PE Exam Exam > PE Exam Notes > Chemical Engineering for PE > Cheatsheet: Chemical Reactions
Cheatsheet: Chemical Reactions
1. Reaction Stoichiometry
1.1 Fundamental Definitions
| Term | Definition |
|---|---|
| Stoichiometric Coefficient | Number of moles of species participating in balanced reaction equation |
| Limiting Reactant | Reactant consumed first, determines maximum product formation |
| Excess Reactant | Reactant present in greater amount than stoichiometric requirement |
| Theoretical Yield | Maximum product obtainable based on stoichiometry and limiting reactant |
| Actual Yield | Measured amount of product obtained from reaction |
1.2 Key Equations
| Equation | Description |
|---|---|
| % Excess = [(nactual - nstoich)/nstoich] × 100 | Percent excess of reactant |
| % Yield = (Actual Yield/Theoretical Yield) × 100 | Percent yield of product |
| Molecular Weight = Σ(ni × MWi) | Sum of atomic weights of all atoms in molecule |
1.3 Extent of Reaction
| Parameter | Formula |
|---|---|
| Extent of Reaction (ξ) | ξ = (ni - ni0)/νi where νi is stoichiometric coefficient |
| Species Mole Balance | ni = ni0 + νiξ |
2. Reaction Thermodynamics
2.1 Heat of Reaction
| Term | Definition |
|---|---|
| Heat of Reaction (ΔHrxn) | Enthalpy change when reaction occurs at constant pressure |
| Exothermic Reaction | ΔHrxn < 0,="" releases="" heat="" to=""> |
| Endothermic Reaction | ΔHrxn > 0, absorbs heat from surroundings |
| Heat of Formation (ΔHf°) | Enthalpy change when 1 mole compound formed from elements at standard state |
| Heat of Combustion (ΔHc°) | Enthalpy change when 1 mole substance completely burns in oxygen |
2.2 Standard Heat of Reaction
| Equation | Description |
|---|---|
| ΔHrxn° = ΣνiΔHf,i° (products) - ΣνjΔHf,j° (reactants) | Standard heat of reaction from heats of formation |
| ΔHrxn(T) = ΔHrxn(Tref) + ∫ΔcpdT | Temperature dependence where Δcp = Σνicp,i |
2.3 Gibbs Free Energy
| Parameter | Formula |
|---|---|
| Gibbs Free Energy Change | ΔG = ΔH - TΔS |
| Standard Free Energy | ΔG° = ΣνiΔGf,i° (products) - ΣνjΔGf,j° (reactants) |
| Spontaneity Criterion | ΔG < 0:="" spontaneous;="" δg="0:" equilibrium;="" δg=""> 0: non-spontaneous |
| Relation to Keq | ΔG° = -RT ln(Keq) |
2.4 Equilibrium Constant
| Type | Expression |
|---|---|
| Kp (gas phase) | Kp = Π(Piνi) where P in atm or bar |
| Kc (concentration) | Kc = Π(Ciνi) where C in mol/L |
| Relationship | Kp = Kc(RT)Δν where Δν = Σνproducts - Σνreactants |
| van't Hoff Equation | d(ln K)/dT = ΔHrxn°/(RT²) or ln(K2/K1) = -(ΔH°/R)(1/T2 - 1/T1) |
3. Reaction Kinetics
3.1 Rate Expressions
| Term | Definition |
|---|---|
| Reaction Rate (r) | Rate of change of concentration with time, r = -dCA/dt |
| Rate Law | r = kCAαCBβ where k is rate constant |
| Reaction Order | Sum of exponents in rate law (α + β) |
| Molecularity | Number of molecules participating in elementary reaction step |
3.2 Elementary Reactions
- Unimolecular: A → products, r = kCA
- Bimolecular: A + B → products, r = kCACB
- Bimolecular (same species): 2A → products, r = kCA²
- Trimolecular: A + B + C → products, r = kCACBCC
3.3 Integrated Rate Laws
| Order | Integrated Form |
|---|---|
| Zero Order | CA = CA0 - kt; t1/2 = CA0/(2k) |
| First Order | ln(CA/CA0) = -kt; t1/2 = 0.693/k |
