ChE Board cheat sheet

Material balance on a steady-state unit: Σ(mass in) = Σ(mass out) + accumulation; set accumulation to zero unless the problem states holdup changes, and count each chemical species separately when reactions occur.

Extent of reaction ξ for species i: n_i = n_i0 + ν_i ξ, where ν_i is the stoichiometric coefficient (negative for reactants); ξ is identical for every species in a single reaction, so one ξ per independent reaction.

Limiting reactant is the one giving the smallest n_i0/(-ν_i) for reactants; fractional conversion X_A = (n_A0 - n_A)/n_A0, and percent excess = (n_fed - n_stoich)/(n_stoich) × 100.

Ideal gas law in process form: PV = nRT with R = 8.314 kJ/(kmol·K) or 0.08206 L·atm/(mol·K); at standard conditions 1 kmol ideal gas occupies 22.414 m³ at 0 °C and 1 atm.

Dalton's law for gas mixtures: p_i = y_i P_total; Raoult's law for ideal vapor-liquid equilibrium gives y_i P = x_i P_i^sat, so relative volatility α_ij = (y_i/x_i)/(y_j/x_j).

Reynolds number Re = ρvD/μ = Dvρ/μ; laminar pipe flow below Re ≈ 2100, transitional to 4000, turbulent above 4000, with friction factor f = 64/Re in the laminar region.

Bernoulli/mechanical energy balance per unit mass: (P1/ρ + v1²/2 + gz1) + W_pump = (P2/ρ + v2²/2 + gz2) + h_f, where h_f is friction loss and pump work is positive when added to the fluid.

Heat conduction: Fourier's law q = -kA(dT/dx); for a composite plane wall, resistances R = L/(kA) add in series, and cylindrical resistance is R = ln(r2/r1)/(2πkL).

Convective heat transfer: q = hAΔT with Nusselt number Nu = hD/k; turbulent flow inside tubes commonly uses Dittus-Boelter Nu = 0.023 Re^0.8 Pr^n, n = 0.4 for heating and 0.3 for cooling of the fluid.

Distillation: minimum reflux from the pinch point on the McCabe-Thiele diagram, minimum stages by Fenske N_min = log[(x_D/(1-x_D))((1-x_B)/x_B)]/log α_avg, and actual stages from Gilliland correlation using R and N_min.

Absorption/stripping design: Kremser equations relate the absorption factor A = L/(mV); for a given removal, more stages are needed as A falls toward 1, and the minimum solvent rate corresponds to A = 1 at infinite stages.

Drying and humidification use the psychrometric chart: humidity ratio Y = 0.622 p_w/(P - p_w), and adiabatic saturation temperature equals wet-bulb temperature for air-water systems.

First law for a steady-flow open system: Q - W = ΔH + ΔKE + ΔPE per unit mass; for nozzles, valves, and turbines with negligible heat loss and kinetic change, W = -ΔH (throttling gives isenthalpic ΔH = 0).

Phase equilibrium criterion: fugacity equality f_i^L = f_i^V; ideal Raoult's law is the limiting case, and the Clausius-Clapeyron equation ln(P2/P1) = -(ΔH_vap/R)(1/T2 - 1/T1) estimates vapor pressure change with temperature.

Chemical potential and Gibbs energy: ΔG = ΔH - TΔS; spontaneity at constant T and P requires ΔG < 0, and at equilibrium ΔG = 0 with the reaction quotient equal to K = exp(-ΔG°/RT).

Arrhenius temperature dependence: k = A exp(-E_a/RT); a plot of ln k versus 1/T gives slope -E_a/R, and doubling k roughly every 10 °C is only an approximation valid near ambient conditions.

Batch reactor design: t = ∫dn_A/(-r_A V); for first-order constant-volume kinetics, -ln(1 - X_A) = kt, and for second-order with equal initial concentrations, X_A/(1 - X_A) = k C_A0 t.

