Reaction Rate Calculator
Calculate reaction rates, rate constants, and analyze chemical kinetics
Rate Law: rate = k[A]^m[B]^n
Calculate reaction rate given rate constant and concentrations
Units depend on overall reaction order
Half-Life Calculator
Calculate half-life based on reaction order and rate constant
Concentration vs Time
Calculate concentration at time t using integrated rate laws
Arrhenius Equation: k = Ae^(-Ea/RT)
Calculate rate constant at different temperatures
Result
Calculation Steps
Additional Information
Reaction Orders and Rate Laws
Zero Order Reactions
Rate Law: rate = k
Integrated Rate Law: [A] = [A]₀ - kt
Half-Life: t₁/₂ = [A]₀ / 2k
Units of k: M/s or M·s⁻¹
Rate is independent of concentration. Rare in solution, common on catalyst surfaces.
First Order Reactions
Rate Law: rate = k[A]
Integrated Rate Law: ln[A] = ln[A]₀ - kt
Half-Life: t₁/₂ = ln(2) / k = 0.693 / k
Units of k: s⁻¹ or time⁻¹
Half-life is constant (independent of concentration). Common for radioactive decay and many decompositions.
Second Order Reactions
Rate Law: rate = k[A]² or rate = k[A][B]
Integrated Rate Law: 1/[A] = 1/[A]₀ + kt
Half-Life: t₁/₂ = 1 / (k[A]₀)
Units of k: M⁻¹s⁻¹ or L·mol⁻¹·s⁻¹
Half-life increases as concentration decreases. Common for bimolecular reactions.
Arrhenius Equation
The Arrhenius equation describes how reaction rate constant (k) depends on temperature:
k = Ae^(-Ea/RT)
or ln(k) = ln(A) - Ea/RT
k = rate constant
A = pre-exponential factor (frequency factor)
Ea = activation energy (J/mol or kJ/mol)
R = gas constant (8.314 J/(mol·K))
T = temperature (Kelvin)
Two-Point Form
ln(k₂/k₁) = (Ea/R)(1/T₁ - 1/T₂)
Use this form to calculate Ea from two rate constants at different temperatures
Example Problems
Example 1: First Order Half-Life
Problem: A first-order reaction has k = 0.0693 s⁻¹. What is the half-life?
Solution:
t₁/₂ = 0.693 / k
t₁/₂ = 0.693 / 0.0693 s⁻¹
t₁/₂ = 10.0 s
Example 2: Concentration vs Time
Problem: For a first-order reaction with k = 0.05 s⁻¹ and [A]₀ = 1.0 M, find [A] at t = 10 s.
Solution:
ln[A] = ln[A]₀ - kt
ln[A] = ln(1.0) - (0.05)(10)
ln[A] = 0 - 0.5 = -0.5
[A] = e^(-0.5) = 0.607 M
Example 3: Arrhenius Equation
Problem: Calculate k at 298 K if Ea = 50 kJ/mol and A = 1.0 × 10¹⁰ s⁻¹.
Solution:
k = Ae^(-Ea/RT)
k = (1.0×10¹⁰)e^(-50000/(8.314×298))
k = (1.0×10¹⁰)e^(-20.18)
k = 1.78 × 10¹ s⁻¹
Applications of Chemical Kinetics
1. Drug Development
Understanding reaction kinetics helps predict drug stability, shelf life, and metabolism rates in the body. First-order kinetics often describes drug elimination.
2. Food Science
Kinetic studies determine optimal storage temperatures and predict food spoilage. The Arrhenius equation helps estimate shelf life at different temperatures.
3. Catalysis
Reaction rate studies reveal catalyst effectiveness and mechanism. Lower activation energy means faster reactions at the same temperature.
4. Environmental Chemistry
Kinetics of pollutant degradation helps predict environmental cleanup times. Understanding reaction orders guides remediation strategies.
5. Industrial Processes
Optimizing reaction conditions for maximum yield and efficiency. Temperature control based on activation energy reduces energy costs.
References
The reaction kinetics calculations are based on fundamental physical chemistry principles from reputable sources:
Note: These calculations assume ideal conditions and elementary reactions. Complex reactions may have different rate laws. Experimental determination of reaction order and rate constants is essential for accurate kinetic analysis. Always consider factors like temperature dependence and catalyst effects in real systems.
Recommended Calculator
Casio FX-991ES Plus
The professional-grade scientific calculator with 417 functions, natural display, and solar power. Perfect for students and professionals.
View on Amazon