Arrhenius Rate Constant Calculator
How to Calculate Rate of Reaction with Temperature
Understanding how temperature influences the speed of a chemical reaction is a fundamental concept in physical chemistry and chemical kinetics. The relationship between temperature and the rate of reaction is mathematically described by the Arrhenius Equation.
This calculator allows you to determine the rate constant ($k$) of a reaction given the temperature, activation energy, and the frequency factor. Below, we break down the formula, the variables involved, and the scientific logic behind why reactions speed up as things get hotter.
The Arrhenius Equation Formula
In 1889, Svante Arrhenius proposed an empirical equation that models the temperature dependence of reaction rates. The formula is:
k = A × e-Ea / (R × T)
Variable Definitions
| Symbol | Name | Description | Standard Units |
|---|---|---|---|
| k | Rate Constant | A coefficient that relates reaction rate to reactant concentrations. | s⁻¹ (for 1st order) |
| A | Frequency Factor | Represents the frequency of collisions between molecules. Also called the Pre-exponential factor. | Same as k |
| Ea | Activation Energy | The minimum energy required for a chemical reaction to occur. | J/mol or kJ/mol |
| R | Gas Constant | A physical constant typically set at 8.314. | J/(mol·K) |
| T | Temperature | The absolute temperature of the system. | Kelvin (K) |
Why Does Rate Increase with Temperature?
There are two primary reasons why increasing the temperature leads to a higher rate of reaction:
- Increased Collision Frequency: As temperature rises, molecules gain kinetic energy and move faster. This leads to more frequent collisions between reactant molecules.
- Higher Energy Collisions: This is the more significant factor. For a reaction to occur, colliding molecules must possess energy equal to or greater than the Activation Energy ($E_a$). At higher temperatures, a significantly larger fraction of molecules possess this necessary threshold energy.
The term e-Ea/RT in the equation represents the fraction of molecules that have enough energy to react. As $T$ increases, this fraction increases exponentially.
How to Use This Calculator
To calculate the rate constant for your specific reaction conditions, follow these steps:
- Step 1: Determine the Frequency Factor (A). This is usually determined experimentally or provided in textbook problems. For first-order reactions, it typically has a value between $10^{10}$ and $10^{14}$ s⁻¹.
- Step 2: Identify the Activation Energy (Ea). Enter this value in kJ/mol. The calculator handles the conversion to Joules for you.
- Step 3: Measure the Temperature. Input the temperature in degrees Celsius. The calculator will automatically convert this to Kelvin ($K = °C + 273.15$).
- Step 4: Calculate. Click the button to solve for $k$.
Example Calculation
Consider a reaction with a frequency factor ($A$) of $1.0 \times 10^{11} s^{-1}$ and an activation energy ($E_a$) of $50 \text{ kJ/mol}$. We want to find the rate constant at $25^\circ\text{C}$.
- T (Kelvin): $25 + 273.15 = 298.15 \text{ K}$
- Ea (Joules): $50 \times 1000 = 50,000 \text{ J/mol}$
- R: $8.314 \text{ J/(mol K)}$
- Exponent: $-50,000 / (8.314 \times 298.15) \approx -20.17$
- k: $10^{11} \times e^{-20.17} \approx 1.74 \times 10^2 s^{-1}$
By using the calculator above, you can quickly verify these results and explore how small changes in temperature or activation energy can have massive impacts on the reaction speed.