PE Chemical cheat sheet

1 atm = 101.325 kPa = 760 mmHg; 1 Btu = 1.055 kJ; 1 hp = 0.7457 kW; 1 lb = 0.4536 kg.

Ideal gas: PV = nRT; at 1 atm and 0°C, molar volume = 22.414 L/mol.

Reynolds number: Re = ρvD/μ = vD/ν; pipe flow is laminar for Re < 2100 and turbulent for Re > 4000.

Henry's law: p_i = H x_i for dilute solute; Raoult's law: p_i = x_i p_sat for ideal mixtures.

Gibbs phase rule for nonreactive systems: F = C - P + 2, where F is intensive degrees of freedom.

Absolute pressure = gauge pressure + atmospheric pressure; use absolute temperature in gas and thermodynamic formulas.

Logarithmic mean driving force: ΔT_lm = (ΔT1 - ΔT2)/ln(ΔT1/ΔT2), with ΔT1 ≠ ΔT2.

Stoichiometric sign convention: reactants have negative coefficients and products positive coefficients in reaction sums.

General balance: accumulation = in - out + generation - consumption.

At steady state, accumulation = 0; for total mass with no reaction, total mass in = total mass out.

Recycle returns unconverted material to raise overall conversion; purge prevents inert or accumulating species from building up.

Bypass reduces the effective conversion or heat transfer because part of the stream skips the unit.

Open steady energy balance neglecting kinetic and potential energy: Q - W = Σ_out m h - Σ_in m h.

Heat of reaction from heats of formation: ΔH_rxn = Σ ν_i ΔH_f,i, with ν_i negative for reactants and positive for products.

Sensible heat: Q = m Cp ΔT; latent heat: Q = m λ at constant temperature.

Percent excess air = (actual air - theoretical air)/theoretical air × 100; theoretical air comes from stoichiometric oxygen demand.

First law for a closed system: ΔU = Q - W; for a differential change, dU = δQ - δW.

Second law: ΔS_univ ≥ 0; for a reversible process, ΔS = Q_rev/T.

Carnot efficiency: η = 1 - T_C/T_H, using absolute temperatures.

Gibbs free energy: ΔG = ΔH - TΔS; a negative ΔG indicates spontaneity at constant T and P.

Equilibrium constant: K = exp(-ΔG°/RT); van't Hoff equation: ln(K2/K1) = -(ΔH°/R)(1/T2 - 1/T1).

Fugacity: f_i = φ_i P; ideal-solution activity coefficient γ_i = 1 and fugacity equals partial pressure.

Phase equilibrium requires equal temperature, equal pressure, and equal fugacity of each component in all phases.

Compressibility factor: Z = PV/(nRT); corresponding states uses reduced temperature T_r = T/T_c and reduced pressure P_r = P/P_c.

Bernoulli equation for steady, incompressible, frictionless flow: P/ρ + v²/2 + gz = constant along a streamline.

Continuity: m = ρAv; for incompressible flow, A1v1 = A2v2.

Darcy-Weisbach friction loss: ΔP = f(L/D)(ρv²/2); f is the Darcy friction factor.

Laminar Hagen-Poiseuille flow: ΔP = 32 μ L v / D².

Pump shaft power: P = ρgQH/η, where H is pump head and η is pump efficiency.

NPSH_a = P_atm/(ρg) + z - P_vap/(ρg) - h_f; cavitation occurs when NPSH_a < NPSH_r.

Drag force: F_D = C_D(1/2 ρv²)A.

Ergun equation for packed beds combines viscous and inertial loss terms; pressure drop rises strongly as void fraction decreases.

Fourier conduction law: q = -kA dT/dx; plane-wall thermal resistance is R = L/(kA).

Convection: q = hA(T_s - T∞); convection resistance is 1/(hA).

Radiation: q = εσA(T_s⁴ - T_sur⁴), with σ = 5.67 × 10⁻⁸ W/m²K⁴.

Overall coefficient: 1/U = 1/h_i + R_fouling + L/k + 1/h_o when all resistances use the same area basis.

LMTD method uses q = U A ΔT_lm; effectiveness-NTU method is convenient when outlet temperatures are unknown.

Biot number: Bi = hL/k; lumped-capacitance analysis is valid for Bi < 0.1.

