Enter in standard notation (1000) or scientific (1e3).
kJ/mol
J/mol
Kelvin (K)
Celsius (°C)
Rate Constant (k):
function calculateRateConstant() {
var A = parseFloat(document.getElementById("preExpFactor").value);
var EaInput = parseFloat(document.getElementById("activationEnergy").value);
var TInput = parseFloat(document.getElementById("temperature").value);
var eaUnit = document.getElementById("eaUnit").value;
var tempUnit = document.getElementById("tempUnit").value;
var resultBox = document.getElementById("resultBox");
var resultValue = document.getElementById("resultValue");
var calculationSteps = document.getElementById("calculationSteps");
// Validation
if (isNaN(A) || isNaN(EaInput) || isNaN(TInput)) {
resultBox.style.display = "block";
resultValue.innerHTML = "Invalid Input";
resultBox.style.backgroundColor = "#fff5f5";
resultBox.style.borderColor = "#fc8181";
resultValue.style.color = "#c53030";
calculationSteps.innerHTML = "Please ensure all fields contain valid numbers.";
return;
}
// Reset styles
resultBox.style.backgroundColor = "#ebf8ff";
resultBox.style.borderColor = "#bee3f8";
resultValue.style.color = "#2c5282";
// Constants
var R = 8.314; // Universal Gas Constant in J/(mol*K)
// Conversions
var Ea_Joules = (eaUnit === "kJ") ? EaInput * 1000 : EaInput;
var T_Kelvin = (tempUnit === "C") ? TInput + 273.15 : TInput;
// Physical validation (Absolute Zero)
if (T_Kelvin <= 0) {
resultBox.style.display = "block";
resultValue.innerHTML = "Error";
calculationSteps.innerHTML = "Temperature must be greater than 0 Kelvin.";
return;
}
// Calculation: k = A * exp(-Ea / (R * T))
var exponent = -Ea_Joules / (R * T_Kelvin);
var exponentialTerm = Math.exp(exponent);
var k = A * exponentialTerm;
// Formatting results
var kFormatted = k.toExponential(4);
var expFormatted = exponentialTerm.toExponential(4);
var exponentValFormatted = exponent.toFixed(4);
// Display
resultBox.style.display = "block";
resultValue.innerHTML = kFormatted;
calculationSteps.innerHTML =
"Calculation Details:\n" +
"R = 8.314 J/(mol·K)\n" +
"T = " + T_Kelvin + " K\n" +
"Ea = " + Ea_Joules + " J/mol\n\n" +
"1. Exponent = -Ea / (R × T)\n" +
" = -" + Ea_Joules + " / (8.314 × " + T_Kelvin + ")\n" +
" = " + exponentValFormatted + "\n\n" +
"2. Exponential Term = e^(" + exponentValFormatted + ")\n" +
" = " + expFormatted + "\n\n" +
"3. k = A × Exponential Term\n" +
" = " + A.toExponential(4) + " × " + expFormatted + "\n" +
" = " + kFormatted;
}
How to Calculate Rate Constant with Temperature
In chemical kinetics, the rate constant ($k$) quantifies the speed of a chemical reaction. It is heavily dependent on temperature. The relationship between the rate constant, temperature, and activation energy is described by the Arrhenius Equation.
This calculator helps you determine the rate constant ($k$) given the pre-exponential factor ($A$), activation energy ($E_a$), and temperature ($T$).
The Arrhenius Equation Formula
k = A × e-(Ea / RT)
Where:
k: The rate constant of the reaction. The units depend on the order of the reaction (e.g., $s^{-1}$ for first-order).
A: The Pre-exponential factor (or Frequency Factor). It represents the frequency of collisions between reactant molecules. It shares the same units as $k$.
Ea: Activation Energy. The minimum energy required for the reaction to occur, typically expressed in Joules per mole ($J/mol$) or Kilojoules per mole ($kJ/mol$).
R: The Universal Gas Constant. Value is approximately $8.314\ J/(mol\cdot K)$.
T: Absolute Temperature in Kelvin ($K$).
Why Does Temperature Affect Reaction Rate?
Temperature is a measure of the average kinetic energy of the particles in a system. As temperature increases:
Increased Collision Frequency: Molecules move faster and collide more often. This is represented by the factor $A$ (though $A$ is weakly dependent on temperature, it is often treated as a constant over small ranges).
Higher Energy Collisions: More importantly, a larger fraction of molecules possess enough kinetic energy to overcome the Activation Energy barrier ($E_a$). This is represented by the exponential term $e^{-E_a/RT}$.
Because the temperature ($T$) is in the exponent, even small changes in temperature can result in significant changes in the rate constant ($k$). A general rule of thumb in chemistry is that the reaction rate often doubles for every $10^{\circ}C$ rise in temperature.
Step-by-Step Calculation Example
Let's calculate the rate constant for a reaction with the following parameters:
Step 1: Convert units to standard SI units.
Activation energy should be in Joules to match the gas constant ($R$).
$E_a = 100\ kJ/mol \times 1000 = 100,000\ J/mol$.
Step 4: Multiply by the Frequency Factor ($A$).
$k = (1.0 \times 10^{13}) \times (3.87 \times 10^{-18})$
$k \approx 3.87 \times 10^{-5}\ s^{-1}$
Common Unit Conversions
When performing these calculations manually, ensuring units match is the most critical step. The calculator above handles these conversions automatically.