In chemical kinetics, the rate constant (k) is a proportionality constant that relates the rate of a chemical reaction to the concentrations of the reactants. The fundamental formula used is the Rate Law:
Rate = k [A]x [B]y
How to Calculate k
Identify the Rate: This is the change in concentration per unit time (M/s).
Determine the Concentrations: Plug in the molarity (M) of the reactants at that specific rate.
Determine the Orders: The exponents (x and y) are determined experimentally.
Solve for k: Divide the rate by the product of the concentrations raised to their powers.
Determining Units
The units of the rate constant change depending on the overall reaction order (n), where n = x + y. The general formula for the units of k is:
M(1-n) · s-1
Overall Order (n)
Rate Constant Units
0 (Zero Order)
M · s-1 or mol · L-1 · s-1
1 (First Order)
s-1
2 (Second Order)
M-1 · s-1 or L · mol-1 · s-1
3 (Third Order)
M-2 · s-1 or L2 · mol-2 · s-1
Example Calculation
Suppose a reaction has a rate of 0.0045 M/s, [A] = 0.2 M with an order of 2, and [B] = 0.5 M with an order of 1.
function calculateRateConstant() {
var rateValue = parseFloat(document.getElementById('reactionRate').value);
var concA = parseFloat(document.getElementById('concA').value);
var orderA = parseFloat(document.getElementById('orderA').value);
var concB = parseFloat(document.getElementById('concB').value);
var orderB = parseFloat(document.getElementById('orderB').value);
// Validate main inputs
if (isNaN(rateValue) || isNaN(concA) || isNaN(orderA)) {
alert("Please enter valid numbers for Rate, Concentration A, and Order A.");
return;
}
// Default values for B if left blank
if (isNaN(concB)) concB = 1;
if (isNaN(orderB)) orderB = 0;
// Calculation logic
var factorA = Math.pow(concA, orderA);
var factorB = (concB === 0 && orderB === 0) ? 1 : Math.pow(concB, orderB);
// Prevent division by zero
var denominator = factorA * factorB;
if (denominator === 0) {
alert("Denominator calculated to zero. Please check concentration and order values.");
return;
}
var k = rateValue / denominator;
var n = orderA + orderB;
// Unit derivation
var units = "";
var mExp = 1 – n;
if (n === 1) {
units = "s⁻¹";
} else if (n === 0) {
units = "M · s⁻¹";
} else {
// Round to 2 decimals for the exponent display if not whole
var displayExp = Number.isInteger(mExp) ? mExp : mExp.toFixed(2);
units = "M" + displayExp + " · s⁻¹";
}
// Output results
document.getElementById('kValue').innerText = k.toExponential(4).replace("e", " x 10^");
document.getElementById('kUnits').innerHTML = units;
document.getElementById('overallOrder').innerText = n;
document.getElementById('rateResult').style.display = "block";
}