Fouling adds thermal resistance, lowers U, and reduces heat duty for a fixed area and driving force.

Film condensation heat transfer increases with higher latent heat and liquid thermal conductivity but decreases with thicker condensate films.

Fick's first law: J_A = -D_AB dC_A/dx.

Mass-transfer coefficient: N_A = k_c(C_Ai - C_A∞).

Sherwood number: Sh = k_c L/D; correlations usually express Sh as a function of Re and Sc.

Schmidt number: Sc = μ/(ρD); Lewis number: Le = α/D.

Packed-column height: Z = HTU × NTU, where HTU is height of a transfer unit and NTU is number of transfer units.

Relative volatility: α = (y_A/x_A)/(y_B/x_B); larger α means easier distillation and fewer stages.

McCabe-Thiele method uses operating lines and equilibrium curve; the q-line represents feed thermal condition.

Gas absorption transfers solute from gas to liquid; stripping transfers solute from liquid to gas.

Rate law: -r_A = k C_A^n; Arrhenius temperature dependence: k = A exp(-E_a/RT).

Batch reactor time: t = N_A0 ∫ dX/(-r_A V) from X = 0 to X.

CSTR design equation: V = F_A0 X/(-r_A), evaluated at outlet conditions.

PFR design equation: V = F_A0 ∫ dX/(-r_A) from X = 0 to X.

Constant-volume batch integrated rates: zero order C_A = C_A0 - kt; first order ln(C_A0/C_A) = kt; second order 1/C_A - 1/C_A0 = kt.

Conversion: X = (F_A0 - F_A)/F_A0 for flow systems or (N_A0 - N_A)/N_A0 for batch systems.

Yield = moles desired product formed per mole reactant fed; selectivity = desired product per undesired product formed.

Catalyst effectiveness factor: η = actual rate/rate at surface conditions; Thiele modulus compares reaction rate to diffusion rate.

Six-tenths rule: C2 = C1(S2/S1)^0.6 for approximate scaling of equipment cost with capacity.

Cost index update: C2 = C1(I2/I1), where I is a cost index such as CEPCI.

Straight-line depreciation: D = (P - S)/n, where P is installed cost, S is salvage value, and n is useful life.

NPV = Σ CF_t/(1+i)^t - initial investment; IRR is the discount rate that makes NPV equal zero.

Payback period is the time for cumulative cash inflows to equal the initial investment; it ignores cash flow after payback.

Total capital investment = fixed capital investment + working capital.

Manufacturing cost = fixed costs + variable costs; raw materials and utilities are usually major variable costs.

Pinch analysis minimizes utility use by matching hot and cold streams and respecting the minimum approach temperature.

PID controller: u = K_c e + (K_c/τ_I)∫e dt + K_c τ_D de/dt.

Proportional action gives immediate response but leaves offset; integral action removes offset; derivative action anticipates change.

First-order process: τ dy/dt + y = K u, where K is process gain and τ is time constant.

Dead time θ appears as e^(-θs) and reduces achievable controller gain and stability margin.

Bode stability criteria use gain margin and phase margin; gain crossover occurs where loop gain magnitude is 1.

Control valves are specified fail-closed or fail-open according to the safe state on loss of signal.

Cascade control uses a fast inner loop and a slower outer loop; the inner loop must be at least several times faster.

Ratio control holds one flow at a fixed ratio to another; feedforward control acts on a measured disturbance before the controlled variable changes.

LFL and UFL bound the flammable concentration range in air; inerting keeps oxygen below the limiting oxygen concentration.

Flash point is the lowest temperature for a flammable vapor near a liquid surface; autoignition temperature is the temperature for self-sustained ignition without an ignition source.

Relief scenarios include blocked outlet, fire exposure, runaway reaction, and utility failure; relief devices are sized for the controlling scenario.

HAZOP applies guide words such as no, more, less, and reverse to process parameters; LOPA evaluates independent protection layers.

Inherent safety hierarchy: minimize, substitute, moderate, and simplify before relying on add-on controls.

TLV and PEL are occupational exposure limits; TWA limits apply to time-weighted average exposure over a work shift.

Waste hierarchy: reduce, reuse, recycle, recover energy, then dispose.

Major accident scenarios include BLEVE, pool fire, jet fire, and vapor cloud explosion; each has distinct consequence modeling assumptions.

