Fundamentals of Engineering (FE) Exam Review
Visit the NCEES FE website or the NCEES YouTube channel for details on the FE exam. The FE exam is offered in seven disciplines; the FE chemical exam is outlined below. The FE exam is a computer-based test. An electronic reference booklet of equations and constants is supplied at the beginning of the exam. The exam uses both the International System of Units (SI) and the US Customary System (USCS).
Chemical exam specifications (6 hours - 110 questions in 16 topic areas)

The FE chemical exam consists of 16 chemical engineering topics: mathematics, engineering probability & statistics, engineering sciences, computational tools, materials science, chemistry, fluid mechanics/dynamics, thermodynamics, material/energy balances, heat transfer, mass transfer and separation, chemical reaction engineering, process design and economics, process control, safety, health and environment, ethics and professional practice.  The 6 hour time frame also includes a tutorial, a break, and a survey.

Study help

  • How to Study: Part 1 - suggestions on how to study based on the psychology literature on learning: part 1 discusses practice testing.
  • How to Study: Part 2 - suggestions on how to study based on the psychology literature on learning: part 2 discusses distributed practice and interleaved practice.
  • How to Study: Part 3 - suggestions on how to study based on the psychology literature on learning: part 3 discusses how to improve retention and what approaches to avoid.
  • How to Study using Screencasts - suggestions on how to study using screencasts based on the psychology literature on learning.
  • How to Study and Take Exams - PDF discussing study techniques
Review videos by exam topics

The videos below are useful review problems. Click on the drop down menus to view the videos for that topic.
1 Mathematics (8-12 questions)
1.1 Analytic geometry
1.2 Roots of equations
1.3 Calculus
1.4 Differential equations
2 Probability and Statistics (4-6 questions)
2.1 Probability distributions (e.g., discrete, continuous, normal, binomial)

  • Binomial Distribution
  • Negative Binomial Distribution
  • 2.2 Expected value (weighted average) in decision making
    2.3 Hypothesis testing
    2.4 Measures of central tendencies and dispersions (e.g., mean, mode, standard deviation)
    2.5 Estimation for a single mean (e.g., point, confidence intervals)
    2.6 Regression and curve fitting

  • Non-Linear Regression Introduction
  • 3 Engineering Sciences (4-6 questions)
    3.1 Applications of vector analysis (e.g., statics)

  • Forces Acting on a Frame
  • 3.2 Basic dynamics (e.g., friction, force, mass, acceleration, momentum)
    3.3 Work, energy, and power (as applied to particles or rigid bodies)
    3.4 Electricity and current and voltage laws (e.g., charge, energy, current, voltage, power, Kirchhoff, Ohm)
    4 Computational Tools (4-6 questions)
    4.1 Numerical methods and concepts (e.g. convergence, tolerance)

  • Euler Method for ODEs
  • Runge-Kutta Method Introduction
  • 4.2 Spreadsheets for chemical engineering calculations
    4.3 Simulators

  • SuperPro Designer: Modeling a Batch Reactor
  • Introduction to Aspen Plus: Choosing a Property Method
  • 5 Materials Science (4-6 questions)
    5.1 Chemical, electrical, mechanical, and physical properties (e.g., effect of temperature, pressure, stress, strain)

  • Atomic Bonding
  • Elastic Properties of Metals
  • Engineering Stress and Strain
  • Electrical Conductivity
  • Pressure-Temperature Diagram
  • Solid-Liquid Phase Diagrams
  • 5.2 Material types and compatibilities (e.g., engineered materials, ferrous and nonferrous materials)
    5.3 Corrosion mechanisms and control
    6 Chemistry (8-12 questions)
    6.1 Inorganic chemistry (e.g., molarity, normality, molality, acids, bases, redox reactions, valence, solubility product, pH, pK, electrochemistry, periodic table)