| Second Order (one species) | 1/CA - 1/CA0 = kt; t1/2 = 1/(kCA0) |
| Second Order (two species) | ln(CBCA0/CACB0) = (CB0 - CA0)kt |
3.4 Temperature Dependence
| Equation | Description |
|---|---|
| Arrhenius Equation | k = A exp(-Ea/RT) where A is pre-exponential factor |
| Linearized Form | ln(k) = ln(A) - Ea/(RT) |
| Two-Temperature Form | ln(k2/k1) = -(Ea/R)(1/T2 - 1/T1) |
| Activation Energy (Ea) | Minimum energy required for reaction to occur, units: J/mol or cal/mol |
3.5 Complex Reactions
3.5.1 Reversible Reactions
| Type | Expression |
|---|---|
| General Form | A ⇌ B with r = kfCA - krCB |
| At Equilibrium | kf/kr = Keq = CB,eq/CA,eq |
3.5.2 Parallel Reactions
- A → B (r1 = k1CA) and A → C (r2 = k2CA)
- Overall: -dCA/dt = (k1 + k2)CA
- Selectivity: SB/C = r1/r2 = k1/k2
3.5.3 Series (Consecutive) Reactions
- A → B → C with r1 = k1CA and r2 = k2CB
- dCA/dt = -k1CA; dCB/dt = k1CA - k2CB; dCC/dt = k2CB
- Maximum intermediate B occurs at tmax = ln(k2/k1)/(k2 - k1)
4. Reactor Design Equations
4.1 Batch Reactor
| Equation | Description |
|---|---|
| General Mole Balance | dNA/dt = rAV where N is moles, V is volume |
| Constant Volume | dCA/dt = rA |
| Time for Conversion | t = NA0∫0XdX/(-rAV) = CA0∫0XdX/(-rA) |
4.2 Continuous Stirred Tank Reactor (CSTR)
| Equation | Description |
|---|---|
| General Mole Balance | FA0 - FA + rAV = 0 |
| Design Equation | V = FA0X/(-rA) = ν0CA0X/(-rA) |
| Space Time (τ) | τ = V/ν0 = CA0X/(-rA) |
| Space Velocity (SV) | SV = 1/τ = ν0/V |
4.3 Plug Flow Reactor (PFR)
| Equation | Description |
|---|---|
| Differential Mole Balance | dFA/dV = rA |
| Design Equation | V = FA0∫0XdX/(-rA) = ν0CA0∫0XdX/(-rA) |
| Space Time | τ = V/ν0 = CA0∫0XdX/(-rA) |
4.4 Conversion and Key Relationships
| Parameter | Formula |
|---|---|
| Conversion (X) | X = (NA0 - NA)/NA0 = (FA0 - FA)/FA0 |
| Concentration | CA = CA0(1 - X) for constant volume |
| Flow Rate | FA = FA0(1 - X) |
| Volumetric Flow (gas) | ν = ν0(1 + εAX)(P0/P)(T/T0) where εA = (δνrxn)yA0 |
4.5 Reactor Performance Comparison
- For same conversion and reaction: VPFR <>CSTR for positive reaction orders
- Multiple CSTRs in series approach PFR performance as N → ∞
- Vtotal minimized when rate is equal across CSTRs in series
- PFR best for high conversion, fast reactions; CSTR best for slow reactions, temperature control
5. Non-Ideal Reactors
5.1 Residence Time Distribution (RTD)
| Function | Definition |
|---|---|
| E(t) | Exit age distribution, E(t) = C(t)/∫0∞C(t)dt for pulse input |
| F(t) | Cumulative distribution, F(t) = ∫0tE(t)dt |
| Mean Residence Time | t̄ = ∫0∞tE(t)dt = V/ν0 |
| Variance | σ² = ∫0∞(t - t̄)²E(t)dt |
5.2 Ideal Reactor RTD
| Reactor Type | E(t) Function |
|---|---|
| CSTR | E(t) = (1/τ)exp(-t/τ) |
| PFR | E(t) = δ(t - τ) where δ is Dirac delta function |
| Laminar Flow | E(t) = τ²/(2t³) for t ≥ τ/2 |
5.3 Segregation and Dispersion Models
| Model | Description |
|---|---|
| Segregated Flow | X = ∫0∞Xbatch(t)E(t)dt for batch reactor performance at each age |
| Maximum Mixedness | Opposite extreme to segregation, oldest fluid mixed with newest |
| Dispersion Number | D/(uL) where D is dispersion coefficient, u is velocity, L is length |
5.4 Tanks-in-Series Model
| Parameter | Formula |
|---|---|
| Number of Tanks (N) | N = t̄²/σ² = τ²/σ² |
