DuckieDai Arrhenius Equation Python Program

chemistry · MIT License

Overview

Calculate an Arrhenius rate constant, a second-temperature rate constant, activation energy, or pre-exponential factor and show the rearrangement used.

Not calculator tested
Downloaded 37 times
Version 1.0.0
1837 bytes
Uses math

Download arrhEQ.py Read the source How to install

Before you run it

TI-84 Plus CE Python · No calculator OS or Python App version has been verified.
TI Connect CE .py transfer is the intended path; calculator OS, Python App, transfer, and execution have not yet been tested for this release
The Arrhenius model and a temperature-independent A and Ea are suitable over the interval.
The two-temperature form compares the same reaction mechanism.
Temperatures, rate constants, and A must be positive; entered Ea is nonnegative except a solved Ea may expose inconsistent data.

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Learn the math

How the Arrhenius equation works

The idea

Reactions go faster when it is hotter, because more molecules have enough energy to get over the activation barrier. The Arrhenius equation puts numbers on that.

A higher activation energy means a slower reaction and one that is more sensitive to temperature.

The formula

k = A*e^(-Ea/(R*T))

ln(k2/k1) = (Ea/R)*(1/T1 - 1/T2)

k: rate constant
A: pre-exponential (frequency) factor, same units as k
Ea: activation energy (kJ/mol)
R: 8.314 J/mol K, built in
T: temperature in kelvin

Using the program

1 finds k from A, Ea, and T.
2 finds the rate constant at a second temperature. 3 finds Ea from two rate constants. 4 finds A.
Press Enter at the end for a quick reference screen.

Worked example

A reaction has A = 1 x 10^13 and Ea = 75 kJ/mol. At 298 K, choose 1 and enter 1e13, 75, and 298.

k = 1e13 x e^(-75000/(8.314 x 298))

The program shows k = 0.713 (it prints more decimal places).

Tips and common mistakes

Enter Ea in kJ/mol. The program converts it to joules.
Type powers of ten with e: 1e13 means 1 x 10^13.
A catalyst lowers Ea. It does not change the temperature dependence of the uncatalyzed path.

Where this comes up

It belongs to the chemical kinetics unit of general chemistry and physical chemistry. Lab reports often use the two-temperature form to find an activation energy from measured rates.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

from math import exp,log

R=8.314

def duckiedai_intro(program_name,wait=True):
 title=program_name[:16]
 empty=16-len(title)
 left=empty//2
 right=empty-left
 print("+----------------------+")
 print("|   "+" "*left+title+" "*right+"   |")
 print("|                      |")
 print("|       __             |")
 print("|   ___(o )>  quack!   |")
 print("|   \\ <_. )           |")
 print("|    `---'             |")
 print("|     by DuckieDai     |")
 print("+----------------------+")
 print("Loading...")
 if wait:
  input("Press enter to start ")
  print("\n"*6)

duckiedai_intro("ARRHENIUS")

def pos(s):
 while 1:
  try:
   x=float(input(s))
   if x>0:return x
  except:pass
  print("Enter a positive #")

def ea():
 while 1:
  try:
   x=float(input("Ea kJ/mol: "))
   if x>=0:return x
  except:pass
  print("Enter 0 or more")

print("ARRHENIUS EQ")
print("1 Find k")
print("2 Find k2")
print("3 Find Ea")
print("4 Find A")
c=""
while c not in ("1","2","3","4"):
 c=input("Choose 1-4: ")

if c=="1":
 a=pos("A: ")
 e=ea()*1000
 t=pos("Temp K: ")
 try:
  k=a*exp(-e/(R*t))
  print("k =",k)
 except OverflowError:print("k too large")

elif c=="2":
 k1=pos("k1: ")
 e=ea()*1000
 t1=pos("T1 K: ")
 t2=pos("T2 K: ")
 try:
  k2=k1*exp((-e/R)*(1/t2-1/t1))
  print("k2 =",k2)
 except OverflowError:print("k2 too large")

elif c=="3":
 k1=pos("k1: ")
 k2=pos("k2: ")
 t1=pos("T1 K: ")
 t2=pos("T2 K: ")
 if t1==t2:print("T1 and T2 differ")
 else:print("Ea kJ/mol =",-R*log(k2/k1)/(1/t2-1/t1)/1000)

