AMIE Section B Chemical cheat sheet

First law for closed system: ΔU = Q − W; for steady-flow open system: ΔH + ΔKE + ΔPE = Q − W_s.

Second law: ΔS_univ ≥ 0; for reversible process ΔS = Q_rev/T; entropy is a state function.

Gibbs free energy: G = H − TS; at constant T and P, spontaneous change requires ΔG < 0.

Chemical potential: μ_i = (∂G/∂n_i)_{T,P,n_j}; phase equilibrium requires μ_i^α = μ_i^β for each component.

Fugacity: f_i = φ_i P y_i; ideal gas φ_i = 1; Lewis-Randall rule for ideal solution: f_i = x_i f_i^pure.

Activity coefficient: γ_i = f_i/(x_i f_i^pure); for ideal solution γ_i = 1; excess Gibbs energy G^E = RT Σ x_i ln γ_i.

Carnot efficiency: η_Carnot = 1 − T_C/T_H; coefficient of performance for refrigerator: COP = T_C/(T_H − T_C).

Clausius-Clapeyron: d ln P_sat/d(1/T) = −ΔH_vap/R; Antoine equation: ln P_sat = A − B/(T + C).

Cubic equations of state: van der Waals: P = RT/(v−b) − a/v²; critical constants: a = 27R²T_c²/(64P_c), b = RT_c/(8P_c).

Reynolds number: Re = ρvD/μ; laminar pipe flow Re < 2100, turbulent Re > 4000; friction factor f = 64/Re for laminar.

Darcy-Weisbach: ΔP_f = f (L/D) (ρv²/2); for packed bed use Ergun equation: ΔP/L = 150μ(1−ε)²v/(ε³d_p²) + 1.75ρ(1−ε)v²/(ε³d_p).

Prandtl number: Pr = μC_p/k; Nusselt number: Nu = hD/k; Dittus-Boelter (turbulent, cooling): Nu = 0.023 Re^0.8 Pr^0.3.

Fourier's law: q = −k ∇T; for plane wall: q/A = k ΔT/Δx; for cylinder: q = 2πkL ΔT / ln(r2/r1).

Fick's law: J_A = −D_AB ∇C_A; for equimolar counterdiffusion: N_A = −D_AB ΔC_A/Δz; for dilute A in stagnant B: N_A = (D_AB P/RTΔz) ln((1−y_A2)/(1−y_A1)).

Sherwood number: Sh = k_c D/D_AB; Schmidt number: Sc = μ/(ρD_AB); mass transfer analog of Dittus-Boelter: Sh = 0.023 Re^0.8 Sc^0.33.

Log mean temperature difference: ΔT_lm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2); for multipass exchangers use correction factor F: Q = U A F ΔT_lm.

Bernoulli equation (frictionless, steady, incompressible): P1/ρ + v1²/2 + gz1 = P2/ρ + v2²/2 + gz2.

Batch reactor design equation: t = N_A0 ∫ dX/(-r_A V); for constant volume: t = C_A0 ∫ dX/(-r_A).

CSTR design equation: V = F_A0 X/(-r_A); CSTR operates at outlet conditions; multiple CSTRs in series approach PFR behavior.

PFR design equation: V = F_A0 ∫ dX/(-r_A); for constant density: τ = C_A0 ∫ dX/(-r_A).

Arrhenius equation: k = A exp(−E/RT); activation energy E from slope of ln k vs 1/T: slope = −E/R.

For first-order reaction in batch: ln(C_A0/C_A) = kt; half-life t_1/2 = ln2/k, independent of initial concentration.

For second-order reaction (A → products, −r_A = kC_A²) in batch: 1/C_A − 1/C_A0 = kt; half-life t_1/2 = 1/(kC_A0).

Yield and selectivity: yield = moles desired product formed/moles reactant consumed; selectivity = moles desired product/moles undesired product.

Non-ideal flow: residence time distribution E(t); mean residence time τ = ∫ t E(t) dt; variance σ² = ∫ (t−τ)² E(t) dt.

Thin-walled cylindrical pressure vessel: hoop stress σ_θ = Pr/t; longitudinal stress σ_L = Pr/(2t); ASME code requires t = Pr/(SE − 0.6P) + corrosion allowance.

For spherical vessel: σ = Pr/(2t); spherical shells are more efficient for high pressure but costlier to fabricate.

Column shell under external pressure: critical buckling pressure P_c = 2E/(1−ν²) (t/D)³; use stiffening rings to increase P_c.

Heat exchanger design: LMTD method Q = U A ΔT_lm; effectiveness-NTU method: ε = Q/Q_max; NTU = UA/C_min.

Pump power: P = ρ g H Q / η; NPSH available = (P_atm − P_v)/(ρg) + z − h_f; NPSH_required must be less than NPSH_available to avoid cavitation.

Compressor power (isentropic): W = (γ/(γ−1)) P1 V1 [(P2/P1)^((γ−1)/γ) − 1]; for multistage, use intercooling to approach isothermal.