  • Mass Composition from Molar Composition
  • Acid Dissociation Constant
  • Balance Redox Reaction: Acidic Solution
  • Hydrogen Ion and Hydroxide Ion Concentrations
  • Oxidation Number
  • Oxidizing and Reducing Agents
  • pH of a Weak Acid
  • Titrate Base with Acid
  • Assigning Oxidation States
  • Formal Charge
  • 6.2 Organic chemistry (e.g., nomenclature, structure, qualitative and quantitative analyses, balanced equations, reactions, synthesis, basic biochemistry)
    7 Fluid Mechanics/Dynamics (8-12 questions)
    7.1 Fluid properties

  • Characteristics of a Fluid
  • Introduction to Viscosity
  • Surface Tension Part 1
  • Viscosity of Fluid from Shear Force
  • What is a Fluid?
  • 7.2 Dimensionless numbers (e.g., Reynolds number)

  • Dimensionless Groups (Reynolds Number Example)
  • Scaling Analysis
  • Utility of Dimensionless Parameters
  • 7.3 Mechanical energy balance (e.g., pipes, valves, fittings, pressure losses across packed beds, pipe networks)

  • Pipe Flow Introduction
  • Pressure Drop as a Function of Pipe Length
  • Pressure Drop in Pipe with Losses (Determine Pressure Drop)
  • Using a Moody Chart
  • 7.4 Bernoulli equation (hydrostatic pressure, velocity head)

  • Hydrostatic Pressure Calculations
  • Draining a Cylindrical Tank
  • Flow Exiting a Tank (Bernoulli)
  • Simple Bernoulli Equation Example
  • 7.5 Laminar and turbulent flow

  • Laminar Flow between Parallel Plates (Navier Stokes)
  • Shear Stress between Parallel Plates
  • Pressure Drop in a Pipe (Laminar Flow)
  • Turbulent Flow
  • Volumetric Flow Rate for Laminar Pipe Flow
  • 7.6 Flow measurement (e.g., orifices, Venturi meters)

  • Force Balance on Inclined Manometer
  • Air Flow Through a Constriction
  • Venturi Effect on Blood Flow
  • Venturi Meter
  • 7.7 Pumps, turbines, and compressors

  • Pipe Flow: Determining Power
  • 7.8 Compressible flow and non-Newtonian fluids

  • Non-Newtonian Fluids Part 1
  • Non-Newtonian Fluids Part 2
  • Non-Newtonian Fluids Part 3
  • Non-Newtonian Fluids Part 4
  • Fluid Pressure vs. Elevation (Incompressible vs. Compressible Cases)
  • Shear Stress vs. Rate of Shearing Strain
  • 8 Thermodynamics (8-12 questions)
    8.1 Thermodynamic properties (e.g., specific volume, internal energy, enthalpy, entropy, free energy)

  • Internal Energy Introduction
  • What is Enthalpy?
  • Entropy: 2 Explanations
  • Heat Capacity Pressure Dependence
  • Gibbs Free Energy: T & P Dependence
  • Gibbs Free Energy Change for Non-Ideal Mixture
  • Mixing Ideal Solutions
  • Chemical Equilibrium: Standard State Gibbs Free Energy
  • 8.2 Properties data and phase diagrams (e.g., steam tables, psychrometric charts, T-s, P-h, x-y, T-x-y)

  • Psychrometric Charts (Humidity Charts)
  • Compare Steam Tables to Ideal Gas Law
  • Energy Balance: Steam Tables
  • Steam Tables: Interpolation
  • T-S and P-H Diagrams
  • PT and PV Phase Diagrams
  • Phase Equilibrium: Txy Diagram
  • Txy Diagram: Lever Rule
  • 8.3 Thermodynamic laws (e.g., 1st law, 2nd law)

  • Ideal Gas Expansion: Determine Final State
  • Real Gas Expansion
  • Second Law Application
  • First Law and State Function
  • First Law/Irreversible Expansion
  • 8.4 Thermodynamic processes (e.g., isothermal, adiabatic, isentropic)

  • Adiabatic Expansion of Steam
  • Irreversible Adiabatic Expansion
  • Isothermal Ideal Gas Compression
  • Reversible Adiabatic Compression of Ideal Gas
  • Adiabatic Compression of an Ideal Gas
  • 8.5 Cyclic processes and efficiency (e.g., power, refrigeration, heat pump)

