and all stream enthalpies are then computed relative to it.

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Enthalpy tables and charts — steam tables, the psychrometric chart, the pressure-enthalpy diagram of a refrigerant — are simply tabulations of this, and the ability to read steam tables is assumed throughout the paper. • Procedure: draw the flowsheet and mark temperatures, phases and flows; complete the material balance first, since the energy balance needs the flows; choose the reference state; construct a table of stream enthalpies; and apply Q = ΔH = (Σ ṅoutHout) − (Σ ṅinHin).

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Because enthalpy is a state function, a convenient hypothetical path may be used — for example cooling the reactants to 25 °C, reacting at 25 °C, and heating the products to the outlet temperature.

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Heat of Reaction, Formation and Combustion • Heat of reaction ΔHrxn is the enthalpy change when the reaction proceeds to the extent indicated by the stoichiometric equation, with reactants and products at the same specified temperature and pressure.

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The sign convention is that ΔH is negative for an exothermic reaction (heat released) and positive for an endothermic one (heat absorbed).

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The standard heat of reaction ΔH°rxn refers to 25 °C and 1 atm with each species in its standard state. • Standard heat of formation ΔH°f is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states at 25 °C and 1 atm.

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The key convention, examined regularly, is that the standard heat of formation of an element in its standard state is zero by definition — so ΔH°f is zero for O₂ gas, N₂ gas, graphite and liquid bromine, but not for O₃, diamond or gaseous bromine. • The working equation: ΔH°rxn = Σ νiΔH°f,products − Σ νiΔH°f,reactants, the stoichiometric coefficients being used as multipliers. • Standard heat of combustion ΔH°c is the enthalpy change on complete combustion of one mole of a substance with oxygen to give CO₂, liquid H₂O and SO₂ at 25 °C and 1 atm; it is always negative.

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The alternative route to the heat of reaction is ΔH°rxn = Σ ΔH°c,reactants − Σ ΔH°c,products — note that the order is reversed compared with the formation equation, which is a classic trap. • Gross (higher) and net (lower) heating value: the gross calorific value assumes the water produced is condensed to liquid and therefore includes its latent heat, while the net value assumes it leaves as vapour; the difference is the latent heat of the water formed, and the gross value is always the larger. • Hess's law underlies all of this: the enthalpy change of a reaction is independent of the path taken and depends only on the initial and final states, so reactions may be added, subtracted and scaled algebraically to obtain an unmeasurable heat of reaction from measurable ones. • Kirchhoff's equation gives the temperature dependence: d(ΔH)/dT = ΔCp, where ΔCp is the difference between the heat capacities of products and reactants — so a heat of reaction quoted at 25 °C is corrected to another temperature by integrating ΔCp.

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Combining Heat of Reaction with Sensible Heat • The general energy balance for a reactor at steady state, in the heat of reaction method, is Q = ξ·ΔH°rxn + ΔHsensible,products − ΔHsensible,reactants, where ξ is the extent of reaction.

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In practice one takes the hypothetical path: bring the reactants from their inlet temperature to 25 °C (sensible heat), carry out the reaction at 25 °C (the standard heat of reaction times the extent), and bring the products from 25 °C to their outlet temperature (sensible heat).

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The alternative heat of formation method tabulates each stream's enthalpy as ΔH°f plus its sensible heat relative to 25 °C and then simply takes the difference of the totals; it is the method used by process simulators and is less error-prone for multiple reactions. • Adiabatic flame (reaction) temperature is the temperature reached when Q = 0, so that all the heat released by the reaction goes into raising the temperature of the products.

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It is the maximum attainable temperature and is reduced by excess air, by inerts, by incomplete combustion, by heat losses and by dissociation at high temperature.

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Its calculation — setting the heat released equal to the sensible heat of the products and solving for T, usually by trial and error because Cp varies with temperature — is a standard examination problem. • Practical applications: sizing heaters, coolers, condensers and reboilers; determining the cooling duty of an exothermic reactor and hence the danger of thermal runaway if it is lost; furnace and boiler efficiency; energy integration and pinch analysis; and utility consumption in plant design.

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This section covers the principal unit processes — oxidation, nitration, halogenation, hydrogenation, hydrolysis and polymerization — with their agents, industrial applications and hazards.

