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: pygal 3.1.3 | Python 3.13.14
Quality: 87/100 | Updated: 2026-06-24
"""
import os
import re
import sys
# Script filename shadows the installed 'pygal' package when run as 'python pygal.py';
# dropping the script directory from sys.path lets the real package resolve.
sys.path.pop(0)
import cairosvg
import numpy as np
import pygal
from pygal.style import Style
from scipy import stats
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint palette — canonical positions 1→8, first series always #009E73
IMPRINT_PALETTE = (
"#009E73", # brand green — position 1
"#C475FD", # lavender — position 2
"#4467A3", # blue — position 3
"#BD8233", # ochre — position 4
"#AE3030", # matte red — position 5
"#2ABCCD", # cyan — position 6
"#954477", # rose — position 7
"#99B314", # lime — position 8
)
# Data — first-order decomposition reaction rate constants spanning 300–600 K
temperature_K = np.array([300, 330, 360, 400, 440, 480, 520, 560, 600])
np.random.seed(42)
activation_energy = 75000 # J/mol (75 kJ/mol)
R = 8.314 # gas constant J/(mol·K)
pre_exponential = 1.0e12 # s⁻¹
rate_constant_k = pre_exponential * np.exp(-activation_energy / (R * temperature_K))
rate_constant_k *= np.exp(np.random.normal(0, 0.25, len(temperature_K)))
# Arrhenius transformed coordinates
inv_T = 1000.0 / temperature_K # 1000/T (×10⁻³ K⁻¹) for readable x-axis
ln_k = np.log(rate_constant_k)
# Linear regression: ln(k) = ln(A) − Ea/R × (1/T)
slope, intercept, r_value, p_value, std_err = stats.linregress(inv_T, ln_k)
r_squared = r_value**2
Ea_extracted = -slope * R * 1000 # factor of 1000 accounts for the 1000/T scaling
# Smooth regression line — 80 points, slightly extended beyond data
x_pad = 0.04
inv_T_fit = np.linspace(float(min(inv_T)) - x_pad, float(max(inv_T)) + x_pad, 80)
ln_k_fit = slope * inv_T_fit + intercept
# Y-axis range tight to data
y_floor = int(np.floor(float(min(ln_k))))
y_ceil = int(np.ceil(float(max(ln_k))))
y_labels_list = list(range(y_floor, y_ceil + 1, 2))
if y_labels_list[-1] < y_ceil:
y_labels_list.append(y_ceil)
# Title fontsize — scaled from 67-char baseline (44 chars here, so ratio=1.0)
title = "line-arrhenius · python · pygal · anyplot.ai"
n = len(title)
ratio = 67 / n if n > 67 else 1.0
title_font_size = max(44, round(66 * ratio))
# Style — Imprint palette + theme-adaptive chrome
custom_style = Style(
background=PAGE_BG,
plot_background=PAGE_BG,
foreground=INK,
foreground_strong=INK,
foreground_subtle=INK_MUTED,
colors=IMPRINT_PALETTE,
title_font_size=title_font_size,
label_font_size=56,
major_label_font_size=44,
legend_font_size=44,
value_font_size=36,
stroke_width=2.5,
opacity=0.92,
opacity_hover=1.0,
title_font_family="sans-serif",
label_font_family="sans-serif",
major_label_font_family="sans-serif",
legend_font_family="sans-serif",
value_font_family="sans-serif",
)
# Chart — canonical 3200×1800 landscape canvas
chart = pygal.XY(
style=custom_style,
width=3200,
height=1800,
title=title,
x_title="1000/T (K⁻¹)",
y_title="ln(k)",
show_dots=True,
dots_size=12,
show_x_guides=False,
show_y_guides=True,
legend_at_bottom=True,
legend_at_bottom_columns=3,
legend_box_size=24,
truncate_legend=-1,
margin=40,
margin_top=70,
margin_bottom=140,
margin_left=140,
margin_right=60,
tooltip_fancy_mode=True,
tooltip_border_radius=8,
x_value_formatter=lambda x: f"{x:.2f}",
y_value_formatter=lambda y: f"{y:.1f}",
range=(y_floor - 0.5, y_ceil + 0.5),
xrange=(float(min(inv_T) - 0.1), float(max(inv_T) + 0.1)),
y_labels=y_labels_list,
y_labels_major_every=1,
print_values=False,
show_minor_x_labels=False,
css=[
"file://style.css",
"file://graph.css",
"inline:"
".axis > .line { stroke: transparent !important; } "
".plot .background { rx: 10; ry: 10; } "
".legends .legend text { font-weight: 500; } "
".title { font-weight: 600; letter-spacing: 1px; }",
],
)
# X-axis labels: 1000/T value with corresponding temperature in parentheses
x_label_temps = np.array([300, 360, 440, 520, 600])
x_label_positions = sorted(1000.0 / x_label_temps)
chart.x_labels = [float(x) for x in x_label_positions]
chart.x_labels_major = [float(x) for x in x_label_positions]
chart.x_label_rotation = 0
chart.x_value_formatter = lambda x: f"{x:.2f} ({int(round(1000.0 / x))} K)"
# Regression fit line — smooth, no dots
fit_points = [
{"value": (float(x), float(y)), "label": f"Fit: ln(k) = {slope:.2f} × (1000/T) + {intercept:.2f}"}
for x, y in zip(inv_T_fit, ln_k_fit, strict=False)
]
chart.add(
f"Linear Fit (R² = {r_squared:.3f})",
fit_points,
show_dots=False,
stroke_style={"width": 4, "linecap": "round", "linejoin": "round"},
)
# Experimental data points — ochre markers with rich tooltips
data_points = [
{"value": (float(x), float(y)), "label": f"T = {int(t)} K\nk = {k:.3e} s⁻¹\nln(k) = {y:.2f}\n1000/T = {x:.3f}"}
for x, y, t, k in zip(inv_T, ln_k, temperature_K, rate_constant_k, strict=False)
]
chart.add("Experimental Data", data_points, stroke=False, dots_size=16)
# Activation energy — visible dot + label at regression line midpoint
mid_x = float(np.median(inv_T))
mid_y = float(slope * mid_x + intercept)
ea_r = -slope * 1000 # Ea/R in K (accounts for 1000/T axis scaling)
chart.add(
f"Eₐ = {Ea_extracted / 1000:.1f} kJ/mol (Eₐ/R = {ea_r:.0f} K)",
[{"value": (mid_x, mid_y), "label": f"Eₐ/R = {ea_r:.0f} K"}],
dots_size=8,
stroke=False,
print_labels=True,
)
# Render SVG and inject Ea/R slope annotation as a text element on the chart
svg_bytes = chart.render()
svg_str = svg_bytes.decode("utf-8")
# Locate the annotation dot (dots_size=8 → r="8") and place label next to it
dot_match = re.search(r'<circle cx="([^"]+)" cy="([^"]+)" r="8"', svg_str)
if dot_match:
cx, cy = float(dot_match.group(1)), float(dot_match.group(2))
annotation = (
f'<text x="{cx + 70:.0f}" y="{cy - 90:.0f}" '
f'font-family="sans-serif" font-size="44" '
f'fill="{INK}" font-weight="500">'
f"Eₐ/R = {ea_r:.0f} K</text>"
)
svg_str = svg_str.replace("</svg>", annotation + "\n</svg>")
annotated_svg = svg_str.encode("utf-8")
cairosvg.svg2png(bytestring=annotated_svg, write_to=f"plot-{THEME}.png")
chart.render_to_file(f"plot-{THEME}.html")
Part of Arrhenius Plot for Reaction Kinetics on anyplot.ai.