Question

In spectrophotometry, if transmittance value of a solution is 75%, then its absorbance would be equal to:

• A. 0.125
• B. 0.301
• C. 0.602
• D. 0.699

Hint:

Remember that \( \log_{10}(2) \approx 0.3 \). If Transmittance is \( 50% \), Absorbance is \( 2 - 1.7 \approx 0.3 \). Because \( 75% \) transmittance allows more light through than \( 50% \), its absorbance must be lower than 0.3, which immediately points to 0.125.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Beer-Lambert law relates the absorption of light to the properties of the material through which the light is traveling. Absorbance (\(A\)) and Transmittance (\(T\)) are logarithmically related.
Key Formula or Approach:
The relationship between Absorbance (\(A\)) and percent Transmittance (\(%T\)) is:
\[ A = 2 - \log_{10}(%T) \]
Alternatively, using fractional transmittance (\(T\)):
\[ A = -\log_{10}(T) \]

Step 2: Detailed Explanation:
The given percent transmittance value is \(%T = 75%\).
Substituting this into our equation:
\[ A = 2 - \log_{10}(75) \]
Using base-10 logarithms:
\[ \log_{10}(75) \approx 1.875 \]
Now, calculate the absorbance:
\[ A = 2 - 1.875 = 0.125 \]

Step 3: Final Answer:
The absorbance value of the solution is approximately 0.125.