Enter two points from your linear kinetic plot to find k.
Zero Order (Plot: [A] vs Time)
First Order (Plot: ln[A] vs Time)
Second Order (Plot: 1/[A] vs Time)
Y-Axis should be Concentration [A].
Seconds (s)
Minutes (min)
Hours (h)
Slope of Line (m):–
Rate Constant (k):–
Units:–
function updateAxisLabels() {
var order = document.getElementById('reactionOrder').value;
var hint = document.getElementById('axis-hint');
var label1 = document.getElementById('labelY1');
var label2 = document.getElementById('labelY2');
if (order === '0') {
hint.innerText = "For Zero Order, the Y-Axis is Concentration [A]. Slope = -k.";
label1.innerText = "Point 1: Conc [A]";
label2.innerText = "Point 2: Conc [A]";
} else if (order === '1') {
hint.innerText = "For First Order, the Y-Axis is Natural Log ln[A]. Slope = -k.";
label1.innerText = "Point 1: ln[A]";
label2.innerText = "Point 2: ln[A]";
} else {
hint.innerText = "For Second Order, the Y-Axis is Inverse 1/[A]. Slope = k.";
label1.innerText = "Point 1: 1/[A]";
label2.innerText = "Point 2: 1/[A]";
}
}
function calculateK() {
var t1 = parseFloat(document.getElementById('time1').value);
var y1 = parseFloat(document.getElementById('yValue1').value);
var t2 = parseFloat(document.getElementById('time2').value);
var y2 = parseFloat(document.getElementById('yValue2').value);
var order = document.getElementById('reactionOrder').value;
var timeUnit = document.getElementById('timeUnit').value;
if (isNaN(t1) || isNaN(y1) || isNaN(t2) || isNaN(y2)) {
alert("Please enter valid numeric coordinates for both points.");
return;
}
if (t1 === t2) {
alert("Time values (x1 and x2) cannot be the same. Division by zero.");
return;
}
// Calculate Slope
var slope = (y2 – y1) / (t2 – t1);
var k = 0;
var units = "";
var warning = "";
// Determine k based on order
if (order === '0') {
// Slope = -k, so k = -slope
k = -slope;
units = "M/" + timeUnit + " (or mol L⁻¹ " + timeUnit + "⁻¹)";
if (slope > 0) warning = "Warning: Zero order plots usually have a negative slope. Check your data.";
} else if (order === '1') {
// Slope = -k, so k = -slope
k = -slope;
units = timeUnit + "⁻¹ (1/" + timeUnit + ")";
if (slope > 0) warning = "Warning: First order plots usually have a negative slope (decay). Check your data.";
} else {
// Second Order: Slope = k
k = slope;
units = "M⁻¹ " + timeUnit + "⁻¹ (L mol⁻¹ " + timeUnit + "⁻¹)";
if (slope < 0) warning = "Warning: Second order plots (1/[A] vs t) usually have a positive slope.";
}
// Display Results
var resultDiv = document.getElementById('result-container');
resultDiv.style.display = 'block';
document.getElementById('slopeResult').innerText = slope.toExponential(4);
// Rate constants must be positive physically, but we show the calc result.
// If data is reversed, k might be negative mathematically, implying data entry error.
document.getElementById('kResult').innerText = k.toExponential(4);
document.getElementById('unitsResult').innerText = units;
var warnDiv = document.getElementById('warningMsg');
if (warning !== "") {
warnDiv.innerText = warning;
warnDiv.style.display = 'block';
} else {
warnDiv.style.display = 'none';
}
}
How to Calculate Rate Constant from a Graph
In chemical kinetics, determining the rate constant ($k$) is essential for understanding the speed of a reaction. The most accurate way to find $k$ is by analyzing the linear plot of concentration data over time. Depending on the reaction order (Zero, First, or Second), the axes of the graph differ, and the slope ($m$) relates to $k$ in specific ways.
This calculator allows you to input two points $(x, y)$ from your straight-line graph to instantly calculate the slope and the corresponding rate constant.
1. Identifying the Reaction Order and Graph Axes
Before calculating, you must ensure you are looking at the correct linear plot. Rate laws integrate into linear equations ($y = mx + b$), where $x$ is always time ($t$), but $y$ changes based on the order.
Reaction Order
Y-Axis Variable
X-Axis Variable
Relationship to Slope
Integrated Rate Law
Zero Order
Concentration $[A]$
Time ($t$)
$k = -\text{slope}$
$[A] = -kt + [A]_0$
First Order
$\ln[A]$ (Natural Log)
Time ($t$)
$k = -\text{slope}$
$\ln[A] = -kt + \ln[A]_0$
Second Order
$1/[A]$ (Inverse)
Time ($t$)
$k = \text{slope}$
$1/[A] = kt + 1/[A]_0$
2. How to Calculate the Slope
To find the rate constant, you first need the slope of the best-fit line. Pick two points on the line—preferably not just raw data points, but points that lie exactly on your trendline.
Slope ($m$) = $(y_2 – y_1) / (x_2 – x_1)$
Where:
$x_1, x_2$: Time values (seconds, minutes, etc.)
$y_1, y_2$: The value on the vertical axis (Conc, ln[Conc], or 1/Conc).
3. Calculating $k$ from the Slope
Once you have the slope ($m$), apply the logic for your specific reaction order:
Zero and First Order
For these reactions, the concentration (or log of concentration) decreases over time, resulting in a negative slope. Since the rate constant $k$ is always a positive value, we negate the slope:
$k = -m$
Second Order
For second-order reactions, we plot the inverse of concentration ($1/[A]$). As concentration decreases, the inverse increases, resulting in a positive slope. Therefore:
$k = m$
4. Units of the Rate Constant
The units of $k$ act as a dimensional correction so that the rate always ends up in M/s (molarity per second). They are crucial for verification:
Zero Order: $M \cdot s^{-1}$ (Molarity per second)
First Order: $s^{-1}$ (Per second)
Second Order: $M^{-1} \cdot s^{-1}$ (Inverse molarity per second)
Example Calculation
Suppose you have a First Order reaction. You plot $\ln[A]$ vs Time and pick two points on the line: