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: d3 7.9.0 | JavaScript 22.22.3
// Quality: 90/100 | Created: 2026-06-24
const t = window.ANYPLOT_TOKENS;
const { width, height } = window.ANYPLOT_SIZE;
const margin = { top: 120, right: 60, bottom: 80, left: 88 };
const iw = width - margin.left - margin.right;
const ih = height - margin.top - margin.bottom;
// N2O decomposition kinetics — 10 experimental measurements (Ea ≈ 80 kJ/mol, A ≈ 1×10¹³ s⁻¹)
// x = 1000/T (10⁻³ K⁻¹), y = ln(k / s⁻¹); noise added to simulate real experiments
const data = [
{ temp: 300, x: 1000 / 300, y: -2.006 },
{ temp: 320, x: 1000 / 320, y: -0.366 },
{ temp: 340, x: 1000 / 340, y: 1.834 },
{ temp: 370, x: 1000 / 370, y: 3.804 },
{ temp: 400, x: 1000 / 400, y: 6.114 },
{ temp: 430, x: 1000 / 430, y: 7.464 },
{ temp: 470, x: 1000 / 470, y: 9.634 },
{ temp: 510, x: 1000 / 510, y: 10.904 },
{ temp: 550, x: 1000 / 550, y: 12.554 },
{ temp: 600, x: 1000 / 600, y: 13.744 },
];
// Pre-computed Arrhenius linear regression: ln(k) = slope·(1000/T) + intercept
const regSlope = -9.607; // units: (10⁻³ K⁻¹)⁻¹
const regIntercept = 29.915; // ln(A)
const r2 = 0.999;
const eaOverR = 9607; // K (= −slope × 1000)
const ea_kJmol = 80; // kJ mol⁻¹
const xDomain = [1.55, 3.45];
const yDomain = [-4, 16];
// SVG
const svg = d3.select("#container")
.append("svg")
.attr("width", width)
.attr("height", height);
const g = svg.append("g")
.attr("transform", `translate(${margin.left},${margin.top})`);
// Scales
const xScale = d3.scaleLinear().domain(xDomain).range([0, iw]);
const yScale = d3.scaleLinear().domain(yDomain).range([ih, 0]);
// Y-axis grid lines (horizontal, subtle)
yScale.ticks(10).forEach(tick => {
g.append("line")
.attr("x1", 0).attr("x2", iw)
.attr("y1", yScale(tick)).attr("y2", yScale(tick))
.attr("stroke", t.grid)
.attr("stroke-width", 1);
});
// Regression line — Imprint blue (palette[2]), dashed
g.append("path")
.datum([
[xDomain[0], regSlope * xDomain[0] + regIntercept],
[xDomain[1], regSlope * xDomain[1] + regIntercept],
])
.attr("d", d3.line().x(d => xScale(d[0])).y(d => yScale(d[1])))
.attr("fill", "none")
.attr("stroke", t.palette[2])
.attr("stroke-width", 2.5)
.attr("stroke-dasharray", "10,5");
// Data points — Imprint brand green (palette[0]), drawn on top of regression line
g.selectAll(".dot")
.data(data)
.join("circle")
.attr("cx", d => xScale(d.x))
.attr("cy", d => yScale(d.y))
.attr("r", 9)
.attr("fill", t.palette[0])
.attr("stroke", t.pageBg)
.attr("stroke-width", 2.5);
// Primary X axis (bottom)
const xAxisEl = g.append("g")
.attr("transform", `translate(0,${ih})`)
.call(d3.axisBottom(xScale).ticks(8).tickFormat(d3.format(".2f")));
xAxisEl.selectAll("text").attr("fill", t.inkSoft).style("font-size", "14px");
xAxisEl.selectAll("line").attr("stroke", t.inkSoft);
xAxisEl.select(".domain").attr("stroke", t.inkSoft);
// Y axis (left)
const yAxisEl = g.append("g")
.call(d3.axisLeft(yScale).ticks(10));
yAxisEl.selectAll("text").attr("fill", t.inkSoft).style("font-size", "14px");
yAxisEl.selectAll("line").attr("stroke", t.inkSoft);
yAxisEl.select(".domain").attr("stroke", t.inkSoft);