  • Compressor Efficiency
  • Maximum Work from a Turbine
  • Carnot Heat Pump
  • Heat Engine Introduction
  • Power Cycle Introduction
  • Refrigeration Cycle Introduction
  • 8.6 Phase equilibrium (e.g., fugacity, activity coefficient)

  • Air/Water Vapor-Liquid Equilibrium
  • Chemical Potential/Thermodynamic Activity
  • Fugacity of a Single Component
  • Which has Higher Fugacity?
  • Equilibrium Constant Introduction
  • Fugacity from Pxy Diagram
  • VLE using Fugacity Coefficients
  • 8.7 Chemical equilibrium

  • Catalytic Selectivity and Equilibrium
  • Description of the Reaction Coordinate
  • Gibbs Phase Rule: Reacting Systems
  • Solid-Liquid Chemical Equilibrium
  • Standard State in Chemical Equilibrium
  • Which Reaction Reaches Equilibrium First? (Interactive)
  • 8.8 Heats of reaction and mixing

  • Heat of Mixing
  • Heat of Reaction (from Heat of Formation)
  • 9 Material/Energy Balances (8-12 questions)
    9.1 Mass balance (steady and unsteady state)

  • General Balance for Material Balances
  • General Mass Balance on Single Tank
  • Material Balance Problem Approach
  • Water Vapor Adsorber Material Balance
  • 9.2 Energy balance (steady and unsteady state)

  • Gas Expansion from a Tank
  • Unsteady-State Energy Balance (Steam Tables)
  • Calculating Enthalpy Changes Using Heat of Reaction Method
  • Calculating Enthalpy Changes Using Heats of Formation Method
  • Steam Reformer Material and Energy Balances
  • 9.3 Recycle/bypass processes

  • Analysis of a Split Point
  • Crystallizer Material Balance with Recycle
  • Multiple Unit Material Balance/Recycle - Decaf Coffee
  • Reactor with Recycle
  • Single Reaction With Recycle
  • 9.4 Reactive systems (e.g., combustion)

  • Adiabatic Flame Temperature
  • Heat of Combustion
  • Hess's Law
  • 10 Heat Transfer (8-12 questions)
    10.1 Conductive heat transfer

  • Boundary Conditions
  • Conduction Equation Derivation
  • Surface Temperature for a Cylindrical Pipe
  • 10.2 Convective heat transfer (natural and forced)

  • Flow over a Flat Plate
  • Solving Convection Problems
  • Rod Center-line Temperature
  • Heat Generation in a Pipe
  • 10.3 Radiation heat transfer

  • Net Radiative Heat Transfer Rate from a Surface
  • Properties of Radiative Heat Transfer
  • Radiation Exchange Between Surfaces
  • View Factors
  • 10.4 Heat transfer coefficients (e.g., overall, local, fouling)

  • Local and Average Heat Transfer Coefficients
  • Overall Heat Transfer Coefficient: Rectangular Coordinates
  • 10.5 Heat transfer equipment, operation, and design (e.g., double pipe, shell and tube, fouling, number of transfer units, log-mean temperature difference, flow configuration)

  • Heat Exchanger: Mass Flow Rate
  • Log Mean Temperature Difference
  • NTU Effectiveness: Counter-Flow Heat Exchanger
  • Sizing a Heat Exchanger: Parallel Flow
  • 11 Mass Transfer and Separation (8-12)
    11.1 Molecular diffusion (e.g., steady and unsteady state, physical property estimation)

  • Diffusion into a Solid
  • Equimolar Counterdiffusion Example
  • Hydrogen Diffusion through Palladium
  • Unimolecular Diffusion Example
  • 11.2 Convective mass transfer (e.g., mass transfer coefficient, eddy diffusion)

  • Convective Mass Transfer
  • 11.3 Separation systems (e.g., distillation, absorption, extraction, membrane processes)

  • Binary Flash Distillation Example
  • Packed Bed Column Height
  • Partially Miscible Liquid-Liquid Extraction
  • Absorption of a Dilute Species
  • 11.4 Equilibrium stage methods (e.g., graphical methods, McCabe-Thiele, efficiency)

