Specific Rate Constant Calculator (Arrhenius Equation)
Calculate the rate constant (k) of a chemical reaction using the Arrhenius Equation based on temperature and activation energy.
Joules per mole (J/mol)
Kilojoules per mole (kJ/mol)
Kelvin (K)
Celsius (°C)
Specific Rate Constant (k):
What is the Specific Rate Constant?
In chemical kinetics, the specific rate constant (k) is a proportionality constant that links the molar concentrations of reactants to the reaction rate. Unlike the reaction rate itself, the specific rate constant is independent of concentration but highly sensitive to changes in temperature and the presence of a catalyst.
Arrhenius Equation: k = A * e^(-Ea / (R * T))
Key Variables Explained
Pre-exponential Factor (A): Also known as the frequency factor, it represents the frequency of collisions between reactant molecules with the correct orientation.
Activation Energy (Ea): The minimum energy required for a chemical reaction to occur. Lower activation energy typically results in a faster reaction.
Gas Constant (R): Use 8.314 J/(mol·K) for standard calculations.
Temperature (T): Absolute temperature is required in Kelvin. (K = °C + 273.15).
Example Calculation
Suppose a reaction has an activation energy of 50 kJ/mol and a pre-exponential factor of 1.0 x 1011 s-1 at a temperature of 25°C (298.15 K).
Convert Ea to J/mol: 50,000 J/mol.
Identify R: 8.314 J/(mol·K).
Calculate the exponent: -50,000 / (8.314 * 298.15) ≈ -20.17.
Calculate k: 1011 * e^(-20.17) ≈ 1.74 x 102 s-1.
function calculateRateConstant() {
var A = parseFloat(document.getElementById("preFactor").value);
var Ea = parseFloat(document.getElementById("activationEnergy").value);
var eaUnit = document.getElementById("eaUnit").value;
var T = parseFloat(document.getElementById("temperature").value);
var tempUnit = document.getElementById("tempUnit").value;
var R = 8.31446261815324; // Universal Gas Constant in J/(mol·K)
if (isNaN(A) || isNaN(Ea) || isNaN(T)) {
alert("Please enter valid numerical values for all fields.");
return;
}
// Convert Temperature to Kelvin
var tempKelvin = T;
if (tempUnit === "c") {
tempKelvin = T + 273.15;
}
if (tempKelvin <= 0) {
alert("Temperature must be above absolute zero.");
return;
}
// Convert Ea to Joules
var eaJoules = Ea;
if (eaUnit === "kj") {
eaJoules = Ea * 1000;
}
// Calculate Exponent: -Ea / (R * T)
var exponent = -eaJoules / (R * tempKelvin);
// Calculate k = A * e^(exponent)
var k = A * Math.exp(exponent);
// Display Result
var resultDiv = document.getElementById("kResult");
var container = document.getElementById("resultContainer");
var pathDiv = document.getElementById("calculationPath");
container.style.display = "block";
// Formatting the output
if (k 10000) {
resultDiv.innerHTML = k.toExponential(4);
} else {
resultDiv.innerHTML = k.toFixed(6);
}
pathDiv.innerHTML = "Calculated at " + tempKelvin.toFixed(2) + " K using R = 8.314 J/(mol·K).";
}