Mole fraction x_i = n_i/Σn_i; mass fraction w_i = m_i/Σm_i; convert between them using component molecular weights.

Parts per million by volume for gases is approximately equal to parts per million by mole.

Standard gravity g = 9.80665 m/s²; water density near 4°C is about 1000 kg/m³.

The logarithmic mean is appropriate for a driving force that varies linearly with the transferred quantity.

Dimensional analysis groups variables into dimensionless numbers such as Re, Pr, Sc, and Nu.

At constant composition, Cp - Cv = R for an ideal gas.

A steady-state process has no accumulation term even when flow rates and temperatures vary with position.

Significant figures should reflect the precision of the least precise input in a calculation.

Component balance with reaction: accumulation_i = in_i - out_i + generation_i - consumption_i.

For a steady reactor with recycle, overall conversion can be high while per-pass conversion is lower.

A purge stream is required when an inert or impurity enters and no reaction consumes it.

Heat exchanger duty: Q = m Cp ΔT for a single stream with no phase change.

Adiabatic energy balance: sensible heat change equals heat released by reaction.

Bypass streams lower the mixed feed temperature or composition change compared with the main unit.

Combustion oxygen demand follows the stoichiometry of carbon, hydrogen, and sulfur in the fuel.

Recycle ratio is recycle flow divided by fresh feed flow and affects reactor size and separation load.

For an ideal gas, ΔH depends only on temperature and ΔU depends only on temperature.

Entropy change for an ideal gas: ΔS = n Cp ln(T2/T1) - nR ln(P2/P1).

A throttling process is isenthalpic; for an ideal gas, temperature does not change.

Isentropic compression of an ideal gas: T2/T1 = (P2/P1)^((γ-1)/γ).

Heat engine efficiency cannot exceed the Carnot efficiency between the same reservoirs.

A positive deviation from Raoult's law gives activity coefficient γ_i > 1 and higher volatility.

At the critical point, vapor and liquid phases become indistinguishable and latent heat goes to zero.

Chemical equilibrium shifts with temperature according to whether the reaction is exothermic or endothermic.

For a Newtonian fluid, shear stress is proportional to velocity gradient: τ = μ du/dy.

The hydraulic diameter of a noncircular duct is D_h = 4A/P_wetted.

Minor losses are expressed as h_m = K v²/(2g), where K is the loss coefficient.

A centrifugal pump curve plots head versus flow; the operating point is where the pump curve meets the system curve.

A positive displacement pump delivers approximately constant flow with varying discharge pressure.

Flow through an orifice: Q = C_d A_o √(2ΔP/ρ).

Terminal settling velocity balances drag, buoyancy, and gravity; Stokes law applies at low Re.

Cavitation damages pumps and valves when local pressure falls below vapor pressure and bubbles collapse.

Prandtl number: Pr = Cp μ/k, comparing momentum and thermal diffusivity.

Nusselt number: Nu = hL/k; correlations express Nu as a function of Re and Pr.

For a cylindrical wall, thermal resistance is R = ln(r2/r1)/(2πkL).

Heat exchanger effectiveness ε = actual heat transfer/maximum possible heat transfer.

NTU = UA/C_min for a heat exchanger.

A counterflow exchanger generally has higher effectiveness than a parallel-flow exchanger for the same NTU.

Thermal radiation from a small object to large surroundings uses q = εσA(T_s⁴ - T_sur⁴).

Boiling curves show nucleate boiling, transition boiling, and film boiling; film boiling has low heat flux and can cause burnout.

Equimolar counterdiffusion: N_A = -N_B and J_A = -D_AB dC_A/dx.

Diffusion through a stagnant gas film gives N_A = (D_AB P/RT L) ln((1-y_A2)/(1-y_A1)).

Overall mass-transfer coefficient combines gas-film and liquid-film resistances using Henry's law equilibrium.

Gas-film control occurs when the solute is sparingly soluble; liquid-film control occurs when it is highly soluble.

Leaching and extraction use solvent contact to transfer solute from one phase to another.

Drying rate curves show constant-rate and falling-rate periods; the critical moisture content separates them.

Membrane separation selectivity depends on permeability and driving force.

Adsorption breakthrough curves show effluent concentration rising after bed capacity is exhausted.