  • Distillation - Murphree Efficiency
  • Distillation - Side Stream Feed
  • McCabe-Thiele: Stepping off Stages
  • 11.5 Continuous contact methods (e.g., number of transfer units, height equivalent to a theoretical plate, height of transfer unit, number of theoretical plates)
    11.6 Humidification and drying
    12 Chemical Reaction Engineering (8-12 questions)
    12.1 Reaction rates and order

  • Steady-State Approximation
  • Steady-State Approximation vs. Rate Determining Step
  • Reaction Rate Explanation
  • Determining Rate Order
  • 12.2 Rate constant (e.g., Arrhenius function)

  • Activation Energy & Arrhenius Relationship
  • Relationship Between the Equilibrium Constants
  • 12.3 Conversion, yield, and selectivity

  • Catalytic Selectivity and Equilibrium
  • Conversion in a PFR vs. CSTR
  • Conversion: PFR vs. CSTR
  • Selectivity: Isothermal vs. Adiabatic
  • Selectivity: PFR vs. CSTR
  • 12.4 Type of reactions (e.g., series, parallel, forward, reverse, homogeneous, heterogeneous, catalysis, biocatalysis)

  • Batch Reactor with Reversible Reaction
  • Diffusion and Bulk Flow for Catalytic Reaction
  • Diffusion and Reaction in a Cylindrical Porous Catalyst
  • Michaelis-Menten Introduction (BIO)
  • Michaelis-Menten: Competitive Inhibition (BIO)
  • Parallel Reactions in a Batch Reactor
  • Series Reaction in a Batch Reactor
  • Langmuir-Hinshelwood Mechanism
  • 12.5 Reactor types (e.g., batch, semibatch, continuous stirred tank, plug flow, gas phase, liquid phase)

  • Batch Reactor Overview
  • Semibatch Reactor Overview
  • CSTR Overview
  • Plug Flow Reactor Overview
  • Comparing Reactors in Series
  • 13 Process Design and Economics (8-12 questions)
    13.1 Process flow diagrams and piping and instrumentation diagrams

  • Basics of BFDs, PFDs, & PIDs
  • Block Flow Diagram Examples
  • Characteristics of BFDs
  • 13.2 Equipment selection (e.g., sizing and scale-up)
    13.3 Cost estimation

  • Capital Cost Comparison: Capitalized Cost Analysis
  • Capital Cost Comparison: Present Worth Analysis
  • 13.4 Comparison of economic alternatives (e.g., net present value, discounted cash flow, rate of return, expected value and risk)

  • Approximate Profitability Measures
  • Gross Economic Profit Analysis
  • Net Present Value and Investor's Rate of Return
  • 13.5 Process design and optimization (e.g., sustainability, efficiency, green engineering, inherently safer design, evaluation of specifications)
    14 Process Control (5-8 questions)
    14.1 Dynamics (e.g., time constants, 2nd order and underdamped transfer functions)

  • Transfer Function Models
  • Inverse Response
  • 14.2 Control strategies (e.g., feedback, feed-forward, cascade, ratio, and PID)
    14.3 Control loop design and hardware (e.g., matching measured and manipulated variables, sensors, control valves, conceputal process control)
    15 Safety, Health, and Environment (5-8 questions)
    15.1 Hazardous properties of materials (e.g., corrosivity, flammability, toxicity, reactivity, handling and storage)
    15.2 Industrial hygiene (e.g., noise, PPE, ergonomics)
    15.3 Process safety and hazard analysis (e.g., layer of protection analysis, HazOps, fault-tree analysis)
    15.4 Overpressure and underpressure protection (e.g., relief, redundant control, intrinsically safe)
    15.5 Waste minimization, waste treatment, and regulation (e.g., air, water, solids, RCRA, CWA, EPA, OSHA)
    16 Ethics and Professional Practice (2-3 questions)
    16.1 Codes of ethics (professional and techincal societies)
    16.2 Agreements and contracts
    16.3 Ethical and legal considerations
    16.4 Professional liability
    16.5 Public protection issues (e.g., licensing boards)