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Unit Processes versus Unit Operations A unit operation is a physical step (distillation, drying, filtration) in which no chemical change occurs; a unit process is a chemical conversion (oxidation, nitration, hydrogenation) in which the molecular identity of the material changes.

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A chemical plant is a designed sequence of both.

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The unit processes below recur across the whole chemical industry, and for each one the examinable material is the agents used, the principal industrial examples, and the characteristic hazard.

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Oxidation • Oxidation is the addition of oxygen, the removal of hydrogen, or more generally the loss of electrons with an increase in oxidation state.

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It is almost always strongly exothermic, which is the dominant design consideration. • Oxidising agents: air or oxygen (by far the cheapest and most used industrially); ozone; hydrogen peroxide; nitric acid; potassium permanganate and potassium dichromate (powerful but expensive, and used mainly in fine chemicals); chlorine and hypochlorite; sulphur trioxide; and peracids. • Liquid-phase oxidation is carried out at moderate temperature with a catalyst (cobalt or manganese salts) and is used where the product would decompose in the vapour phase — the oxidation of p-xylene to terephthalic acid for polyester, of cyclohexane to cyclohexanone and adipic acid for nylon, and of acetaldehyde to acetic acid.

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Vapour-phase (catalytic) oxidation over a fixed or fluidised bed is used for SO₂ to SO₃ in the contact process (V₂O₅ catalyst), ammonia to nitric oxide in the Ostwald process (platinum-rhodium gauze), methanol to formaldehyde, ethylene to ethylene oxide (silver catalyst) and naphthalene to phthalic anhydride. • Hazards and control: the reaction is exothermic and often operates near the flammability limits, so there is a real risk of thermal runaway, ignition and explosion.

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Control depends on efficient heat removal (jackets, internal coils, recycle of cooled product, fluidised beds with high heat transfer), operating outside the explosive range, dilution with inert gas or steam, and careful temperature monitoring and emergency relief.

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Nitration • Nitration introduces a nitro group (−NO₂) into an organic molecule.

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The reaction proceeds through the nitronium ion NO₂⁺, which is why the nitrating agent is not nitric acid alone. • Nitrating agents: the standard industrial reagent is 'mixed acid' — concentrated nitric acid with concentrated sulphuric acid, in which the sulphuric acid serves two essential purposes: it generates the nitronium ion, and it absorbs the water formed, which would otherwise dilute the nitric acid and stop the reaction.

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Other agents are nitric acid alone, nitrogen dioxide, acetyl nitrate and nitronium salts. • Industrial products, largely explosives and intermediates: nitrobenzene (from benzene, the route to aniline and thence to dyes and polyurethanes);

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TNT (trinitrotoluene) from toluene by successive nitration; nitroglycerine from glycerol, the basis of dynamite and also a vasodilator drug; nitrocellulose (guncotton) from cellulose; picric acid; and ammonium nitrate, both a fertiliser and an explosive. • Hazards: nitration is highly exothermic and the products are thermally unstable and often explosive.

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The classic control measures are efficient cooling and vigorous agitation (loss of agitation is a recognised cause of runaway), slow controlled addition of the acid, strict temperature limits, avoidance of the accumulation of unreacted acid, and careful disposal of spent acid.

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Several of the worst accidents in chemical industry history have been nitration runaways.

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Halogenation • Halogenation introduces a halogen — chlorine, bromine, fluorine or iodine — into a molecule, by substitution (replacing hydrogen, as in the chlorination of methane or benzene) or addition (across a double bond, as in ethylene to ethylene dichloride). • Importance: chlorination in particular is one of the most important industrial processes, because the chlorine atom is a good leaving group and therefore an excellent handle for further synthesis, and because the products are valuable in their own right.

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Major products: vinyl chloride monomer (from ethylene dichloride) for PVC — the largest single use of chlorine in organics; chloroform and carbon tetrachloride; chlorobenzene; chlorinated solvents; hypochlorite bleach and water disinfectants; refrigerants; pesticides; and fluoropolymers such as PTFE. • Conditions: substitution is generally a free-radical chain reaction initiated by heat, light or a peroxide, and therefore gives a mixture of mono-, di- and poly-substituted products requiring separation; aromatic substitution uses a Lewis acid catalyst such as FeCl₃ or AlCl₃; addition is ionic and more selective. • Hazards: chlorine is highly toxic and corrosive, the reactions are exothermic, hydrogen chloride is produced as a corrosive by-product requiring absorption and neutralisation, many chlorinated solvents are toxic or carcinogenic, and chlorofluorocarbons deplete stratospheric ozone and have been phased out under the Montreal Protocol.