Distillation column: minimum reflux from Underwood equations; minimum stages from Fenske equation: N_min = log[(x_D/(1−x_D))((1−x_B)/x_B)] / log α_avg.

Pipe sizing: economic diameter from heuristic: D_opt ≈ 0.363 m^0.45 (SI, with m in kg/s for liquid); or use velocity guidelines: liquid 1–3 m/s, gas 10–30 m/s.

Capital cost estimation: six-tenths rule: C2 = C1 (Q2/Q1)^0.6; Lang factor: fixed capital = Lang factor × purchased equipment cost (3.1 for fluids, 4.7 for solids).

Depreciation: straight-line: D = (P − S)/n; MACRS uses accelerated schedules; book value declines over time.

Profitability: net present value (NPV) = Σ (cash flow)_t/(1+i)^t; internal rate of return (IRR) is i when NPV = 0; payback period = fixed capital/annual cash flow.

Piping and instrumentation diagram (P&ID) uses ISA symbols: control valve, transmitter, controller; instrument tag: XX-123 where XX is function (e.g., FT for flow transmitter).

Safety: flammability limits (LFL/UFL); flash point; autoignition temperature; use nitrogen inerting to keep oxygen below limiting oxygen concentration (LOC).

HAZOP study uses guide words (no, more, less, reverse, as well as, part of, other than) applied to process parameters to identify deviations.

Relief valve sizing: API 520/521; for gas/vapor: A = (W/(K_d K_b K_c)) √(TZ/(M P)) / (C K_p); for liquid: A = Q/(K_d K_w K_c K_v) √(G/ΔP).

Control loop tuning: PID controller: output = K_c (e + (1/τ_I)∫e dt + τ_D de/dt); Ziegler-Nichols tuning rules based on ultimate gain and period.

Basis selection: choose a convenient basis (e.g., 100 kg or 1 kmol) and convert all flows to consistent units (mass or moles).

Stoichiometry: for reaction aA + bB → cC + dD, extent of reaction ξ: n_i = n_i0 + ν_i ξ; ν_i positive for products, negative for reactants.

Limiting reactant: reactant that is completely consumed; percent excess = (moles supplied − moles stoichiometric)/moles stoichiometric × 100.

Conversion: X = (moles reacted)/(moles fed); selectivity = moles desired product/moles undesired product; yield = moles desired product/moles reactant fed.

Material balance without reaction: Σ input = Σ output + accumulation; with reaction: Σ input + generation = Σ output + consumption + accumulation.

Energy balance: Q − W = ΔH + ΔKE + ΔPE; for steady-state adiabatic reactor: ΔH = 0; use heat of reaction at reference temperature and sensible heats.

Combustion calculations: theoretical oxygen demand from stoichiometry; excess air = (actual air − theoretical air)/theoretical air × 100; use Orsat analysis for flue gas composition.

Ideal gas law: PV = nRT; at standard conditions (0°C, 1 atm): 1 kmol = 22.414 m³; at 25°C, 1 atm: 1 kmol = 24.45 m³.

Stress-strain: elastic modulus E = σ/ε in linear region; yield strength at 0.2% offset; ultimate tensile strength is maximum stress; ductility from % elongation.

Corrosion cell requires anode, cathode, electrolyte, and electrical connection; oxidation occurs at anode (metal dissolution), reduction at cathode.

Galvanic series: metals with more negative electrode potential (e.g., Mg, Zn, Al) are anodic and corrode preferentially when coupled to more noble metals (e.g., Cu, stainless steel).

Pitting corrosion: localized breakdown of passive film (e.g., chloride on stainless steel); use pitting resistance equivalent number (PREN) = %Cr + 3.3%Mo + 16%N.

Cathodic protection: sacrificial anode (use metal with lower potential) or impressed current; protects structure by making it the cathode.

Corrosion rate: from weight loss: mpy = (534 W)/(ρ A t) where W in mg, ρ in g/cm³, A in in², t in hours; or from current density: CR (mpy) = 0.128 i (μA/cm²) (E.W.)/ρ.

Material selection: consider temperature, pressure, corrosive environment, cost; common materials: carbon steel (cheap, limited corrosion resistance), stainless steel 304/316, Hastelloy, titanium.

Polymers: glass transition temperature T_g; semicrystalline polymers have T_m; creep and stress relaxation are time-dependent behaviors.

Air pollution: primary pollutants (SO2, NOx, CO, particulates, VOCs); secondary pollutants (ozone, PAN) formed in atmosphere.

Particulate control: cyclones (efficiency depends on particle size, cut diameter d50), baghouses (high efficiency for fine particles), electrostatic precipitators (high efficiency, low pressure drop), scrubbers.

Gas absorption for SO2 removal: use limestone slurry (wet flue gas desulfurization); reaction: CaCO3 + SO2 + ½O2 + 2H2O → CaSO4·2H2O + CO2.

NOx control: selective catalytic reduction (SCR) with NH3: 4NH3 + 4NO + O2 → 4N2 + 6H2O; selective non-catalytic reduction (SNCR) at higher temperature.

