Calculate the rate constant using Rate Law data or the Arrhenius Equation.
Method 1: From Rate Law (Concentrations & Rate)
Method 2: Arrhenius Equation (Activation Energy & Temp)
Often denoted as frequency factor.
kJ/mol
J/mol
Kelvin (K)
Celsius (°C)
Calculated Rate Constant (k)
0
How to Calculate Rate Constant in Chemistry
The rate constant ($k$) is a crucial proportionality constant in chemical kinetics that quantifies the speed of a chemical reaction. Unlike the reaction rate itself, which changes as concentrations change, the rate constant is specific to a reaction at a given temperature.
Method 1: Using the Rate Law Equation
The most common way to determine the rate constant experimentally is by using the rate law equation. If you know the reaction rate and the concentrations of the reactants along with their reaction orders, you can rearrange the rate law to solve for $k$.
Rate = k [A]m [B]n
Solving for k:
k = Rate / ([A]m [B]n)
Rate: The speed of reaction (usually in $M/s$ or $mol \cdot L^{-1} \cdot s^{-1}$).
[A], [B]: Molar concentrations of reactants.
m, n: The order of reaction with respect to each reactant.
Method 2: Using the Arrhenius Equation
The rate constant is highly dependent on temperature. The Arrhenius equation allows you to calculate $k$ if you know the activation energy, temperature, and the frequency factor (pre-exponential factor).
k = A × e-(Ea / RT)
A: The pre-exponential factor (frequency of collisions).
Ea: The activation energy (energy barrier to reaction).
R: The universal gas constant ($8.314\ J \cdot mol^{-1} \cdot K^{-1}$).
T: The absolute temperature in Kelvin.
Units of the Rate Constant (k)
The units of $k$ vary depending on the overall order of the reaction. The overall order is the sum of the exponents ($m + n$).
Reaction Order
Rate Law
Units of k
Zero Order (0)
Rate = k
$M \cdot s^{-1}$
First Order (1)
Rate = k[A]
$s^{-1}$
Second Order (2)
Rate = k[A]²
$M^{-1} \cdot s^{-1}$
Third Order (3)
Rate = k[A]³
$M^{-2} \cdot s^{-1}$
Example Calculation
Problem: A reaction is second order with respect to Reactant A. If the concentration of A is 0.10 M and the initial rate is $0.005\ M/s$, what is the rate constant?
Solution:
Identify the formula: $Rate = k[A]^2$
Rearrange for k: $k = Rate / [A]^2$
Plug in values: $k = 0.005 / (0.10)^2$
Calculate: $k = 0.005 / 0.01 = 0.5\ M^{-1}s^{-1}$
function toggleInputs() {
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var arrDiv = document.getElementById('arrheniusInputs');
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if (method === 'rateLaw') {
rateDiv.classList.remove('hidden');
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// Hide result when switching tabs to avoid confusion
resultBox.style.display = 'none';
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function calculateRateConstant() {
var method = document.getElementById('calcMethod').value;
var k = 0;
var resultHtml = "";
var unitHtml = "";
if (method === 'rateLaw') {
// Get Rate Law Inputs
var rate = parseFloat(document.getElementById('reactionRate').value);
var concA = parseFloat(document.getElementById('concA').value);
var orderA = parseFloat(document.getElementById('orderA').value);
var concB = document.getElementById('concB').value;
var orderB = document.getElementById('orderB').value;
// Validation
if (isNaN(rate) || isNaN(concA) || isNaN(orderA)) {
alert("Please enter valid numbers for Rate, Concentration [A], and Order [A].");
return;
}
// Parse B if exists, else treat as negligible (factor of 1)
var termB = 1;
var orderBVal = 0;
if (concB && concB !== "" && !isNaN(parseFloat(concB))) {
var cb = parseFloat(concB);
var ob = orderB && orderB !== "" ? parseFloat(orderB) : 0;
termB = Math.pow(cb, ob);
orderBVal = ob;
}
var termA = Math.pow(concA, orderA);
// k = Rate / ([A]^m * [B]^n)
if (termA * termB === 0) {
alert("Concentrations cannot result in division by zero.");
return;
}
k = rate / (termA * termB);
// Determine Units based on overall order
var overallOrder = orderA + orderBVal;
// General unit formula: M^(1-order) * s^-1
var molarityPower = 1 – overallOrder;
if (molarityPower === 0) {
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} else if (molarityPower === 1) {
unitHtml = "M ċ s-1";
} else {
unitHtml = "M" + molarityPower + " ċ s-1";
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} else {
// Get Arrhenius Inputs
var A = parseFloat(document.getElementById('freqFactor').value);
var Ea = parseFloat(document.getElementById('activationEnergy').value);
var temp = parseFloat(document.getElementById('temperature').value);
var eUnit = document.getElementById('energyUnit').value;
var tUnit = document.getElementById('tempUnit').value;
// Validation
if (isNaN(A) || isNaN(Ea) || isNaN(temp)) {
alert("Please enter valid numbers for A, Activation Energy, and Temperature.");
return;
}
// Convert to standard units: Joules and Kelvin
var R = 8.314; // J/(mol*K)
// Convert Ea to Joules if in kJ
if (eUnit === 'kJ') {
Ea = Ea * 1000;
}
// Convert Temp to Kelvin if in Celsius
if (tUnit === 'C') {
temp = temp + 273.15;
}
if (temp <= 0) {
alert("Temperature must be greater than 0 Kelvin.");
return;
}
// k = A * exp(-Ea / RT)
var exponent = -Ea / (R * temp);
k = A * Math.exp(exponent);
// Units for Arrhenius k match the units of A usually
unitHtml = "(Matches units of A)";
}
// Formatting Result
// Scientific notation for very small or large numbers
var displayK;
if (k === 0) {
displayK = "0";
} else if (Math.abs(k) 10000) {
displayK = k.toExponential(4);
} else {
displayK = k.toFixed(5);
}
document.getElementById('kValue').innerHTML = displayK;
document.getElementById('kUnits').innerHTML = unitHtml;
document.getElementById('result').style.display = 'block';
}