An Arrhenius plot displays ln(k) versus 1/T to determine the activation energy of a chemical reaction from experimental rate constant data. The Arrhenius equation predicts a linear relationship on this transformed scale, where the slope equals -Ea/R (activation energy divided by the gas constant). This visualization is fundamental in physical chemistry and chemical engineering for characterizing reaction kinetics and comparing catalytic performance.
// anyplot.ai
// line-arrhenius: Arrhenius Plot for Reaction Kinetics
// Library: chartjs 4.4.7 | JavaScript 22.22.3
// Quality: 91/100 | Created: 2026-06-24
const t = window.ANYPLOT_TOKENS;
// H₂O₂ decomposition over MnO₂ catalyst — experimental ln(k) vs 1/T
const temperatures = [300, 320, 340, 360, 380, 400, 425, 450, 475, 500, 525, 550];
const lnK = [0.01, 1.62, 3.59, 4.79, 6.41, 7.28, 8.85, 9.73, 11.13, 11.78, 12.88, 13.36];
const invT = temperatures.map(T => 1 / T);
// Linear regression: slope = -Ea/R, intercept = ln(A)
const nn = invT.length;
const xm = invT.reduce((a, b) => a + b, 0) / nn;
const ym = lnK.reduce((a, b) => a + b, 0) / nn;
const slope = invT.reduce((s, x, i) => s + (x - xm) * (lnK[i] - ym), 0) /
invT.reduce((s, x) => s + (x - xm) ** 2, 0);
const intercept = ym - slope * xm;
// R² and activation energy
const ssTot = lnK.reduce((s, y) => s + (y - ym) ** 2, 0);
const ssRes = invT.reduce((s, x, i) => s + (lnK[i] - (slope * x + intercept)) ** 2, 0);
const r2 = 1 - ssRes / ssTot;
const Ea_kJ = (-slope * 8.314 / 1000).toFixed(1);
// x-axis bounds (slightly wider than data range)
const X_MIN = 1 / 565;
const X_MAX = 1 / 290;
const scatterData = invT.map((x, i) => ({ x, y: lnK[i] }));
const regLineData = [
{ x: X_MIN, y: slope * X_MIN + intercept },
{ x: X_MAX, y: slope * X_MAX + intercept },
];
const canvas = document.createElement("canvas");
document.getElementById("container").appendChild(canvas);
// Inline annotation plugin: Ea/R and R² in bottom-left (away from data cluster)
const annotPlugin = {
id: "annot",
afterDraw(chart) {
const { ctx, chartArea: ca } = chart;
const line1 = `Eₐ/R = ${(-slope).toFixed(0)} K → Eₐ = ${Ea_kJ} kJ/mol`;
const line2 = `R² = ${r2.toFixed(4)}`;
const x = ca.left + 14;
const y1 = ca.bottom - 74;
const y2 = ca.bottom - 48;
ctx.save();
ctx.font = "bold 14px sans-serif";
const boxW = Math.max(ctx.measureText(line1).width, ctx.measureText(line2).width) + 18;
ctx.globalAlpha = 0.82;
ctx.fillStyle = t.elevatedBg;
ctx.fillRect(x - 6, y1 - 18, boxW, 62);
ctx.globalAlpha = 1;
ctx.fillStyle = t.ink;
ctx.textAlign = "left";
ctx.fillText(line1, x, y1);
ctx.fillText(line2, x, y2);
ctx.restore();
},
};
const titleStr = "line-arrhenius · javascript · chartjs · anyplot.ai";
new Chart(canvas, {
data: {
datasets: [
{
type: "line",
label: "Arrhenius fit",
data: regLineData,
borderColor: t.palette[2],
borderWidth: 3.0,
backgroundColor: "transparent",
pointRadius: 0,
tension: 0,
fill: false,
},
{
type: "scatter",
label: "Experimental ln(k)",
data: scatterData,
backgroundColor: t.palette[0],
borderColor: t.pageBg,
borderWidth: 2,
pointRadius: 9,
pointHoverRadius: 11,
},
],
},
options: {
responsive: true,
maintainAspectRatio: false,
animation: false,
layout: { padding: { top: 6, right: 24, bottom: 6, left: 8 } },
plugins: {
title: {
display: true,
text: titleStr,
color: t.ink,
font: { size: 22, weight: "500" },
padding: { top: 8, bottom: 12 },
},
legend: {
labels: {
color: t.ink,
font: { size: 14 },
padding: 20,
boxWidth: 30,
},
},
},
scales: {
x: {
type: "linear",
min: X_MIN,
max: X_MAX,
title: {
display: true,
text: "1/T (K⁻¹)",
color: t.ink,
font: { size: 15 },
padding: { top: 8 },
},
ticks: {
color: t.inkSoft,
font: { size: 13 },
maxTicksLimit: 8,
callback: (v) => v.toExponential(2),
},
grid: { color: t.grid },
},
y: {
title: {
display: true,
text: "ln(k)",
color: t.ink,
font: { size: 15 },
},
ticks: {
color: t.inkSoft,
font: { size: 13 },
},
grid: { color: t.grid },
},
x2: {
type: "linear",
position: "top",
min: X_MIN,
max: X_MAX,
title: {
display: true,
text: "Temperature (K)",
color: t.ink,
font: { size: 15 },
padding: { bottom: 8 },
},
afterBuildTicks(scale) {
scale.ticks = [550, 500, 450, 400, 360, 320, 300].map(T => ({ value: 1 / T }));
},
ticks: {
color: t.inkSoft,
font: { size: 13 },
callback: (v) => `${Math.round(1 / v)}`,
},
grid: { display: false },
border: { display: false },
},
},
},
plugins: [annotPlugin],
});
Part of Arrhenius Plot for Reaction Kinetics on anyplot.ai.