| E(t) for N tanks | E(t) = [NNtN-1/((N-1)!τN)]exp(-Nt/τ) |
| Design Equation | CA,N = CA0/(1 + kτ/N)N for first-order reaction |
6. Catalytic Reactions
6.1 Heterogeneous Catalysis Fundamentals
| Term | Definition |
|---|---|
| Catalyst | Substance that increases reaction rate without being consumed |
| Active Site | Location on catalyst surface where reaction occurs |
| Turnover Frequency (TOF) | Number of reactant molecules converted per active site per time |
| Catalyst Deactivation | Loss of catalytic activity due to poisoning, fouling, sintering, or coking |
6.2 Langmuir-Hinshelwood Mechanisms
6.2.1 Single Reactant A → Products
| Step | Rate Equation |
|---|---|
| Adsorption Controlled | r = kPA |
| Surface Reaction Controlled | r = kKAPA/(1 + KAPA) |
| Desorption Controlled | r = kKAPA/(1 + KAPA)² |
6.2.2 Dual Site Mechanism: A + B → Products
- Both species adsorb on different sites
- r = kKAKBPAPB/(1 + KAPA + KBPB)²
6.2.3 Eley-Rideal Mechanism
- One species adsorbs (A), other reacts from gas phase (B)
- r = kKAPAPB/(1 + KAPA)
6.3 Site Balance
| Equation | Description |
|---|---|
| Ct = Cv + CA·S + CB·S + ... | Total sites = vacant + occupied sites |
| Cv/Ct = 1/(1 + KAPA + KBPB + ...) | Fraction of vacant sites |
6.4 Packed Bed Reactor
| Parameter | Formula |
|---|---|
| Catalyst Weight | W = ρbV where ρb is bulk density |
| Design Equation | W = FA0∫0XdX/(-r'A) where r' is per mass catalyst |
| Pressure Drop (Ergun) | -dP/dz = (G/ρgcDp)[(1-φ)/φ³][150(1-φ)μ/Dp + 1.75G] |
| Modified Pressure Drop | dP/dW = -(α/2ρ0)(T/T0)(P0/P)(FT/FT0) where α is Ergun constant |
6.5 Effectiveness Factor
| Parameter | Definition |
|---|---|
| Effectiveness Factor (η) | η = (actual rate with diffusion)/(rate without diffusion limitation) |
| Thiele Modulus (φ) | φ = L√(k/De) where L is characteristic length, De is effective diffusivity |
| η for First Order | η = (tanh φ)/φ for slab; η = 3(φ coth φ - 1)/φ² for sphere |
| Weisz-Prater Criterion | CWP = (-r'A,obs)ρcR²/(DeCAs) < 1="" for="" no=""> |
7. Multiple Reactions
7.1 Selectivity and Yield
| Parameter | Definition |
|---|---|
| Instantaneous Selectivity | SD/U = rD/rU where D is desired, U is undesired product |
| Overall Selectivity | S̃D/U = FD/FU at reactor exit |
| Yield | YD = (moles D formed)/(moles A fed) |
| Fractional Yield | YD = FD/FA0 |
7.2 Maximizing Desired Product
7.2.1 Parallel Reactions
| Scenario | Strategy |
|---|---|
| A → D (r1 = k1CAα₁), A → U (r2 = k2CAα₂) | If α₁ > α₂: use high CA; If α₁ < α₂:="" use="" low="">A |
| Ea1 vs Ea2 | If Ea1 > Ea2: use high T; If Ea1 <>a2: use low T |
7.2.2 Series Reactions
- A → D → U: maximize D by stopping at optimal conversion
- Use PFR for better control than CSTR
- Lower residence time to prevent over-reaction to U
- If k1 >> k2: high conversion acceptable; If k1 ≈ k2: limit conversion
7.3 Reactor Selection for Multiple Reactions
| Configuration | Application |
|---|---|
| PFR | Series reactions, better selectivity control for most cases |
| CSTR | When low reactant concentration favors desired product |
| Recycle Reactor | Combine high conversion with concentration control |
| Membrane Reactor | Remove products to shift equilibrium, add reactants gradually |
8. Energy Balance in Reactors
