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: muix 7.29.1 | JavaScript 22.22.3
// Quality: 88/100 | Created: 2026-06-24
//# anyplot-orientation: landscape
// anyplot.ai
// line-arrhenius: Arrhenius Plot for Reaction Kinetics
// Library: MUI X Charts | React | Node 22
// License: @mui/x-charts — MIT (community). Pro/Premium are out of scope.
// Quality: pending | Created: 2026-06-24
import { LineChart } from "@mui/x-charts/LineChart";
import Box from "@mui/material/Box";
import Typography from "@mui/material/Typography";
const t = window.ANYPLOT_TOKENS;
const sz = window.ANYPLOT_SIZE;
// LCG for deterministic noise (no Math.random — banned in workflow)
let lcgSeed = 42;
function nextLcg() {
lcgSeed = (Math.imul(lcgSeed, 1664525) + 1013904223) >>> 0;
return lcgSeed / 4294967296;
}
// Synthetic Arrhenius data — NO₂ thermal decomposition (2NO₂ → 2NO + O₂)
const R_GAS = 8.314; // J/(mol·K)
const Ea_true = 111000; // J/mol (~111 kJ/mol — literature value)
const lnA = 28.55; // ln(2.5 × 10¹² s⁻¹) pre-exponential factor
const temps_K = [310, 330, 350, 370, 390, 410, 430, 450, 470, 490, 510];
const xData = temps_K.map((T) => parseFloat((1000 / T).toFixed(4)));
const yData = temps_K.map((T) => {
const lnK_true = lnA - Ea_true / (R_GAS * T);
return parseFloat((lnK_true + (nextLcg() - 0.5) * 0.3).toFixed(4));
});
// Linear regression: ln(k) = intercept + slope × (1000/T)
const n = xData.length;
const sumX = xData.reduce((a, b) => a + b, 0);
const sumY = yData.reduce((a, b) => a + b, 0);
const sumXY = xData.reduce((s, x, i) => s + x * yData[i], 0);
const sumX2 = xData.reduce((s, x) => s + x * x, 0);
const slope = (n * sumXY - sumX * sumY) / (n * sumX2 - sumX * sumX);
const intercept = (sumY - slope * sumX) / n;
const yMean = sumY / n;
const ssRes = yData.reduce(
(s, y, i) => s + (y - (slope * xData[i] + intercept)) ** 2,
0
);
const ssTot = yData.reduce((s, y) => s + (y - yMean) ** 2, 0);
const r2 = 1 - ssRes / ssTot;
// slope = -Ea / (R × 1000) → Ea = -slope × R × 1000
const Ea_kJ = (-slope * R_GAS).toFixed(1); // kJ/mol
const EaR_K = (-slope * 1000).toFixed(0); // Ea/R in K
const regData = xData.map((x) =>
parseFloat((slope * x + intercept).toFixed(4))
);
export default function Chart() {
return (
<Box sx={{ position: "relative", width: sz.width, height: sz.height }}>
{/* Chart title */}
<Typography
sx={{
position: "absolute",
top: 14,
left: 0,
right: 0,
textAlign: "center",
color: t.ink,
fontSize: 22,
fontWeight: 600,
zIndex: 1,
pointerEvents: "none",
}}
>
line-arrhenius · javascript · muix · anyplot.ai
</Typography>
<LineChart
width={sz.width}
height={sz.height}
skipAnimation
margin={{ top: 110, bottom: 110, left: 110, right: 60 }}
colors={[t.palette[0], t.palette[1]]}
grid={{ horizontal: true }}
xAxis={[
{
id: "invT",
data: xData,
label: "1000 / T (K⁻¹)",
valueFormatter: (v) => v.toFixed(2),
scaleType: "linear",
position: "bottom",
tickNumber: 7,
tickLabelStyle: { fontSize: 14, fill: t.inkSoft },
labelStyle: { fontSize: 16, fill: t.ink },
},
{
id: "tempK",
data: xData,
label: "Temperature (K)",
valueFormatter: (v) => `${Math.round(1000 / v)}`,
scaleType: "linear",
position: "top",
tickNumber: 5,
tickLabelStyle: { fontSize: 14, fill: t.inkSoft },
labelStyle: { fontSize: 16, fill: t.ink },
},
]}
yAxis={[
{
id: "lnk",
label: "ln(k)",
labelStyle: { fontSize: 18, fill: t.ink },
tickLabelStyle: { fontSize: 14, fill: t.inkSoft },
},
]}
series={[
{
id: "experimental",
data: yData,
label: "Experimental ln(k)",
showMark: true,
curve: "linear",
xAxisKey: "invT",
},
{
id: "regression",
data: regData,
label: "Linear regression",
showMark: false,
curve: "linear",
xAxisKey: "invT",
},
]}
topAxis="tempK"
bottomAxis="invT"
leftAxis="lnk"
rightAxis={null}
slotProps={{
legend: {
position: { vertical: "bottom", horizontal: "middle" },
direction: "row",
itemMarkWidth: 18,
itemMarkHeight: 3,
itemGap: 28,
labelStyle: { fontSize: 14, fill: t.inkSoft },
},
}}
/>
{/* Regression statistics annotation */}
<Box
sx={{
position: "absolute",
top: "18%",
right: "5%",
bgcolor: t.elevatedBg,
px: 2,
py: 1.5,
borderRadius: 1.5,
border: `1px solid ${t.inkSoft}55`,
zIndex: 2,
}}
>
<Typography
sx={{ color: t.ink, fontSize: 15, fontFamily: "monospace", lineHeight: 1.9 }}
>
R² = {r2.toFixed(4)}
</Typography>
<Typography
sx={{ color: t.ink, fontSize: 15, fontFamily: "monospace", lineHeight: 1.9 }}
>
Eₐ / R = {EaR_K} K
</Typography>
<Typography
sx={{ color: t.ink, fontSize: 15, fontFamily: "monospace", lineHeight: 1.9 }}
>
Eₐ = {Ea_kJ} kJ mol⁻¹
</Typography>
</Box>
</Box>
);
}
Part of Arrhenius Plot for Reaction Kinetics on anyplot.ai.