PE Chemical problems chain decisions — basis, model, method — before arithmetic pays off. Readiness checks: write a five-line plan (quantity, basis, equation, data, decision) before computing; match bubble, dew, and flash to their governing equations; balance a recycle loop with a purge so overall conversion differs from per-pass conversion; choose LMTD or effectiveness-NTU from the given data; assemble rate law, stoichiometry, and design equation for a stated reactor type. Sequence: short problem sets per topic, the problem-audit drill across mixed topics, timed mixed sets with the NCEES handbook, then targeted work on your weakest audit scores. Administrative details such as registration and scheduling are set by NCEES; see ncees.org.
Building a Written Solution Plan Before Any Arithmetic
Before computing, write four lines: the quantity requested with units, a basis, the governing equation, and the property data needed. This plan exposes missing information early and keeps multi-step problems from drifting into algebra errors.
Choose the basis to make the arithmetic simple: 100 mol/h when mole fractions are given, 1 hour when rates are involved, or a mass basis when a density or weight percent appears. Convert every stream to the same basis immediately, including fuel compositions reported on a dry basis versus wet. When a problem gives a production rate, work the balance on a convenient basis and scale at the end; scaling mole fractions or ratios directly never works because they are intensive quantities.
Treat the written plan as the deliverable: if the plan names the equation and the unknown, the computation becomes mechanical. Practice retrieving equations from the NCEES-supplied reference handbook rather than from memory, because locating the right equation is part of the speed you build. A plan that names two candidate methods — for example, dew point versus flash — is stronger than one that silently picks a path; writing both candidates forces the comparison the problem is asking you to make.
Recycle and Purge: Why Per-Pass and Overall Conversions Differ
A recycle stream means the reactor balance and the process balance are different calculations. Define per-pass conversion around the reactor and overall conversion around the entire loop including the purge, then connect them through the recycle ratio.
The purge exists to stop inert accumulation: without it, inerts recycle forever and build up until the circulating flow is enormous. Overall conversion of the reactant exceeds single-pass conversion because unreacted material returns, but fresh reactant leaves the loop only through reaction and through purge losses. Setting up the balance requires one unknown recirculating flow, found either from a component balance on the inert or from a specified recycle ratio.
Worked scenario: fresh feed is 100 mol/h of A plus 5 mol/h of inert; the reactor converts A at 50 percent per pass, product is fully removed, and the purge takes 20 percent of the recycle. A plausible mistake is reporting 50 percent as the overall conversion. The better decision: the inert balance gives 20 mol/h of recycled inert, the A balance gives a reactor feed of 166.7 mol/h, and overall conversion is 0.5 × 166.7/100 = 83.3 percent, not 50. That figure drives fresh feed demand and purge duty.
Phase Equilibrium: Matching the Calculation to the Known Stream
Bubble and dew calculations start with a known liquid or vapor and find the condition where the other phase first appears; a flash starts with a mixed feed and finds the split. Match the tool to the known stream.
Bubble, dew, and flash calculations answer different questions. A bubble or dew point locates a boundary: one phase has the known composition because the other phase is only just appearing. A flash sits between the bubble and dew conditions, so both phases exist in appreciable amounts and you must solve the vapor fraction and phase compositions together. Check your position first by computing the bubble and dew conditions of the feed, and only run a flash calculation if the operating point falls between those two boundaries.
Model selection follows the stated physics, not habit. Raoult's law assumes an ideal liquid mixture in equilibrium with an ideal vapor at modest pressure. Henry's law applies to a dilute dissolved gas in a liquid, such as oxygen in water, where the solute does not follow Raoult's law. When the problem supplies activity coefficients or relative volatility data, use the model that data support; silently substituting a simpler relation changes the vapor composition and every downstream balance built on it.
| Situation | Known information | Method |
|---|---|---|
| Bubble point | Liquid composition; find T or P where the first vapor forms | Sum of y_i = K_i x_i over all components equals 1 |
| Dew point | Vapor composition; find T or P where the first liquid forms | Sum of x_i = y_i / K_i over all components equals 1 |
| Flash | Feed composition plus T and P; find V/F and phase compositions | Rachford-Rice equation combined with component mass balances |
| Model choice | Ideal liquid, low pressure, similar components; or dilute dissolved gas | Raoult's law; Henry's law for the dilute gas; activity or fugacity models when nonideality is stated |
Fluid Systems: Energy Equation Setup and NPSH Checks
Write the mechanical energy equation between two labeled points, keeping pressure head, elevation head, velocity head, and friction as consistent terms. Then size the pump requirement from the difference, and confirm NPSH available exceeds the pump's requirement.
