DuckieDai Beer-Lambert Law Python Program

chemistry · MIT License

Overview

Solve A = epsilon*c*l and convert between absorbance and transmittance while keeping units and model limits visible.

Not calculator tested
Downloaded 34 times
Version 1.0.0
2111 bytes
Uses math

Download beer.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 sample is homogeneous and follows a linear Beer-Lambert response at the selected wavelength.
Scattering, stray light, chemical equilibria, and instrument effects are negligible.
Divisors and intensity values must be positive; A, epsilon, and concentration are nonnegative in the primary solve modes.

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Learn the math

How the Beer-Lambert law works

The idea

A colored solution absorbs more light when it is more concentrated or when the light travels further through it. Absorbance is directly proportional to both.

That straight-line relationship is how a spectrophotometer turns a light reading into a concentration.

The formula

A = epsilon*c*l

A = -log10(I/I0)

A: absorbance (no units)
epsilon: molar absorptivity (L/mol cm)
c: concentration (mol/L)
l: path length (cm)
I/I0: fraction of light transmitted

Using the program

1 finds absorbance. 2 finds concentration. 3 finds epsilon. 4 finds path length.
5 converts transmitted light to absorbance. 6 converts absorbance back to transmitted light.

Worked example

NADH has epsilon = 6220 L/mol cm at 340 nm. For a 0.0001 mol/L solution in a 1 cm cuvette, choose 1 and enter 6220, 0.0001, and 1.

A = 6220 x 0.0001 x 1

The program shows A = 0.622.

Tips and common mistakes

Path length is in centimeters. A standard cuvette is 1 cm.
The law holds for dilute solutions. Above an absorbance of about 1 to 2, readings stop being linear.
An absorbance of 1 means 10% of the light gets through; 2 means 1%.

Where this comes up

It is used in every spectrophotometry lab, from general chemistry to biochemistry and analytical chemistry, to turn an absorbance reading into a concentration or to build a calibration line.

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 log

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)

def num(s,zero=0):
 while 1:
  try:
   x=float(input(s))
   if x>0 or zero and x>=0:return x
  except:pass
  print("Enter a valid #")

def ratio():
 while 1:
  x=num("I/I0: ")
  if x<=1:return x
  print("I/I0 must be <=1")

duckiedai_intro("BEER LAMBERT")
print("BEER-LAMBERT LAW")
print("1 Find A")
print("2 Find conc")
print("3 Find epsilon")
print("4 Find path")
print("5 A from I/I0")
print("6 Light from A")
c=""
while c not in ("1","2","3","4","5","6"):
 c=input("Choose 1-6: ")

if c=="1":
 e=num("epsilon: ",1)
 x=num("Conc mol/L: ",1)
 l=num("Path cm: ")
 a=e*x*l
 print("A =",a)

elif c=="2":
 a=num("Absorbance A: ",1)
 e=num("epsilon: ")
 l=num("Path cm: ")
 print("Conc mol/L =",a/(e*l))

elif c=="3":
 a=num("Absorbance A: ",1)
 x=num("Conc mol/L: ")
 l=num("Path cm: ")
 print("epsilon =",a/(x*l))
 print("L/(mol*cm)")

elif c=="4":
 a=num("Absorbance A: ",1)
 e=num("epsilon: ")
 x=num("Conc mol/L: ")
 print("Path cm =",a/(e*x))

elif c=="5":
 print("1 Enter I and I0")
 print("2 Enter I/I0")
 q=""
 while q not in ("1","2"):
  q=input("Choose 1 or 2: ")
 if q=="1":
  i0=num("I0: ")
  i=num("I: ")
  r=i/i0
 else:r=ratio()
 print("A =",-log(r,10))
 print("I/I0 =",r)
 print("%T =",r*100)

else:
 a=num("Absorbance A: ",1)
 r=10**(-a)
 print("I/I0 =",r)
 print("%T =",r*100)
 q=input("Find I? 1=yes: ")
 if q=="1":print("I =",num("I0: ")*r)

input("ENTER for guide: ")
print("QUICK GUIDE")
print("A=epsilon*c*l")
print("A=-log(I/I0)")
print("Higher A: less light")
print("A has no units")
print("DuckieDai: done!")
input("ENTER to exit: ")

from math import log
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)
def num(s,zero=0):
while 1:
try:
x=float(input(s))
if x>0 or zero and x>=0:return x
except:pass
print("Enter a valid #")
def ratio():
while 1:
x=num("I/I0: ")
if x<=1:return x
print("I/I0 must be <=1")
duckiedai_intro("BEER LAMBERT")
print("BEER-LAMBERT LAW")
print("1 Find A")
print("2 Find conc")
print("3 Find epsilon")
print("4 Find path")
print("5 A from I/I0")
print("6 Light from A")
c=""
while c not in ("1","2","3","4","5","6"):
c=input("Choose 1-6: ")
if c=="1":
e=num("epsilon: ",1)
x=num("Conc mol/L: ",1)
l=num("Path cm: ")
a=e*x*l
print("A =",a)
elif c=="2":
a=num("Absorbance A: ",1)
e=num("epsilon: ")
l=num("Path cm: ")
print("Conc mol/L =",a/(e*l))
elif c=="3":
a=num("Absorbance A: ",1)
x=num("Conc mol/L: ")
l=num("Path cm: ")
print("epsilon =",a/(x*l))
print("L/(mol*cm)")
elif c=="4":
a=num("Absorbance A: ",1)
e=num("epsilon: ")
x=num("Conc mol/L: ")
print("Path cm =",a/(e*x))
elif c=="5":
print("1 Enter I and I0")
print("2 Enter I/I0")
q=""
while q not in ("1","2"):
q=input("Choose 1 or 2: ")
if q=="1":
i0=num("I0: ")
i=num("I: ")
r=i/i0
else:r=ratio()
print("A =",-log(r,10))
print("I/I0 =",r)
print("%T =",r*100)
else:
a=num("Absorbance A: ",1)
r=10**(-a)
print("I/I0 =",r)
print("%T =",r*100)
q=input("Find I? 1=yes: ")
if q=="1":print("I =",num("I0: ")*r)
input("ENTER for guide: ")
print("QUICK GUIDE")
print("A=epsilon*c*l")
print("A=-log(I/I0)")
print("Higher A: less light")
print("A has no units")
print("DuckieDai: done!")
input("ENTER to exit: ")

Filename: beer.py
Size: 2111 bytes
SHA-256: f83924f329db3a636204ccf0d19041002cb6e5d0a4b25a420d766df22c4596cf

Usage

Inputs

Solve mode and the required absorbance, molar absorptivity, concentration, or path length
Incident and transmitted intensity, or their dimensionless ratio

Outputs

Absorbance, concentration, molar absorptivity, path length, transmittance ratio, or percent transmittance

Units: A is dimensionless; epsilon uses L/(mol*cm), c uses mol/L, and l uses cm. I and I0 must use the same intensity unit.

Assumptions and limitations

Assumptions

The sample is homogeneous and follows a linear Beer-Lambert response at the selected wavelength.
Scattering, stray light, chemical equilibria, and instrument effects are negligible.

Constraints

Divisors and intensity values must be positive; A, epsilon, and concentration are nonnegative in the primary solve modes.

Known failures

I greater than I0 gives negative absorbance and usually indicates a baseline, reference, or measurement issue.
High concentration or high absorbance can depart from linear behavior.

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: BEER — 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 BEER 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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