The arrhenius equation calculator is a computational tool designed to analyze the temperature dependence of chemical reaction rates with k = A × e^(-Ea/RT) formula.
The calculator implements the fundamental Arrhenius equation, proposed by Swedish chemist Svante Arrhenius in 1889.
Consider a reaction where k₁ = 2.33 × 10⁻³ s⁻¹ at T₁ = 300 K, and we need to find k₂ at T₂ = 315 K with Eₐ = 55.5 kJ/mol.Using the calculator:
- Input known values
- The calculator processes through the exponential relationship
- Outputs k₂ = 6.47 × 10⁻³ s⁻¹
Arrhenius Equation Calculator
| Temperature (K) | Rate Constant (s⁻¹) | Activation Energy (kJ/mol) | Pre-exponential Factor (s⁻¹) |
|---|---|---|---|
| 298 | 1.86 × 10⁻⁴ | 50.0 | 5.0 × 10¹⁰ |
| 308 | 5.24 × 10⁻⁴ | 50.0 | 5.0 × 10¹⁰ |
| 318 | 1.39 × 10⁻³ | 50.0 | 5.0 × 10¹⁰ |
| 323 | 2.56 × 10⁻³ | 50.0 | 5.0 × 10¹⁰ |
| 333 | 4.76 × 10⁻³ | 50.0 | 5.0 × 10¹⁰ |
| 343 | 8.77 × 10⁻³ | 50.0 | 5.0 × 10¹⁰ |
| 353 | 1.62 × 10⁻² | 50.0 | 5.0 × 10¹⁰ |
| 363 | 2.99 × 10⁻² | 50.0 | 5.0 × 10¹⁰ |
| 373 | 5.56 × 10⁻² | 50.0 | 5.0 × 10¹⁰ |
| 383 | 1.03 × 10⁻¹ | 50.0 | 5.0 × 10¹⁰ |
| 393 | 1.92 × 10¹ | 50.0 | 5.0 × 10¹⁰ |
Arrhenius Equation Formula
The Arrhenius equation is mathematically expressed as:
k = A × e^(-Eₐ/RT)Where:
- k represents the rate constant
- A is the pre-exponential factor
- Eₐ is the activation energy
- R is the universal gas constant (8.314 J/mol·K)
- T is the absolute temperature in Kelvin
For a reaction with A = 5.0 × 10¹⁰ s⁻¹, Eₐ = 50 kJ/mol at T = 298 K:
k = (5.0 × 10¹⁰) × e^(-50,000/(8.314 × 298)) = 1.86 × 10⁻⁴ s⁻¹What is an Arrhenius equation?
The Arrhenius equation represents a fundamental relationship in physical chemistry that describes how the rate constant of a chemical reaction depends on temperature and activation energy. This equation embodies the observation that most chemical reactions proceed faster at higher temperatures.
Practical Example:
The decomposition of hydrogen peroxide (H₂O₂) follows Arrhenius behavior:
- At 20°C: k = 1.0 × 10⁻⁴ s⁻¹
- At 30°C: k = 2.7 × 10⁻⁴ s⁻¹
How is the Arrhenius equation calculated?
The calculation process involves these steps:
- Logarithmic Form: ln(k) = ln(A) – (Eₐ/R)(1/T)
- Two-Point Form: ln(k₂/k₁) = -(Eₐ/R)(1/T₂ – 1/T₁)
Given k₁ = 1.0 × 10⁻⁴ s⁻¹ at T₁ = 293 K and k₂ = 2.7 × 10⁻⁴ s⁻¹ at T₂ = 303 K:ln(2.7 × 10⁻⁴/1.0 × 10⁻⁴) = -(Eₐ/8.314)(1/303 - 1/293)Solving for Eₐ = 52.6 kJ/mol
How do you calculate the pre-exponential factor?
The pre-exponential factor (A) can be calculated by rearranging the Arrhenius equation:
A = k/e^(-Eₐ/RT)With k = 1.0 × 10⁻⁴ s⁻¹, Eₐ = 52.6 kJ/mol, T = 293 K:
A = (1.0 × 10⁻⁴)/e^(-52,600/(8.314 × 293)) = 4.2 × 10⁸ s⁻¹
Activation Energy at Two Temperatures
The equation for calculating activation energy using two temperature points is:
Eₐ = -R × ln(k₂/k₁) × (T₁T₂/(T₂-T₁))For a reaction with:
- k₁ = 2.0 × 10⁻² s⁻¹ at T₁ = 300 K
- k₂ = 8.0 × 10⁻² s⁻¹ at T₂ = 320 K
Eₐ = -(8.314) × ln(8.0 × 10⁻²/2.0 × 10⁻²) × (300 × 320/20) = 46.3 kJ/molReferences:
- Physical Chemistry Chemical Physics: https://pubs.rsc.org/en/journals/journalissues/cp
- Chemical Reviews: https://pubs.acs.org/journal/chreay
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