For a first-order reaction in a CSTR, conversion X = kτ/(1 + kτ), where τ = V/Q.

For a first-order reaction in a PFR, X = 1 - exp(-kτ).

Multiple CSTRs in series approach PFR behavior as the number of tanks increases.

For positive-order reactions, a PFR requires less volume than a CSTR for the same conversion.

Reversible exothermic reactions have higher conversion at lower temperature but slower rate; an optimum temperature policy exists.

Runaway reaction risk rises when heat generation exceeds heat removal capacity.

Catalyst deactivation lowers activity over time and can be modeled as a decay in rate constant.

Residence time distribution characterizes nonideal flow; the tanks-in-series model fits many real reactors.

Equipment cost estimates become more accurate from order-of-magnitude to study to definitive estimates.

Fixed capital includes equipment, installation, piping, instrumentation, and buildings; working capital covers inventories and receivables.

Utility costs include steam, cooling water, electricity, refrigeration, and fuel.

Operating labor cost often scales weakly with plant capacity, so larger plants have lower labor cost per unit.

The minimum acceptable rate of return is used as the discount rate in profitability analysis.

Sensitivity analysis tests how NPV changes with feed cost, product price, and capacity.

Heat integration reduces both heating and cooling utility requirements.

A process flow diagram shows major equipment and streams; a piping and instrumentation diagram adds controls and line details.

A self-regulating process reaches a new steady state after a step disturbance without controller action.

An integrating process ramps when input and output are unbalanced.

Controller tuning tradeoffs include speed of response, overshoot, and robustness.

Derivative action should be avoided on noisy measurements unless filtered.

Anti-windup prevents integral action from accumulating when a valve is saturated.

A control valve's installed characteristic depends on the system pressure drop, not only the valve's inherent characteristic.

Closed-loop time constant is affected by controller gain and process dynamics.

Alarm and trip setpoints should be separated from normal operating and control setpoints.

A flammable vapor cloud can explode if it ignites within its flammability range in a confined or congested area.

Static electricity ignition can be controlled by grounding and bonding equipment.

Toxic exposure risk depends on concentration, duration, and toxicity; ventilation reduces concentration.

A safety instrumented function has a safety integrity level related to probability of failure on demand.

Emergency relief systems protect equipment from overpressure but must discharge to a safe location.

Spill containment and secondary containment reduce environmental release consequences.

Process safety management includes hazard analysis, operating procedures, training, and management of change.

Waste minimization at the source is preferred over end-of-pipe treatment.

A degree-of-freedom analysis counts unknowns and independent equations before solving a material balance.

Basis selection simplifies balances; choose a convenient amount such as 100 mol or 1 kg of feed.

Tie components are species that do not appear in added streams and can be used to relate stream sizes.

Element balances can be used when reaction stoichiometry is unknown.

Recycle plus purge is common when a reactant is expensive and an inert accumulates.

Heat of mixing is negligible for ideal solutions but can be significant for nonideal mixtures.

Unsteady-state balance: dM/dt = ṁ_in - ṁ_out for total mass.

Energy balance around a heat exchanger includes enthalpy changes of both streams and any heat loss.

For a reversible adiabatic process, entropy is constant.

For an irreversible adiabatic process, entropy increases.

The Joule-Thomson coefficient determines whether a real gas cools or heats on throttling.

A vapor-compression refrigeration cycle uses compressor work to move heat from low to high temperature.

Coefficient of performance for a refrigerator is Q_C/W.

Chemical potential differences drive mass transfer between phases.

Excess Gibbs energy relates activity coefficients to nonideal solution behavior.

The Clapeyron equation relates saturation pressure slope to latent heat and volume change.

Viscosity of liquids decreases with increasing temperature; viscosity of gases increases with increasing temperature.

For laminar flow in a pipe, velocity profile is parabolic and average velocity is half the maximum velocity.

For turbulent pipe flow, the velocity profile is flatter and wall roughness affects friction factor.

A U-tube manometer measures pressure difference as ΔP = ρgΔh.

A venturi meter has lower permanent pressure loss than an orifice meter.

Fluidization begins when bed pressure drop equals bed weight per unit area.

Two-phase flow pressure drop includes friction, acceleration, and elevation components.

Water hammer results from rapid valve closure and pressure wave propagation in a liquid line.