8.1 General Energy Balance
| Term | Expression |
|---|---|
| Accumulation | dE/dt = d(U + KE + PE)/dt ≈ dU/dt for reactors |
| Flow Terms | ΣFi0Hi0 - ΣFiHi where H = U + PV |
| Heat Exchange | Q̇ = UA(Ta - T) for heat transfer |
| Work | Ẇs (shaft work, zero for most reactors) |
8.2 Adiabatic Reactor Energy Balance
| Reactor Type | Energy Balance |
|---|---|
| Adiabatic Batch | NA0Σθicp,i(T - T0) = (-ΔHrxn)NA0X |
| Adiabatic CSTR | FA0Σθicp,i(T - T0) = (-ΔHrxn)FA0X |
| Adiabatic PFR | FA0Σθicp,i(dT/dX) = (-ΔHrxn)FA0 |
| Adiabatic Temperature | T = T0 + [(-ΔHrxn)X]/(Σθicp,i) |
8.3 Non-Adiabatic CSTR
| Equation | Description |
|---|---|
| Energy Balance | FA0Σθicp,i(T - T0) = (-ΔHrxn)FA0X - UA(T - Ta) |
| Heat Removal Line | Q̇r = FA0Σθicp,i(T - T0) + UA(T - Ta) |
| Heat Generation Line | Q̇g = (-ΔHrxn)FA0X |
8.4 Non-Adiabatic PFR
| Parameter | Expression |
|---|---|
| Differential Balance | FA0Σθicp,i(dT/dV) = (-ΔHrxn)(-rA) - Ua(T - Ta) |
| Heat Transfer per Volume | a = 4/dt for tubular reactor with diameter dt |
| Coupled with Mole Balance | dX/dV = (-rA)/FA0 and dT/dV equation solved simultaneously |
8.5 Multiple Steady States
- Occur when heat generation and removal curves intersect at multiple points
- Low conversion (stable), intermediate conversion (unstable), high conversion (stable)
- Hysteresis: different startup vs. shutdown paths
- Runaway criterion: slope of Q̇g > slope of Q̇r at intersection
9. Gas-Liquid and Gas-Solid Reactions
9.1 Mass Transfer Fundamentals
| Term | Definition |
|---|---|
| Mass Transfer Coefficient (kL) | Proportionality constant in flux equation, units: m/s or cm/s |
| Two-Film Theory | Resistance to mass transfer exists in thin films at interface |
| Overall Mass Transfer Coefficient | 1/KL = 1/kL + H/(kG) where H is Henry's constant |
9.2 Gas-Liquid Reactions
| Regime | Condition |
|---|---|
| Slow Reaction | Reaction rate < mass="" transfer="" rate,="" liquid="" bulk="" concentration=""> |
| Fast Reaction | Reaction occurs in liquid film, concentration gradient in film |
| Instantaneous Reaction | Reaction infinitely fast at interface, plane of reaction in film |
9.3 Enhancement Factor
| Parameter | Formula |
|---|---|
| Enhancement Factor (E) | E = (rate with reaction)/(rate without reaction) |
| Hatta Number (Ha) | Ha = √(kDL)/kL where k is reaction rate constant, DL is diffusivity |
| Fast Reaction Criterion | Ha > 3: reaction in film; Ha < 0.3:="" slow="" reaction=""> |
9.4 Gas-Solid Reactions
9.4.1 Shrinking Core Model
| Controlling Step | Time for Complete Conversion |
|---|---|
| External Mass Transfer | τ = ρBR/(bkgCAg) |
| Ash Layer Diffusion | τ = ρBR²/(6bDeCAg) |
| Chemical Reaction | τ = ρBR/(bksCAg) |
9.4.2 Fractional Conversion
| Controlling Step | X vs. Time |
|---|---|
| External Mass Transfer | X = t/τ |
| Ash Layer Diffusion | 1 - 3(1-X)2/3 + 2(1-X) = t/τ |
| Chemical Reaction | 1 - (1-X)1/3 = t/τ |
10. Reactor Safety and Stability
10.1 Thermal Stability Criteria
| Criterion | Condition |
|---|---|
| van Heerden Criterion | ∂Q̇g/∂T <>r/∂T for stability at steady state |
| Semenov Number (Se) | Se = [(-ΔHrxn)EaCA0]/(ρcpRT²) < critical=""> |
| Damköhler Number (Da) | Da = (reaction rate)/(flow rate) = kτ for first-order reaction |
10.2 Parametric Sensitivity
