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: echarts 5.5.1 | JavaScript 22.22.3
// Quality: 90/100 | Created: 2026-06-24
//# anyplot-orientation: landscape
const t = window.ANYPLOT_TOKENS;
// --- Data (deterministic, in-memory) ----------------------------------------
// First-order thermal decomposition of hydrogen peroxide (H₂O₂ → H₂O + ½O₂)
const temps_K = [300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550];
const R_GAS = 8.314; // J/(mol·K)
const EA_TRUE = 95000; // J/mol — activation energy
const LN_A = 27.0; // ln(A) where A is the pre-exponential factor in s⁻¹
// Deterministic perturbations to simulate experimental measurement scatter
const noise = [0.12, -0.08, 0.15, -0.11, 0.09, 0.07, -0.13, 0.10, -0.06, 0.14, -0.09];
const inv_T = temps_K.map(T => 1 / T);
const ln_k = temps_K.map((T, i) => LN_A - EA_TRUE / (R_GAS * T) + noise[i]);
// Linear regression: ln(k) = slope * (1/T) + intercept (slope = -Ea/R)
const n = inv_T.length;
const sx = inv_T.reduce((a, b) => a + b, 0);
const sy = ln_k.reduce((a, b) => a + b, 0);
const sxy = inv_T.reduce((a, xi, i) => a + xi * ln_k[i], 0);
const sx2 = inv_T.reduce((a, xi) => a + xi * xi, 0);
const slope = (n * sxy - sx * sy) / (n * sx2 - sx * sx);
const intercept = (sy - slope * sx) / n;
// R² coefficient of determination
const y_mean = sy / n;
const ss_res = ln_k.reduce((a, yi, i) => a + (yi - (slope * inv_T[i] + intercept)) ** 2, 0);
const ss_tot = ln_k.reduce((a, yi) => a + (yi - y_mean) ** 2, 0);
const r_sq = (1 - ss_res / ss_tot).toFixed(4);
// Extracted activation energy from Arrhenius slope: slope = -Ea/R
const Ea_kJ = (-slope * R_GAS / 1000).toFixed(1);
const Ea_over_R = (-slope).toFixed(0);
// Regression line (51 points for smooth rendering, extended beyond data range)
const x_lo = Math.min(...inv_T) * 0.995;
const x_hi = Math.max(...inv_T) * 1.005;
const line_data = Array.from({ length: 51 }, (_, i) => {
const x = x_lo + (x_hi - x_lo) * i / 50;
return [x, slope * x + intercept];
});
// --- Init -------------------------------------------------------------------
const chart = echarts.init(document.getElementById("container"));
// --- Option -----------------------------------------------------------------
chart.setOption({
animation: false,
color: t.palette,
backgroundColor: "transparent",
title: {
text: "line-arrhenius · javascript · echarts · anyplot.ai",
left: "center",
top: 22,
textStyle: { color: t.ink, fontSize: 22, fontWeight: "bold" }
},
legend: {
data: ["Experimental data", "Arrhenius fit"],
top: 60,
textStyle: { color: t.inkSoft, fontSize: 14 },
itemWidth: 22,
itemHeight: 14
},
tooltip: {
trigger: "item",
backgroundColor: t.elevatedBg,
borderColor: t.inkSoft,
textStyle: { color: t.ink, fontSize: 13 },
formatter: function(params) {
if (params.seriesType === "scatter") {
const T = Math.round(1 / params.data[0]);
return (
"T = " + T + " K<br>" +
"1/T = " + (params.data[0] * 1000).toFixed(3) + " ×10⁻³ K⁻¹<br>" +
"ln(k) = " + params.data[1].toFixed(3)
);
}
return "";
}
},
grid: { left: 90, right: 224, top: 102, bottom: 115 },
xAxis: {
type: "value",
name: "1/T (×10⁻³ K⁻¹)",
nameLocation: "middle",
nameGap: 65,
nameTextStyle: { color: t.inkSoft, fontSize: 14 },
min: x_lo,
max: x_hi,
axisLabel: {
color: t.inkSoft,
fontSize: 14,
formatter: function(val) {
return (val * 1000).toFixed(2) + "\n(" + Math.round(1 / val) + " K)";
}
},
axisLine: { lineStyle: { color: t.inkSoft } },
splitLine: { show: false },
axisTick: { lineStyle: { color: t.inkSoft } }
},
yAxis: {
type: "value",
name: "ln(k)",
nameLocation: "middle",
nameGap: 56,
nameTextStyle: { color: t.inkSoft, fontSize: 14 },
axisLabel: { color: t.inkSoft, fontSize: 13 },
axisLine: { lineStyle: { color: t.inkSoft } },
splitLine: { lineStyle: { color: t.grid } },
axisTick: { lineStyle: { color: t.inkSoft } }
},
series: [
{
name: "Experimental data",
type: "scatter",
symbolSize: 14,
data: inv_T.map((x, i) => [x, ln_k[i]]),
itemStyle: {
color: t.palette[0],
borderColor: t.pageBg,
borderWidth: 2
},
z: 10
},
{
name: "Arrhenius fit",
type: "line",
data: line_data,
lineStyle: { color: t.palette[1], width: 3 },
itemStyle: { color: t.palette[1] },
symbol: "none",
smooth: false,
z: 5
}
],
graphic: [
{
type: "group",
x: 1390,
y: 108,
children: [
{
type: "rect",
shape: { x: 0, y: 0, width: 186, height: 116, r: 5 },
style: {
fill: t.elevatedBg,
stroke: t.inkSoft,
lineWidth: 0.8
}
},
{
type: "text",
x: 14,
y: 18,
style: {
text: "Kinetics Summary",
fill: t.ink,
fontSize: 13,
fontWeight: "bold"
}
},
{
type: "text",
x: 14,
y: 46,
style: {
text: "R² = " + r_sq,
fill: t.inkSoft,
fontSize: 13
}
},
{
type: "text",
x: 14,
y: 70,
style: {
text: "Ea = " + Ea_kJ + " kJ/mol",
fill: t.inkSoft,
fontSize: 13
}
},
{
type: "text",
x: 14,
y: 94,
style: {
text: "Ea/R = " + Ea_over_R + " K",
fill: t.inkSoft,
fontSize: 13
}
}
]
}
]
});
Part of Arrhenius Plot for Reaction Kinetics on anyplot.ai.