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Hydrogenation • Hydrogenation is the addition of hydrogen to a molecule, almost always in the presence of a catalyst; the reverse, dehydrogenation, is equally important industrially. • Catalysts: nickel (Raney nickel — the cheap workhorse of fat hardening), platinum, palladium, rhodium and copper chromite. • The industrial hydrogenation of fats and oils is the example named in the syllabus and is important in Nepal, where vanaspati ghee is made this way.

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Purpose: to convert liquid unsaturated vegetable oils into semi-solid or solid fats by saturating the carbon-carbon double bonds of the fatty acid chains, which raises the melting point, improves texture and greatly increases resistance to oxidative rancidity, thereby extending shelf life.

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Process: the refined, bleached oil is heated to about 150-200 °C in a batch or continuous reactor, hydrogen is sparged in at 1-5 atm, and a finely divided nickel catalyst (0.05-0.2 %) is suspended with vigorous agitation; the reaction is exothermic and the degree of hardening is followed by iodine value and refractive index, after which the catalyst is filtered off and the product deodorised.

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Selective (partial) hydrogenation is used to harden only as far as required. • The health issue, which is examinable: partial hydrogenation isomerises some cis double bonds to the trans configuration, producing trans fatty acids, which raise LDL and lower HDL cholesterol and are now restricted or banned in many countries; modern practice therefore favours full hydrogenation followed by interesterification, or fractionation, to avoid trans fats. • Other industrial hydrogenations: ammonia synthesis (N₂ + 3H₂), methanol synthesis, hydrotreating and hydrocracking of petroleum, nitrobenzene to aniline, and the hydrogenation of coal.

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Hazards: hydrogen is extremely flammable with very wide explosive limits and a very low ignition energy, so leak-tight equipment, inerting and elimination of ignition sources are essential; the catalysts are pyrophoric when dry.

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Hydrolysis • Hydrolysis is the chemical decomposition of a compound by reaction with water, usually catalysed by acid, alkali or an enzyme. • Industrial hydrolysis of fats (saponification): fats and oils are triglycerides — esters of glycerol with three fatty acids.

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Hydrolysis splits them into fatty acids and glycerol; when carried out with alkali (NaOH or KOH) the products are the sodium or potassium salts of the fatty acids, that is soap, together with glycerol as a valuable by-product — the process called saponification.

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Industrially it is done by the batch kettle process, by the continuous Colgate-Emery high-pressure countercurrent splitting at about 250 °C and 50 atm, or by enzymatic (lipase) splitting.

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Soap is then finished by salting out, washing, neutralising, drying and milling; sodium soaps are hard and potassium soaps soft. • Hydrolysis of carbohydrates — starch to dextrose: starch is a polymer of glucose, and its hydrolysis yields progressively dextrins, maltose and finally dextrose (glucose), the extent being measured by the dextrose equivalent (DE).

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Two routes: acid hydrolysis with dilute hydrochloric or sulphuric acid under pressure — fast and cheap but less selective, giving colour and bitter by-products; and enzymatic hydrolysis, the modern method, using α-amylase for liquefaction followed by glucoamylase for saccharification, which is milder, far more selective and gives a purer product of higher DE.

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The glucose syrup may then be isomerised with glucose isomerase to high-fructose corn syrup, or fermented to ethanol — a route of direct relevance to sugar and starch industries in Nepal. • Other hydrolyses: esters to acid and alcohol, proteins to amino acids, cellulose to glucose in second-generation biofuels, and the hydration of ethylene to ethanol.