For steady one-dimensional conduction with no generation, heat rate is constant through each layer.

Thermal contact resistance lowers heat transfer between joined surfaces.

Fins increase surface area but have efficiency less than one.

Fin effectiveness compares fin heat transfer with heat transfer from the bare base area.

For natural convection, heat transfer depends on Grashof and Prandtl numbers.

For forced convection in tubes, Dittus-Boelter is Nu = 0.023 Re^0.8 Pr^n, with n = 0.4 for heating and 0.3 for cooling.

Heat exchanger fouling factors are added as resistances and reduce overall U.

Radiation heat transfer becomes important at high temperature because it scales with T⁴.

Diffusivity in gases increases with temperature and decreases with pressure.

Diffusivity in liquids is much lower than in gases and increases with temperature.

Mass-transfer coefficients depend on flow regime, geometry, and diffusivity.

For dilute absorption, the operating line and equilibrium line are often approximated as straight.

Minimum solvent rate corresponds to an infinite number of stages or a pinch at the column end.

Steam distillation is used for heat-sensitive materials that are immiscible with water.

Crystallization yield depends on solubility versus temperature and on mother-liquor composition.

Chromatographic separation depends on differential adsorption or partitioning between phases.

For zero-order reaction, conversion in a CSTR is X = kτ/C_A0, valid while C_A remains positive.

For second-order reaction in a CSTR, X satisfies kτ = X/(C_A0(1-X)²).

For second-order reaction in a PFR, kτC_A0 = X/(1-X).

Higher temperature increases rate constant but may reduce equilibrium conversion for exothermic reversible reactions.

Mixing scale affects selectivity when reactions have different orders or when local concentrations matter.

Heat removal in a stirred tank reactor depends on jacket area, coolant temperature, and overall coefficient.

Catalyst pellet size affects internal diffusion resistance and effectiveness.

A recycle reactor can approximate a CSTR or PFR depending on recycle ratio.

Battery limits define the boundary of a process unit for cost and responsibility.

A block flow diagram shows major process steps without detailed piping.

Pump and compressor costs depend strongly on power and materials of construction.

Material selection affects capital cost and maintenance cost.

Economies of scale reduce cost per unit capacity but may be limited by equipment fabrication limits.

The discounted payback period accounts for the time value of money.

Break-even analysis finds the production rate at which revenue equals total cost.

A profitability analysis should include raw materials, utilities, labor, maintenance, taxes, and depreciation.

A feedback controller measures the controlled variable and adjusts the manipulated variable.

A feedforward controller measures a disturbance and adjusts the manipulated variable before the controlled variable responds.

Loop pairing should match manipulated and controlled variables with strong interaction and favorable dynamics.

Relative gain array analysis identifies interactions in multivariable control.

A first-order plus dead time model is often used for controller tuning.

Ziegler-Nichols tuning can produce aggressive settings with overshoot.

A split-range controller uses one controller output to operate two valves over different ranges.

Safety instrumented systems are independent of basic process control systems.

Dust explosions require combustible dust, dispersion, confinement, and an ignition source.

Hot work permits control ignition sources during maintenance.

Lockout/tagout isolates energy sources before maintenance.

A combustible gas detector alarm setpoint is usually a fraction of the lower flammability limit.

Pressure relief valve set pressure must not exceed equipment maximum allowable working pressure.

A rupture disk provides fast relief and is often used before a relief valve in corrosive service.

Environmental permits may limit air emissions, wastewater discharge, and hazardous waste.

Life cycle assessment compares environmental impacts across a product or process life cycle.

Mass and molar flow are related by m = n × molecular weight.

Density of an ideal gas is ρ = PM/(RT).

Specific gravity of a liquid is density relative to water at a specified temperature.

Vapor pressure increases exponentially with temperature.

A material balance around a black box does not require internal process details.

Units of viscosity: 1 cP = 0.001 Pa·s.

Units of thermal conductivity: 1 Btu/(h·ft·°F) ≈ 1.7307 W/(m·K).

A dimensionless group preserves the ratio of competing physical effects.

For a steady process with reaction, total mass is conserved but total moles may change.

Extent of reaction ξ gives n_i = n_i0 + ν_i ξ.

Conversion of the limiting reactant is often the basis for reactor sizing.

Excess of one reactant can shift equilibrium and improve selectivity.

