Calculate k from experimental concentration and rate data.
From table row
Exponent m
From table row
Exponent n
The observed rate from the table
Calculated Rate Constant (k):—
Reaction Order (Total):—
Units:—
Formula Used: k = Rate / ([A]m [B]n)
How to Calculate Rate Constant k from Table Data
Determining the rate constant ($k$) is a fundamental task in chemical kinetics. Typically, you are presented with a table of experimental data showing the initial concentrations of reactants and the resulting initial reaction rates. This guide explains how to extract the necessary values from such a table and calculate $k$ accurately.
Understanding the Rate Law
Before calculating $k$, you must understand the general form of the rate law equation:
Rate = k [A]m [B]n
Rate: The speed of the reaction (usually in M/s or mol L-1 s-1).
k: The rate constant (temperature-dependent).
[A], [B]: Molar concentrations of reactants.
m, n: The reaction orders with respect to A and B.
Step-by-Step Calculation Guide
1. Determine the Reaction Orders (m and n)
If the problem does not provide the orders, you must find them using the "Method of Initial Rates" from your table:
Find two experiments (rows) where the concentration of [B] is constant but [A] changes.
Compare the ratio of the rates to the ratio of the concentrations.
Example: If [A] doubles and the Rate doubles, the order ($m$) is 1. If Rate quadruples, $m$ is 2.
2. Select a Data Row
Once you know the orders ($m$ and $n$), you can determine $k$ using data from any single experiment in your table. Theoretically, $k$ should be the same for every row (assuming constant temperature).
3. Rearrange and Solve
Rearrange the rate law to solve for $k$:
k = Rate / ([A]m [B]n)
Plug in the concentration and rate values from your chosen row into the calculator above.
Example Calculation
Consider the following data for the reaction A + B → C:
Exp
[A] (M)
[B] (M)
Rate (M/s)
1
0.10
0.10
2.0 x 10-3
2
0.20
0.10
4.0 x 10-3
3
0.10
0.20
8.0 x 10-3
Finding Orders:
Comparing Exp 1 and 2: [B] is constant. [A] doubles (0.10 to 0.20), Rate doubles (2.0 to 4.0). Order $m = 1$.
Comparing Exp 1 and 3: [A] is constant. [B] doubles (0.10 to 0.20), Rate quadruples (2.0 to 8.0). Order $n = 2$.
The units of $k$ vary depending on the overall order of the reaction (sum of exponents). The calculator automatically generates the correct units for you.
Zero Order: M/s (or M s-1)
First Order: 1/s (or s-1)
Second Order: 1/(M·s) (or M-1 s-1)
Third Order: 1/(M2·s) (or M-2 s-1)
function validateInput(input) {
// Simple validation visualization
if(input.value < 0) {
input.style.borderColor = "red";
} else {
input.style.borderColor = "#cbd5e0";
}
}
function calculateK() {
// 1. Get Elements
var concAInput = document.getElementById("concA");
var orderAInput = document.getElementById("orderA");
var concBInput = document.getElementById("concB");
var orderBInput = document.getElementById("orderB");
var rateInput = document.getElementById("initialRate");
var resultArea = document.getElementById("result-area");
var kValueDisplay = document.getElementById("kValue");
var totalOrderDisplay = document.getElementById("totalOrderDisplay");
var unitDisplay = document.getElementById("unitDisplay");
// 2. Parse Values
var concA = parseFloat(concAInput.value);
var orderA = parseFloat(orderAInput.value);
var rate = parseFloat(rateInput.value);
// Handle optional Reactant B
var concB = parseFloat(concBInput.value);
var orderB = parseFloat(orderBInput.value);
// 3. Validation
if (isNaN(concA) || isNaN(orderA) || isNaN(rate)) {
alert("Please enter valid numbers for Concentration A, Order A, and Rate.");
return;
}
if (concA <= 0 || rate <= 0) {
alert("Concentration and Rate must be positive numbers.");
return;
}
// 4. Logic Calculation
// Calculate term for A: [A]^m
var termA = Math.pow(concA, orderA);
// Calculate term for B: [B]^n (Default to 1 if inputs are empty)
var termB = 1;
var actualOrderB = 0;
if (!isNaN(concB) && !isNaN(orderB)) {
if(concB k = Rate / (termA * termB)
var denominator = termA * termB;
if (denominator === 0) {
alert("Denominator resulted in zero. Check your concentrations.");
return;
}
var k = rate / denominator;
var totalOrder = orderA + actualOrderB;
// 5. Determine Units
// General Formula: M^(1-totalOrder) * s^-1
// Or: 1 / (M^(totalOrder-1) * s)
var unitString = "";
if (totalOrder === 0) {
unitString = "M s⁻¹";
} else if (totalOrder === 1) {
unitString = "s⁻¹";
} else {
var mExp = 1 – totalOrder;
if (mExp === 1) {
unitString = "M s⁻¹";
} else {
// Using standard scientific notation M^(-x) s^(-1)
unitString = "M" + superscript(mExp) + " s⁻¹";
}
}
// 6. Output Formatting
// Use scientific notation if k is very small or very large
var displayK = "";
if (k 1000) {
displayK = k.toExponential(3);
} else {
displayK = k.toFixed(4);
}
// 7. Update DOM
resultArea.style.display = "block";
kValueDisplay.innerHTML = displayK;
totalOrderDisplay.innerHTML = totalOrder;
unitDisplay.innerHTML = unitString;
}
// Helper to generate superscript text for units
function superscript(num) {
var str = num.toString();
var sup = "";
var map = {
'-': '⁻',
'0': '⁰',
'1': '¹',
'2': '²',
'3': '³',
'4': '⁴',
'5': '⁵',
'6': '⁶',
'7': '⁷',
'8': '⁸',
'9': '⁹'
};
for (var i = 0; i < str.length; i++) {
sup += map[str[i]] || str[i];
}
return sup;
}