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Polymerization • Polymerization joins many small molecules (monomers) into a large one (polymer), the degree of polymerization being the number of repeating units. • Two classes of reaction: addition (chain-growth) polymerization, in which unsaturated monomers add to a growing chain with no by-product and the polymer has the same empirical formula as the monomer, proceeding by initiation, propagation and termination through free-radical, cationic, anionic or Ziegler-Natta coordination mechanisms — polyethylene, polypropylene, PVC, polystyrene, PTFE and acrylics; and condensation (step-growth) polymerization, in which monomers bearing two functional groups react with the elimination of a small molecule, usually water — nylon, polyester (PET), phenol-formaldehyde (Bakelite), urea-formaldehyde, polyurethanes and polycarbonate. • Classification of polymers: by source (natural, semi-synthetic, synthetic); by structure (linear, branched, cross-linked/network); by monomer (homopolymer or copolymer — random, alternating, block or graft); by thermal behaviour — thermoplastics soften on heating and can be remoulded repeatedly because the chains are not cross-linked (polyethylene, PVC, PET), whereas thermosets are irreversibly cross-linked on curing and char rather than melt (Bakelite, epoxy, vulcanised rubber); and by application (plastics, fibres, elastomers, coatings, adhesives). • The four methods of polymerization, a standard examination table: bulk (mass) — monomer plus initiator only, giving the purest product but with severe problems of heat removal and viscosity; solution — carried out in a solvent, giving good temperature control but requiring solvent removal and recovery and limiting molecular weight by chain transfer; suspension (bead/pearl) — monomer droplets dispersed in water with a stabiliser, giving excellent heat control and a granular product that is easily separated, the standard route for PVC and polystyrene; and emulsion — monomer emulsified in water with a surfactant and a water-soluble initiator, giving the fastest rate together with the highest molecular weight and excellent heat control, but leaving surfactant residues in the product, used for synthetic rubber and paints. • Properties and hazards: molecular weight and its distribution, crystallinity, glass transition temperature and cross-link density govern the properties.

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The reactions are exothermic and prone to runaway (the Trommsdorff gel effect raises the rate as viscosity increases), many monomers are toxic or carcinogenic (vinyl chloride is a recognised human carcinogen), and plastic waste and microplastics are now the dominant environmental concern of the industry.

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This section covers mathematical techniques in chemical engineering, the concepts of process modelling and simulation, the strategy for simulation, approaches to model development, the types of model and of equation, and the corresponding solution strategies.

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Mathematical Techniques in Chemical Engineering • Chemical engineering problems reduce to mathematics of a few recognisable kinds, and knowing which kind determines the solution method. • Algebraic equations, linear and non-linear, arise from steady-state material and energy balances and from equilibrium relations.

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Ordinary differential equations arise from unsteady-state lumped-parameter systems (a batch reactor, a stirred tank, a surge vessel) and from steady-state distributed systems in one dimension (a plug flow reactor along its length).

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Partial differential equations arise when a property varies with more than one independent variable — position and time, or several space dimensions — as in unsteady heat conduction, diffusion and fluid flow.

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Integral equations, difference equations, statistical and optimisation methods complete the list. • Analytical solutions are exact and give general insight into how the answer depends on the parameters, but are available only for simple, usually linear, cases.

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Numerical solutions are approximate and specific to the numbers used, but can handle non-linearity, complex geometry and realistic property variation — which is why every industrial problem is solved numerically.

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The standard numerical methods are Gaussian elimination and matrix inversion for linear systems;

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Newton-Raphson, bisection and successive substitution for non-linear equations;

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Euler and Runge-Kutta methods for ordinary differential equations; and finite difference, finite element and finite volume methods for partial differential equations.

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Every numerical method raises the questions of convergence, stability, step size and accumulated round-off error.

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Models and Modelling • A model is a representation of a real system that captures the features relevant to a particular purpose and omits the rest.

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Process modelling is the activity of constructing such a representation for a chemical process, and simulation is the use of the model to predict the behaviour of the process under specified conditions — modelling builds the description, simulation exercises it. • Why model: to understand the process and the interaction of its variables; to design equipment and size it; to evaluate alternatives and optimise operating conditions; to predict the effect of a change without disturbing the plant; to design and tune control systems; to train operators; to analyse safety scenarios and 'what-if' cases; and to do all of this at far lower cost and risk than experimentation on the real plant.

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The governing caution is that a model is only as good as its assumptions and its data, and extrapolation beyond the range over which it was validated is unsafe — hence the engineer's maxim that all models are wrong but some are useful. • Model building requires: defining the objective and the required accuracy; drawing the system boundary; listing the assumptions explicitly; writing the conservation equations (mass, energy, momentum) together with the constitutive and equilibrium relations, rate expressions and physical property correlations; counting the degrees of freedom; specifying initial and boundary conditions; solving; and — the step most often neglected — validating the model against plant or laboratory data and then performing a sensitivity analysis.