| Parameter | Description |
|---|---|
| Sensitivity (S) | S = (∂T/∂parameter)/(T/parameter) |
| High Sensitivity | Small parameter changes cause large temperature changes |
| Critical Values | Feed temperature, coolant temperature, flow rate most sensitive |
10.3 Runaway Conditions
- Exothermic reactions with insufficient heat removal
- Temperature rises → reaction accelerates → more heat generated
- Preventive measures: emergency cooling, pressure relief, quench systems
- Monitor: temperature, pressure, flow rates continuously
10.4 Safe Operating Regions
| Factor | Consideration |
|---|---|
| Temperature Limits | Maximum allowable temperature for materials and safety |
| Pressure Limits | Equipment rated pressure, relief valve settings |
| Flammability | Keep composition outside flammability limits |
| Residence Time | Minimum for conversion, maximum to prevent decomposition |
10.5 Explosion Severity Parameters
| Parameter | Definition |
|---|---|
| KG Value | KG = (dP/dt)maxV1/3, deflagration index for gases |
| KSt Value | KSt = (dP/dt)maxV1/3, deflagration index for dusts |
| Minimum Ignition Energy (MIE) | Lowest energy spark that can ignite dust cloud or vapor |
| Maximum Explosion Pressure | Pmax for vessel design and relief sizing |
The document Cheatsheet: Chemical Reactions is a part of the PE Exam Course Chemical Engineering for PE.
All you need of PE Exam at this link: PE Exam
About this Document
Apr 20, 2026
Last updated
Related Exams
Document Description: Cheatsheet: Chemical Reactions for PE Exam 2026 is part of Chemical Engineering for PE preparation.
The notes and questions for Cheatsheet: Chemical Reactions have been prepared according to the PE Exam exam syllabus. Information about Cheatsheet: Chemical Reactions covers topics
like and Cheatsheet: Chemical Reactions Example, for PE Exam 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Cheatsheet: Chemical Reactions.
Introduction of Cheatsheet: Chemical Reactions in English is available as part of our Chemical Engineering for PE
for PE Exam & Cheatsheet: Chemical Reactions in Hindi for Chemical Engineering for PE course.
Download more important topics related with notes, lectures and mock test series for PE Exam
Exam by signing up for free. PE Exam: Cheatsheet: Chemical Reactions
Description
Cheatsheet: Chemical Reactions of Chemical Engineering to help you remember important concepts with short tricks. Start learning for PE Exam exam & improve retention with EduRev.
Information about Cheatsheet: Chemical Reactions
In this doc you can find the meaning of Cheatsheet: Chemical Reactions defined & explained in the simplest way possible. Besides explaining types of
Cheatsheet: Chemical Reactions theory, EduRev gives you an ample number of questions to practice Cheatsheet: Chemical Reactions tests, examples and also practice PE Exam
tests
Related Searches
Exam, mock tests for examination, Sample Paper, Viva Questions, video lectures, Important questions, study material, MCQs, ppt, Semester Notes, past year papers, pdf , Free, Cheatsheet: Chemical Reactions, shortcuts and tricks, Previous Year Questions with Solutions, Objective type Questions, practice quizzes, Summary, Extra Questions, Cheatsheet: Chemical Reactions, Cheatsheet: Chemical Reactions;