Wastewater treatment: primary (physical), secondary (biological, activated sludge), tertiary (advanced); BOD5 measures biodegradable organic matter; COD measures chemically oxidizable matter.

Activated sludge: food-to-microorganism ratio F/M = Q S0/(V X); sludge age (mean cell residence time) θ_c = V X/(Q_w X_r + Q_e X_e).

Air dispersion: Gaussian plume model: C(x,y,z) = (Q/(2π u σ_y σ_z)) exp(−y²/(2σ_y²)) [exp(−(z−H)²/(2σ_z²)) + exp(−(z+H)²/(2σ_z²))].

Noise pollution: sound pressure level L_p = 20 log10(P/P0) dB, P0 = 20 μPa; sound power level L_w = 10 log10(W/W0) dB, W0 = 10⁻¹² W.

Crude oil characterization: API gravity = (141.5/SG) − 131.5; sweet crude has low sulfur (<0.5%), sour crude has high sulfur.

Distillation units: atmospheric distillation separates crude into fractions (gas, naphtha, kerosene, diesel, gas oil, residue); vacuum distillation processes heavy residue without thermal cracking.

Octane number: measure of gasoline antiknock quality; iso-octane = 100, n-heptane = 0; cetane number for diesel fuel (hexadecane = 100).

Catalytic cracking (FCC): converts heavy gas oil to gasoline using zeolite catalyst; reaction: hydrocarbons → smaller hydrocarbons + coke; regenerator burns coke to restore activity.

Hydrotreating: removes sulfur, nitrogen, and metals by reaction with hydrogen over Co-Mo/Al2O3 or Ni-Mo/Al2O3 catalyst; produces H2S and NH3.

Reforming: converts low-octane naphtha to high-octane aromatics and branched paraffins over Pt/Al2O3 catalyst; produces hydrogen as byproduct.

Petrochemical building blocks: ethylene (from steam cracking of ethane/naphtha), propylene, butadiene, benzene, toluene, xylene; ethylene used for polyethylene, ethylene oxide, vinyl chloride.

Natural gas processing: remove H2S and CO2 (amine treating), dehydrate (glycol absorption), recover NGLs (cryogenic expansion), and fractionate.

Degree of polymerization (DP) = number of repeating units; number-average molecular weight M_n = Σ N_i M_i/Σ N_i; weight-average M_w = Σ N_i M_i²/Σ N_i M_i; polydispersity index PDI = M_w/M_n.

Step-growth polymerization: monomers react to form dimers, trimers, etc.; high molecular weight only at high conversion; Carothers equation: X_n = 1/(1−p) for stoichiometric AA+BB, where p is extent of reaction.

Chain-growth polymerization: initiation, propagation, termination; free-radical, ionic, coordination (Ziegler-Natta); molecular weight depends on initiator concentration and chain transfer.

Copolymer composition: reactivity ratios r1 = k11/k12, r2 = k22/k21; Mayo-Lewis equation: d[M1]/d[M2] = (M1/M2)(r1 M1 + M2)/(M1 + r2 M2).

Glass transition temperature T_g: amorphous polymers below T_g are glassy, above are rubbery; T_g increases with chain stiffness, crystallinity, and crosslinking.

Polymer processing: extrusion (screw extruder), injection molding, blow molding, compression molding, calendering; melt flow index (MFI) measures ease of flow.

Thermosets vs thermoplastics: thermoplastics can be remelted; thermosets crosslink irreversibly (e.g., epoxy, phenol-formaldehyde).

Elastomers: highly crosslinked, low T_g, high extensibility; vulcanization of natural rubber with sulfur improves elasticity and strength.

Michaelis-Menten kinetics: v = V_max S/(K_m + S); K_m is substrate concentration at half V_max; Lineweaver-Burk plot: 1/v = (K_m/V_max)(1/S) + 1/V_max.

Enzyme inhibition: competitive inhibitor increases apparent K_m; noncompetitive inhibitor decreases V_max; uncompetitive inhibitor decreases both K_m and V_max.

Monod growth kinetics: μ = μ_max S/(K_s + S); yield coefficient Y_X/S = ΔX/ΔS; maintenance coefficient m_s accounts for energy used for non-growth functions.

Bioreactor design: batch, fed-batch, continuous (chemostat); chemostat at steady state: μ = D (dilution rate); biomass concentration X = Y_X/S (S0 − S).

Sterilization: thermal death kinetics: N/N0 = exp(−kt); k = A exp(−E/RT); use D-value (decimal reduction time) and z-value (temperature change for 10-fold D change).

Oxygen transfer: OTR = k_L a (C* − C_L); k_L a depends on agitation and aeration; critical oxygen concentration for aerobic cultures.

Downstream processing: centrifugation, filtration, chromatography (ion exchange, gel filtration, affinity), extraction, crystallization, drying.

Immobilized enzymes/cells: advantages include reuse, stability, continuous operation; mass transfer limitations may reduce apparent activity.