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Types of Model Basis Types Origin of the equations Theoretical (mechanistic, first-principles, 'white box') — derived from conservation laws and physical theory; the most general and extrapolable, but demanding to build.

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Empirical (black box) — fitted to data with no physical basis (a regression correlation, a neural network); quick and accurate within its data range but unsafe to extrapolate.

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Semi-empirical (grey box) — a theoretical structure with empirically fitted parameters, which is what most practical models are Time dependence Steady-state (no accumulation; algebraic equations; used for design and for rating) versus unsteady-state (dynamic) (differential equations in time; used for start-up and shut-down, batch operation, control system design and safety analysis) Spatial variation Lumped parameter — properties uniform throughout, giving ordinary differential or algebraic equations (a well-mixed stirred tank); distributed parameter — properties vary with position, giving partial differential equations (a packed bed, a heat exchanger along its length) Nature of the variables Deterministic — a given input always gives the same output; stochastic (probabilistic) — random variation is included, as in residence time distribution or Monte Carlo risk analysis Linearity Linear (superposition applies, analytical solution often possible) or non-linear (the usual case in chemical engineering, because of the Arrhenius term, equilibrium relations and property variation) Other Continuous or discrete; physical (pilot plant) or mathematical; static or dynamic Types of Equation and Solution Strategy Equation type Where it arises Solution method Linear algebraic Steady-state balances on a linear flowsheet Matrix methods — Gaussian elimination, LU decomposition, matrix inversion Non-linear algebraic Steady state with reaction, equilibrium or recycle Newton-Raphson, successive substitution, bisection; needs a good initial guess and may converge slowly or not at all Ordinary differential (initial value) Unsteady lumped systems — batch reactor, tank level Euler, improved Euler, Runge-Kutta (4th order is the standard workhorse); stiff systems, in which time constants differ by orders of magnitude, require implicit methods such as Gear's Ordinary differential (boundary value) Steady-state distributed systems — dispersion in a reactor, conduction in a slab Shooting method or finite differences Partial differential Unsteady or multi-dimensional transport Finite difference, finite element, finite volume; classified as parabolic (unsteady diffusion), elliptic (steady-state potential) or hyperbolic (wave, convection) Differential-algebrai c (DAE) Dynamic models with equilibrium constraints Specialised DAE solvers Optimisation Design and operating point selection Linear programming, non-linear programming, genetic algorithms Strategy for Simulation and Approaches to Model Development • Strategy for simulation, in order:

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(1) state the problem and the objective precisely;

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(2) collect the data and physical properties;

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(3) develop the model with its assumptions stated;

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(4) check the degrees of freedom;

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(5) select the solution method;

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(6) code or configure it in a simulator;

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(7) verify that the equations are being solved correctly;

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(8) validate against real data;

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(9) perform sensitivity and case studies; and (10) interpret and report.

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Verification asks whether the equations are solved right; validation asks whether the right equations are being solved — a distinction worth remembering. • Approaches to model development: deductive (top-down, from first principles), inductive (bottom-up, from experimental data), and the usual combined approach; and in terms of detail, the hierarchical or successive refinement approach, in which a simple model is built first and complexity added only where the results demand it. • Flowsheet simulation uses two architectures: the sequential modular approach, in which each unit is solved in turn in the order of the flowsheet, with recycle loops converged by iteration on tear streams — intuitive, robust and the basis of Aspen Plus and HYSYS; and the equation-oriented (simultaneous) approach, in which all the equations of the entire flowsheet are assembled and solved together — much faster for large problems with many recycles and far better suited to optimisation and dynamic simulation, but harder to initialise and to diagnose when it fails.

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Modern simulators offer both. • Software used in practice:

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Aspen Plus, Aspen HYSYS, ChemCAD, DWSIM and PRO/II for flowsheet simulation;

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MATLAB, Python, Polymath and Mathematica for custom models;

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ANSYS Fluent and COMSOL for computational fluid dynamics; and gPROMS for dynamic and equation-oriented work.