Calculating Absorbance Values from Percent Transmission
To calculate absorbance values from percent transmission (%T), use the formula A = -log(T), where T is the decimal form of %T (divide %T by 100). 1
Absorbance Calculation Formula
The Beer-Lambert law relates absorbance to transmittance through the following equation:
A = -log₁₀(T) = -log₁₀(%T/100)
Where:
- A = Absorbance (no units)
- T = Transmittance (decimal form)
- %T = Percent Transmission
Calculations for the Given Values
Let's calculate the absorbance values for each of the provided %T values:
a. 34%T
T = 34/100 = 0.34 A = -log₁₀(0.34) = 0.4685 Absorbance = 0.47 (rounded to 2 decimal places)
b. 78%T
T = 78/100 = 0.78 A = -log₁₀(0.78) = 0.1079 Absorbance = 0.11 (rounded to 2 decimal places)
c. 21%T
T = 21/100 = 0.21 A = -log₁₀(0.21) = 0.6778 Absorbance = 0.68 (rounded to 2 decimal places)
Understanding the Relationship Between Transmission and Absorbance
The relationship between transmission and absorbance is inverse and logarithmic:
- Higher %T values indicate that more light is passing through the sample (less absorption)
- Lower %T values indicate that less light is passing through the sample (more absorption)
- Absorbance values typically range from 0 (100% transmission) to 2 (1% transmission)
Applications in Spectrophotometry
This calculation is fundamental in spectrophotometric analyses used in:
- Quantification of compounds in solution
- Enzyme activity measurements 1
- Determination of protein concentrations
- Analysis of drug concentrations
Common Pitfalls to Avoid
- Remember that absorbance has no units
- Ensure %T is converted to decimal form before calculating absorbance
- For accurate measurements, absorbance values should ideally fall between 0.1 and 1.0, as values outside this range may have higher measurement error
- Always calibrate spectrophotometers properly before taking measurements to ensure accuracy
The Beer-Lambert law (A = εcl) can be used to determine concentration once absorbance is known, where ε is the molar absorptivity coefficient, c is concentration, and l is path length 1.