Question

If a 10 mM solution of a biomolecule in a cuvette of path length 10 mm absorbs 90% of the incident light at 280 nm, the molar extinction coefficient of the biomolecule at this wavelength is _______ M(^{-1})cm(^{-1}). (Round off to two decimal places)

Hint:

When working with Beer-Lambert Law, ensure to convert all units properly; specifically, path length should be in centimeters for standard calculations.

Answer 1

To find the molar extinction coefficient, \( \epsilon \), we use the Beer-Lambert Law: \[ A = \epsilon \cdot c \cdot l \]

Where:

• \( A \) is the absorbance.
• \( \epsilon \) is the molar extinction coefficient.
• \( c \) is the concentration in molarity.
• \( l \) is the path length in centimeters.

Step 1: Calculating Absorbance.

Given that 90% of the incident light is absorbed, the absorbance \( A \) can be calculated using:

\[ A = -\log(1 - 0.90) = -\log(0.10) = 1 \] Step 2: Given Parameters.

• Concentration: \( c = 10 \) mM = \( 0.01 \) M
• Path length: \( l = 10 \) mm = \( 1 \) cm

Step 3: Substituting into Beer-Lambert Law. \[ 1 = \epsilon \cdot 0.01 \cdot 1 \] \[ \epsilon = \frac{1}{0.01} = 100 \, \text{M}^{-1} \text{cm}^{-1} \] Conclusion:

Therefore, the molar extinction coefficient is approximately \( 100 \, \text{M}^{-1} \text{cm}^{-1} \), with reasonable estimates between 98 and 102 \( \text{M}^{-1} \text{cm}^{-1} \) based on rounding and experimental considerations.