Two habits keep hydraulic problems stable. First, label point 1 and point 2 explicitly and assign each term a sign convention; the pressure term changes meaning depending on whether a point is a tank surface or a discharge. Second, carry units of head (length) throughout, converting pressure with the fluid density, so friction losses taken from the handbook in head terms drop directly into the equation without a second unit conversion.
NPSH available is computed at the pump suction from the source pressure, liquid level, elevation difference, suction-line friction, and vapor pressure; compare it against the pump's requirement at the operating flow. When a question asks for a maximum flow or a maximum temperature, compute the NPSH margin at that candidate condition rather than reading the pump curve alone — the margin closing to its limit is the constraint being tested. Read operating points as the intersection of the system curve and the pump curve, not a value from either curve alone.
Heat Exchangers: Resistance Networks and LMTD Versus NTU
Build the resistance network first: film convection on both sides, wall conduction, and fouling where stated. For sizing with all four temperatures known use LMTD; for rating with only inlet temperatures known use effectiveness-NTU.
The total resistance is a series sum of inside film, wall conduction, outside film, and fouling resistances, each referenced to the same area basis. Area-basis inconsistency is the trap to watch: an inside-based coefficient must multiply the inside area or be converted before combining. For cylindrical walls, convert resistances per unit length carefully before summing; adding a heat transfer coefficient directly to a conduction term mixes units and corrupts the entire result.
LMTD requires both outlet temperatures, because the log-mean correction depends on them. If a rating question gives only inlet temperatures and asks for outlet conditions, the effectiveness-NTU method applies: compute NTU from UA and the capacity rates, find effectiveness for the flow arrangement, and back out the outlet temperatures. Choosing LMTD with unknown outlets forces a trial-and-error loop that the NTU method avoids; recognizing that decision from the data given is the skill to practice on exchanger problems.
Reaction Engineering: Rate Law, Stoichiometry, and Design Equation
Build reactor problems in a fixed order: define conversion, express concentrations through stoichiometry, insert the rate law, then integrate the design equation for the stated reactor type. Selectivity questions need rate ratios, not conversion alone.
The mole balance for each reactor type is the skeleton: for a plug-flow reactor the design equation integrates over volume or catalyst, while for a CSTR it solves algebraically at the exit condition. Stoichiometry enters through the concentration expressions — for gas-phase reactions with a change in moles, the volumetric flow varies with conversion and pressure, so concentration terms must include that expansion rather than assuming constant flow throughout the reactor.
For multiple reactions, selectivity and yield come from ratios of rates or of formation terms evaluated at the relevant conditions; a high conversion answer can still be a poor selectivity answer. When a question offers a temperature or concentration choice, evaluate how the rate ratio changes, since the desired and undesired reactions typically respond differently to each variable. Write the rate ratio explicitly before integrating anything, so the comparison driving the design decision is visible on the page.
Separations: Shortcut Versus Staged Methods and Minimum Rates
Distillation design splits into shortcut methods (Fenske, Underwood, Gilliland) for stage estimates and stage-by-stage methods for profiles; absorption hinges on choosing a solvent rate above the minimum set by the operating-line pinch.
Distillation splits into shortcut methods — Fenske for minimum stages at total reflux, Underwood for minimum reflux, then a correlation linking actual stages and reflux between those limits — and stage-by-stage methods that produce composition profiles. The shortcut set assumes roughly constant relative volatility and key-component recoveries, so it estimates a design, not a profile. For absorption, the parallel decision is rate selection: the minimum solvent rate occurs where the operating line pinches the equilibrium line, so any design rate must sit above that minimum.
Worked scenario: a 100 mol/h gas stream with 5 mol percent solute A must lose 90 percent of A to a pure solvent; equilibrium is y* = 1.5x. A plausible mistake is computing removal as 0.9 × 100 = 90 mol/h, treating the entire gas as solute. Better: solute in is 5 mol/h, removed 4.5 mol/h; the minimum L/G is 1.5 × (0.0526 − 0.0053)/0.0526 = 1.35, giving L_min ≈ 128 mol/h. Designing at 1.4 times minimum, about 180 mol/h, keeps L/G = 1.89 above m = 1.5.
- Problem-audit exercise: pick any practice problem and, before computing, write (1) the requested quantity with units, (2) the basis, (3) the governing equation, (4) the property data needed, (5) the decision point — which method or model applies and why.
- Score each audit item 0 or 1; a complete plan scores 5. Repeated scores of 4 or above are a learning milestone showing your planning step is solid — they are not a predicted exam result.
- Repeat the drill across different topic areas — a recycle balance, a flash, a heat exchanger rating, a reactor design, an absorber — so the plan format transfers between them; target whatever your audit scores flag as weakest.
References and further reading
Use these references to explore the concepts and check the latest information from the relevant organizations.