CSTR vs PFR: CSTR volume V = F_A0 X/(-r_A) evaluated at exit conditions; PFR volume V = F_A0 ∫dX/(-r_A), so a CSTR is always larger than a PFR for positive-order kinetics at the same conversion.

Flash point is the lowest temperature at which a liquid gives off enough vapor to ignite; it is measured by closed-cup (Pensky-Martens, Tag) or open-cup (Cleveland) methods, and closed-cup values are lower.

Flammable limits define the concentration range in air supporting combustion: below the LFL the mixture is too lean, above the UFL too rich; the UFL is not a safety margin because dilution by air can re-enter the flammable range.

Dust and vapor explosions require fuel, oxidizer, ignition source, dispersion, and confinement; inerting with nitrogen lowers oxygen below the limiting oxygen concentration (LOC).

HAZOP uses guide words (no, more, less, reverse, as well as, part of, other than) applied to process parameters at nodes to generate deviations; it is a qualitative, team-based hazard identification method.

LOPA and layer-of-protection analysis quantify risk reduction: risk = frequency × consequence, and independent protection layers must be specific, independent, dependable, and auditable to claim credit.

Relief system sizing uses the API 520/521 basis: required relief area depends on worst-credible scenario (fire, runaway reaction, blocked outlet), and two-phase or reactive relief may need DIERS methodology rather than ideal-gas equations.

Capital cost estimation: six-tenths rule scales equipment cost as C2 = C1(S2/S1)^0.6; the Lang factor multiplies delivered equipment cost to give fixed capital, and the chemical engineering plant cost index updates costs to a new year.

Profitability measures: payback period = fixed capital/annual cash flow; net present value discounts cash flows at the hurdle rate; return on investment compares annual profit to capital, and depreciation is a non-cash expense that reduces taxable income.

Engineering ethics and codes: the professional engineer signs and seals only work within competence, holds paramount the public safety, and reports known violations to the licensing board; pressure vessels and relief devices follow ASME and local code requirements.

Fick's first law: J_A = -D_AB (dC_A/dx); for dilute A diffusing through stagnant B, N_A = J_A/(1 - y_A), and equimolar counterdiffusion gives N_A = J_A directly.

Mass transfer coefficient correlations mirror heat transfer: Sherwood Sh = k_c D/D_AB, Schmidt Sc = μ/(ρD_AB), and for turbulent pipe flow Sh = 0.023 Re^0.83 Sc^0.33.

Two-film theory gives overall coefficients 1/K_OG = 1/k_G + H/k_L; the resistance in the phase with the smaller individual coefficient controls the rate when the Henry constant is near unity.

Heat exchanger design: q = U A ΔT_lm F, with log-mean temperature difference ΔT_lm = (ΔT1 - ΔT2)/ln(ΔT1/ΔT2); F corrects for multipass and crossflow arrangements and is 1.0 for pure countercurrent.

Overall heat transfer coefficient from resistances: 1/U = 1/h_i + R_fi + L/(k_wall) + R_fo + 1/h_o, with fouling factors often dominating the design margin.

Filtration: constant-pressure cake filtration follows V² + 2V V_e = K t; the plot of t/V versus V is linear, with slope related to specific cake resistance and intercept to medium resistance.

Extraction and leaching: distribution coefficient K = y/x, and the separation factor depends on K and phase ratio; countercurrent stages are solved graphically on a triangular or right-angle diagram or by the Kremser analog.

Membrane and adsorption separations: rejection R = 1 - C_p/C_f for reverse osmosis, and adsorption isotherms follow Langmuir q = q_max K C/(1 + K C) or Freundlich q = K C^(1/n) for fitting equilibrium data.

Dimensional analysis: Buckingham Pi theorem reduces variables to dimensionless groups; common chemical engineering groups include Reynolds, Prandtl, Nusselt, Sherwood, Schmidt, and Damköhler numbers.