Energy balance for a reactor includes heat of reaction, sensible heat, and heat exchange.

Heat integration can reduce external utility demand.

A purge stream composition is the same as the recycle stream composition at the purge point.

Overall material balance includes fresh feed, product, purge, and any waste streams.

For an ideal gas, enthalpy is independent of pressure.

For a real gas, enthalpy depends on pressure through residual properties.

The Clausius-Clapeyron equation gives ln(P2/P1) = -(ΔH_vap/R)(1/T2 - 1/T1).

A phase envelope shows bubble-point and dew-point curves for a mixture.

The critical temperature is the highest temperature at which a gas can be liquefied by pressure alone.

The compressibility factor chart uses reduced properties for corresponding states.

Activity coefficients can be predicted by models such as Margules or van Laar.

Azeotropes occur when vapor and liquid compositions are equal.

Reynolds number for a packed bed uses particle diameter and superficial velocity with void fraction corrections.

Pressure drop in a pipe increases with the square of velocity in turbulent flow.

A globe valve gives better throttling control than a gate valve.

A centrifugal compressor is used for high-volume gas service; a reciprocating compressor is used for high pressure.

Cavitation in a control valve can be avoided by selecting a valve with adequate pressure recovery factor.

A siphon can cause vacuum conditions and collapse piping if not vented.

Flow measurement with a rotameter is based on a float position in a tapered tube.

Non-Newtonian fluids may have shear-thinning or shear-thickening behavior.

For a sphere, conduction resistance is R = (r2 - r1)/(4πk r1 r2).

The lumped capacitance time constant is τ = ρV Cp/(hA).

A larger heat transfer coefficient reduces the outside film resistance.

A thin-wall heat exchanger has negligible wall conduction resistance.

Radiation view factors depend on geometry and orientation.

A gray surface has emissivity independent of wavelength.

Condensation can be dropwise or filmwise; dropwise gives higher heat transfer but is difficult to maintain.

Heat transfer with phase change often gives much higher coefficients than single-phase convection.

Mass balance around an absorption column: L(x_in - x_out) = G(y_out - y_in) for dilute systems.

The operating line slope is L/G for absorption.

The equilibrium curve relates solute concentration in gas and liquid phases.

A higher solvent-to-gas ratio reduces the required number of stages.

Packed column random packing gives higher capacity but lower efficiency than structured packing.

Membrane flux is proportional to permeability and driving force divided by membrane thickness.

Drying requires heat for evaporation and mass transfer of vapor away from the surface.

Extraction selectivity depends on solvent affinity for the solute.

For an adiabatic CSTR, heat generation and heat removal curves determine steady states.

Multiple steady states can occur in exothermic CSTRs with nonlinear heat generation.

A runaway reaction can occur when heat removal cannot match heat generation.

Catalyst selectivity can change with conversion because secondary reactions consume desired product.

For parallel reactions, higher reactant concentration favors the reaction with higher order.

For series reactions, mixing can affect selectivity if local concentration gradients exist.

A membrane reactor can remove product and shift equilibrium.

Reaction calorimetry measures heat release for safety and scale-up.

A feasibility study estimates capital and operating costs before detailed design.

Grassroots cost is the cost of building a new plant; battery-limit cost excludes utilities and site infrastructure.

Location affects labor, utility, and transportation costs.

Contingency is included in cost estimates to cover unknown future costs.

Working capital is recovered at the end of a project life in a simplified cash flow.

Inflation affects both capital and operating costs and should be treated consistently.

A decision tree can evaluate staged investments under uncertainty.

Optimization balances capital cost against operating cost.

A dead-band in a controller prevents excessive valve movement from small errors.

A measurement lag can destabilize a control loop.

A transmitter range should cover normal and abnormal operating conditions.

A control valve should be sized for the maximum expected flow and minimum pressure drop.

Cascade control requires the inner loop to be faster than the outer loop.

Feedforward control does not correct unmeasured disturbances or model error.

Model predictive control uses a process model to predict future behavior and optimize inputs.

A safety interlock trip is separate from normal regulatory control.

Vapor cloud explosion severity depends on cloud size, confinement, and ignition location.

A pool fire heat flux decreases with distance from the flame.

A jet fire occurs when pressurized flammable gas escapes and ignites.

