Reaction Kinetics (engineering)
Reaction kinetics in engineering quantifies the rate at which reactants are converted to products under specified conditions of concentration, temperature, pressure, and catalyst presence. The rate expression (rate law) relates reaction rate to reactant concentrations via a rate constant, and the Arrhenius equation describes the temperature dependence of that constant. Engineering application of kinetics enables the sizing of reactors, optimisation of operating conditions, and prediction of yield and selectivity in industrial chemical processes.
Key Formula
k = A × exp(−Ea / RT)
LaTeX: k = A \cdot e^{-E_a / (RT)}
| Symbol | Meaning | Unit |
|---|---|---|
| k | Rate constant | varies (depends on reaction order) |
| A | Pre-exponential (frequency) factor | same units as k |
| E_a | Activation energy | J/mol |
| R | Universal gas constant (8.314) | J/(mol·K) |
| T | Absolute temperature | K |
Worked Example
Problem
A reaction has activation energy Ea = 75,000 J/mol and pre-exponential factor A = 1.5 × 10¹⁰ s⁻¹. Calculate the rate constant at 300 K and at 350 K and find the ratio k(350)/k(300).
Solution
Step 1: At T = 300 K: k₁ = 1.5×10¹⁰ × exp(−75,000 / (8.314 × 300)) = 1.5×10¹⁰ × exp(−30.08) = 1.5×10¹⁰ × 8.02×10⁻¹⁴ = 1.20×10⁻³ s⁻¹. Step 2: At T = 350 K: k₂ = 1.5×10¹⁰ × exp(−75,000 / (8.314 × 350)) = 1.5×10¹⁰ × exp(−25.78) = 1.5×10¹⁰ × 6.34×10⁻¹² = 9.51×10⁻² s⁻¹. Step 3: Ratio k₂/k₁ = 9.51×10⁻² / 1.20×10⁻³ = 79.3.
Answer
k(300 K) = 1.20×10⁻³ s⁻¹; k(350 K) = 9.51×10⁻² s⁻¹; ratio ≈ 79 (rate increases 79× with 50 K rise)
Reaction Order, Rate Laws, and Integrated Rate Equations
| Order | Rate Law | Integrated Form | Half-Life t½ | Units of k |
|---|---|---|---|---|
| Zero | r = k | C_A = C_A0 − kt | C_A0/(2k) | mol/(L·s) |
| First | r = k·C_A | ln(C_A/C_A0) = −kt | 0.693/k | s⁻¹ |
| Second | r = k·C_A² | 1/C_A − 1/C_A0 = kt | 1/(k·C_A0) | L/(mol·s) |
| Pseudo-first | r = k'·C_A | ln(C_A/C_A0) = −k't | 0.693/k' | s⁻¹ |
Interactive Tools
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Related Terms
Chemical Reactor Design
Chemical reactor design is the discipline of selecting and sizing reactor vessels that achieve a desired chemical conversion at specified conditions of temperature, pressure, and flow rate. It integrates reaction kinetics, thermodynamics, and transport phenomena to predict concentration and temperature profiles within the reactor. Industrial applications range from petroleum refining and polymer synthesis to pharmaceutical manufacturing and environmental remediation.
CSTR
A Continuously Stirred Tank Reactor (CSTR) is an idealised reactor in which perfect mixing is assumed, meaning concentration and temperature are uniform throughout the vessel and equal to the exit stream values. It operates at steady state with continuous feed and product streams, and is described by an algebraic design equation rather than a differential one. CSTRs are widely used in liquid-phase reactions, biological fermenters, and wastewater treatment due to their ease of temperature control and scale-up.
Plug Flow Reactor
A Plug Flow Reactor (PFR) is an idealised tubular reactor in which fluid flows with a flat velocity profile (no axial mixing) so that all fluid elements have the same residence time. Concentration and temperature vary continuously along the reactor length, requiring a differential design equation for analysis. PFRs are preferred for gas-phase reactions, high-temperature processes, and situations where high conversion is required with minimum reactor volume compared to CSTRs.
"Kinetics" from Greek "kinetikos" (of motion), from "kinein" (to move). The field was founded by Wilhelmy (1850, first rate law), van't Hoff (1884, rate equations), and Arrhenius (1889, temperature dependence). The Arrhenius equation emerged from his observations on sucrose inversion rates, earning him the 1903 Nobel Prize in Chemistry.