else:
 k=pos("k: ")
 e=ea()*1000
 t=pos("Temp K: ")
 try:
  print("A =",k*exp(e/(R*t)))
 except OverflowError:print("A too large")

input("ENTER for guide: ")
print("QUICK GUIDE")
print("Higher T: larger k")
print("Higher Ea: smaller k")
print("Catalyst lowers Ea")
print("R=8.314 J/mol K")
print("DuckieDai: done!")
input("ENTER to exit: ")

from math import exp,log
R=8.314
def duckiedai_intro(program_name,wait=True):
title=program_name[:16]
empty=16-len(title)
left=empty//2
right=empty-left
print("+----------------------+")
print("| "+" "*left+title+" "*right+" |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n"*6)
duckiedai_intro("ARRHENIUS")
def pos(s):
while 1:
try:
x=float(input(s))
if x>0:return x
except:pass
print("Enter a positive #")
def ea():
while 1:
try:
x=float(input("Ea kJ/mol: "))
if x>=0:return x
except:pass
print("Enter 0 or more")
print("ARRHENIUS EQ")
print("1 Find k")
print("2 Find k2")
print("3 Find Ea")
print("4 Find A")
c=""
while c not in ("1","2","3","4"):
c=input("Choose 1-4: ")
if c=="1":
a=pos("A: ")
e=ea()*1000
t=pos("Temp K: ")
try:
k=a*exp(-e/(R*t))
print("k =",k)
except OverflowError:print("k too large")
elif c=="2":
k1=pos("k1: ")
e=ea()*1000
t1=pos("T1 K: ")
t2=pos("T2 K: ")
try:
k2=k1*exp((-e/R)*(1/t2-1/t1))
print("k2 =",k2)
except OverflowError:print("k2 too large")
elif c=="3":
k1=pos("k1: ")
k2=pos("k2: ")
t1=pos("T1 K: ")
t2=pos("T2 K: ")
if t1==t2:print("T1 and T2 differ")
else:print("Ea kJ/mol =",-R*log(k2/k1)/(1/t2-1/t1)/1000)
else:
k=pos("k: ")
e=ea()*1000
t=pos("Temp K: ")
try:
print("A =",k*exp(e/(R*t)))
except OverflowError:print("A too large")
input("ENTER for guide: ")
print("QUICK GUIDE")
print("Higher T: larger k")
print("Higher Ea: smaller k")
print("Catalyst lowers Ea")
print("R=8.314 J/mol K")
print("DuckieDai: done!")
input("ENTER to exit: ")

Filename: arrhEQ.py
Size: 1837 bytes
SHA-256: 6ab61f3be9266dd9123bc38a0f3309fcb6150a5b8a36391c5307b6cffa24a245

Usage

Inputs

Solve mode: k, k2, Ea, or A
Positive rate constants and absolute temperatures as required
Activation energy in kJ/mol; pre-exponential factor in the same rate units as k

Outputs

Requested rate quantity, activation energy, or pre-exponential factor
Exponent or rate ratio where the interactive mode provides it

Units: Temperature is kelvin, activation energy is kJ/mol, R is 8.314 J/(mol*K), and A and k use matching rate units.

Assumptions and limitations

Assumptions

The Arrhenius model and a temperature-independent A and Ea are suitable over the interval.
The two-temperature form compares the same reaction mechanism.

Constraints

Temperatures, rate constants, and A must be positive; entered Ea is nonnegative except a solved Ea may expose inconsistent data.

Known failures

Extreme exponents can overflow or underflow floating-point display.
A mechanism change or non-Arrhenius behavior can make the model misleading.

Compatibility and review

Review status: Not calculator tested
Tested on: The owner reports personally testing the supplied archive programs on a calculator; exact model, OS, and Python App versions were not recorded
What happened: Owner reported interactive testing is disclosed, but the published bytes are not labeled independently calculator tested because the environment is unrecorded and Arrhenius received a narrow intake correction
Dependencies: math
Suggested calculator name: ARRHEQ — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as ARRHEQ or another name, then open the Python App and try the worked example on this page first. This release has no verified calculator OS or Python App version; treat transfer and execution as unverified until independently tested.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

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