A BLEVE occurs when a pressurized liquid container fails and the liquid flashes.

Emergency response planning includes evacuation routes and communication.

Personal protective equipment is the last line of defense in the hierarchy of controls.

Process hazard analysis should be updated when there is a management-of-change modification.

Environmental risk assessment evaluates fate, transport, and toxicity of releases.

The ideal gas law is a limiting law valid at low pressure and high temperature.

The van der Waals equation corrects for molecular volume and attractive forces.

Mole percent equals volume percent for ideal gases.

Weight percent is not equal to mole percent unless molecular weights are equal.

A conversion factor cancels units but not physical meaning.

A flowchart helps identify streams, units, and recycle loops in a balance.

Boundary selection changes which streams cross the system boundary.

A steady-state assumption is valid after startup transients decay.

For a distillation column, overall material balance: F = D + B and Fz_F = Dx_D + Bx_B.

Reflux ratio is L/D and affects purity and energy use.

A condenser duty equals vapor latent heat removed plus subcooling if present.

A reboiler duty supplies latent heat to vaporize liquid.

For a flash drum, vapor and liquid products are in equilibrium.

A mixer balance combines stream enthalpies; adiabatic mixing conserves total enthalpy.

A splitter balance uses specified split fractions.

Purge composition equals recycle composition for a simple purge from a recycle loop.

The Gibbs phase rule for reacting systems includes independent reactions: F = C - P + 2 - r.

The reaction coordinate reduces the number of independent components.

The equilibrium extent is found by minimizing Gibbs free energy.

For an ideal gas reaction, K_p depends only on temperature.

K_c and K_p are related by K_p = K_c(RT)^Δn.

Le Chatelier's principle predicts equilibrium shifts when pressure, temperature, or concentration changes.

A higher pressure favors the side with fewer moles of gas.

A catalyst does not change equilibrium position; it changes the rate of approach.

The friction factor in laminar flow is f = 64/Re.

The Colebrook equation is implicit in f and applies to turbulent pipe flow.

A Moody chart plots f versus Re and relative roughness.

The equivalent length method accounts for fittings as additional pipe length.

A centrifugal pump has a maximum efficiency at its best efficiency point.

Pumps in series add head; pumps in parallel add flow.

A fan moves gas at low pressure rise; a blower moves gas at moderate pressure rise.

A compressor raises gas pressure significantly and requires cooling between stages.

The Stefan-Boltzmann law gives total emissive power E = εσT⁴.

Kirchhoff's law states that emissivity equals absorptivity at the same wavelength and temperature.

A blackbody has emissivity equal to one.

A gray body has constant emissivity across wavelengths.

Thermal insulation reduces heat loss by adding conduction resistance.

Critical insulation radius can cause increased heat loss if insulation is too thin on a small pipe.

A heat exchanger with phase change on one side has a nearly constant temperature stream.

Fouling can be reduced by proper velocity and water treatment.

The number of transfer units NTU = ∫ dy/(y - y*) for absorption.

The height of a transfer unit HTU = G/(K_y a).

Packed column capacity is limited by flooding.

Loading occurs before flooding and reduces efficiency.

Aeration and stripping remove volatile contaminants from water.

Ion exchange removes ions by exchanging them with resin-bound ions.

Reverse osmosis uses pressure to overcome osmotic pressure.

Ultrafiltration separates by molecular size.

For a reversible first-order reaction, equilibrium conversion depends on the equilibrium constant.

The rate of a catalytic reaction can be limited by external film diffusion or internal pore diffusion.

External diffusion resistance reduces the observed rate when mass transfer is slow.

Internal diffusion resistance is characterized by the Thiele modulus.

A catalyst with small pores can suffer from diffusion limitations.

A fluidized bed reactor provides good temperature control and continuous catalyst regeneration.

A fixed bed reactor can develop hot spots if heat removal is poor.

A slurry reactor provides good mixing and temperature control.

A process flowsheet should show major equipment, streams, and recycle loops.

A piping and instrumentation diagram includes instruments, control loops, and line sizes.

Equipment specification includes materials, design pressure, and design temperature.

Design pressure is usually above the maximum operating pressure.

Design temperature covers the maximum and minimum expected temperatures.

Relief system design is part of process design and safety.

Utility selection depends on temperature level and cost.