// Secondary x-axis at top of plot area — Temperature (K) reference ticks
const tempTicks = [300, 350, 400, 500, 600];
const secG = g.append("g");
secG.append("line")
.attr("x1", 0).attr("x2", iw)
.attr("y1", 0).attr("y2", 0)
.attr("stroke", t.inkSoft)
.attr("stroke-width", 1);
tempTicks.forEach(temp => {
const xp = xScale(1000 / temp);
secG.append("line")
.attr("x1", xp).attr("x2", xp)
.attr("y1", 0).attr("y2", -8)
.attr("stroke", t.inkSoft)
.attr("stroke-width", 1);
secG.append("text")
.attr("x", xp).attr("y", -16)
.attr("text-anchor", "middle")
.attr("fill", t.inkSoft)
.style("font-size", "13px")
.text(`${temp} K`);
});
// Secondary axis header label
svg.append("text")
.attr("x", margin.left + iw / 2)
.attr("y", margin.top - 40)
.attr("text-anchor", "middle")
.attr("fill", t.inkSoft)
.style("font-size", "14px")
.text("Temperature (K)");
// X axis label
svg.append("text")
.attr("x", margin.left + iw / 2)
.attr("y", height - 22)
.attr("text-anchor", "middle")
.attr("fill", t.ink)
.style("font-size", "16px")
.text("1/T × 10³ (K⁻¹)");
// Y axis label (rotated)
svg.append("text")
.attr("transform", "rotate(-90)")
.attr("x", -(margin.top + ih / 2))
.attr("y", 22)
.attr("text-anchor", "middle")
.attr("fill", t.ink)
.style("font-size", "16px")
.text("ln(k / s⁻¹)");
// Annotation box — upper-right area of plot (empty: high 1/T region, high y is unoccupied)
const boxX = xScale(2.65);
const boxY = yScale(14.0);
const boxW = 255;
const boxH = 90;
g.append("rect")
.attr("x", boxX).attr("y", boxY)
.attr("width", boxW).attr("height", boxH)
.attr("fill", t.elevatedBg)
.attr("stroke", t.grid)
.attr("stroke-width", 1)
.attr("rx", 6);
g.append("text")
.attr("x", boxX + 14).attr("y", boxY + 27)
.attr("fill", t.ink)
.style("font-size", "15px")
.style("font-weight", "600")
.text(`R² = ${r2.toFixed(3)}`);
g.append("text")
.attr("x", boxX + 14).attr("y", boxY + 52)
.attr("fill", t.ink)
.style("font-size", "15px")
.text(`Ea/R = ${eaOverR.toLocaleString()} K`);
g.append("text")
.attr("x", boxX + 14).attr("y", boxY + 74)
.attr("fill", t.inkSoft)
.style("font-size", "13px")
.text(`Ea ≈ ${ea_kJmol} kJ mol⁻¹`);
// Small legend in bottom-left (T≈590K region, ln(k)≈−1 — no data or line here)
const legX = xScale(1.7);
const legY = yScale(-1.0);
g.append("circle")
.attr("cx", legX + 10).attr("cy", legY)
.attr("r", 7)
.attr("fill", t.palette[0])
.attr("stroke", t.pageBg)
.attr("stroke-width", 2);
g.append("text")
.attr("x", legX + 24).attr("y", legY + 5)
.attr("fill", t.inkSoft)
.style("font-size", "13px")
.text("Experimental data");
g.append("line")
.attr("x1", legX + 2).attr("x2", legX + 18)
.attr("y1", legY + 22).attr("y2", legY + 22)
.attr("stroke", t.palette[2])
.attr("stroke-width", 2.5)
.attr("stroke-dasharray", "6,3");
g.append("text")
.attr("x", legX + 24).attr("y", legY + 27)
.attr("fill", t.inkSoft)
.style("font-size", "13px")
.text("Arrhenius fit");
// Title
svg.append("text")
.attr("x", width / 2)
.attr("y", 44)
.attr("text-anchor", "middle")
.attr("fill", t.ink)
.style("font-size", "22px")
.style("font-weight", "600")
.text("line-arrhenius · javascript · d3 · anyplot.ai");
Part of Arrhenius Plot for Reaction Kinetics on anyplot.ai.