Pinch analysis identifies the minimum heating and cooling utility targets.

A controller output can be direct-acting or reverse-acting depending on valve action and process gain.

A control loop is stable if disturbances decay over time.

A loop with too much gain can oscillate or become unstable.

A loop with too little gain can be sluggish.

Integral time is the time for integral action to repeat the proportional output.

Derivative time is the time by which derivative action anticipates the error.

A filter reduces noise but adds lag.

A valve positioner improves control valve response.

A safety data sheet provides hazard, handling, and emergency information for a chemical.

A flammable liquid has a flash point below a specified threshold.

A combustible liquid has a higher flash point than a flammable liquid.

Oxidizers can increase fire intensity and must be segregated from flammables.

A confined space entry requires atmospheric testing and a permit.

Noise exposure can cause hearing loss and is controlled by engineering and administrative measures.

Wastewater treatment may include primary, secondary, and tertiary treatment.

Air pollution control equipment includes scrubbers, filters, and catalytic oxidizers.

A unit conversion should be checked by dimensional analysis.

A calculation should use consistent units throughout.

Temperature differences in °C and K are equal in magnitude.

Absolute temperature must be used in the ideal gas law.

Pressure can be expressed as gauge, absolute, or differential.

A vacuum pressure is below atmospheric pressure.

A mole is 6.022 × 10²³ entities.

Molecular weight is numerically equal to molar mass in g/mol.

A purge stream prevents accumulation of inert gas in a recycle loop.

A recycle stream increases overall conversion but increases separation load.

A bypass stream reduces conversion in a reactor.

A splitter divides a stream into specified fractions.

A mixer combines streams and conserves mass and energy.

A flash drum separates vapor and liquid at equilibrium.

A distillation column separates by relative volatility.

An absorber removes solute from gas by liquid contact.

Entropy is a state function.

Enthalpy is a state function.

Internal energy is a state function.

Heat and work are path functions.

A reversible process produces maximum work.

An irreversible process produces entropy.

The Carnot cycle consists of two isothermal and two adiabatic steps.

A heat pump uses work to transfer heat from cold to hot.

A Newtonian fluid has constant viscosity.

A non-Newtonian fluid has viscosity that depends on shear rate.

A Bingham plastic requires a yield stress before flow.

A pseudoplastic fluid is shear-thinning.

A dilatant fluid is shear-thickening.

A thixotropic fluid has time-dependent viscosity.

A rheopectic fluid also has time-dependent viscosity.

Viscosity is a measure of resistance to flow.

Conduction requires a temperature gradient.

Convection requires fluid motion.

Radiation does not require a medium.

A heat exchanger transfers heat between two fluids.

A shell-and-tube exchanger is common for high pressure.

A plate exchanger has high area density.

A fin increases heat transfer area.

Insulation reduces heat loss.

Diffusion is molecular movement from high to low concentration.

Convection enhances mass transfer.

A concentration gradient drives diffusion.

A mass-transfer coefficient describes convective mass transfer.

The Sherwood number is dimensionless.

The Schmidt number is dimensionless.

The Lewis number is dimensionless.

The Peclet number is dimensionless.

A catalyst increases reaction rate without being consumed.

A catalyst does not change equilibrium.

An enzyme is a biological catalyst.

A homogeneous catalyst is in the same phase as reactants.

A heterogeneous catalyst is in a different phase.

A catalyst can be poisoned.

A catalyst can be regenerated.

Catalyst selectivity is important in industrial reactions.

Capital cost is the investment in equipment and facilities.

Operating cost is the ongoing cost of production.

Fixed cost does not vary with production rate.

Variable cost varies with production rate.

Depreciation is a noncash expense.

Taxes affect after-tax cash flow.

Inflation affects economic analysis.

A feasibility study evaluates project viability.

A sensor measures a process variable.

A transmitter sends a signal.

A controller compares measurement to setpoint.

A final control element changes the process.

A valve is a common final control element.

A control loop has a setpoint and a measured variable.

A disturbance affects the process.

A feedback loop corrects error.

A hazard is a potential source of harm.

A risk is the combination of probability and consequence.

A safety barrier reduces risk.

A permit-to-work controls maintenance.

A hazard analysis identifies hazards.

A safety audit checks compliance.

An incident investigation identifies root causes.

Emergency response reduces consequences.