Question

If a 100 $\mu$M solution of NADH exhibits an absorbance of 0.62 at a wavelength of 340 nm in a 1 cm cell, then its molar extinction coefficient would be equal to:

• A. 6.2 $\text{cm}^2\text{ mol}^{-1}$
• B. $6.2 \times 10^2\text{ cm}^2\text{ mol}^{-1}$
• C. $6.2 \times 10^4\text{ cm}^2\text{ mol}^{-1}$
• D. $6.2 \times 10^6\text{ cm}^2\text{ mol}^{-1}$

Hint:

To convert the molar extinction coefficient from standard units ($\text{L mol}^{-1}\text{ cm}^{-1}$) to $\text{cm}^2\text{ mol}^{-1}$, multiply the value by $1000$.
For NADH at $340\text{ nm}$, $\epsilon \approx 6200\text{ L mol}^{-1}\text{ cm}^{-1} = 6.2 \times 10^6\text{ cm}^2\text{ mol}^{-1}$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Beer-Lambert Law relates the absorption of light by a substance to its concentration and the path length of the sample cell.
The molar extinction coefficient ($\epsilon$) is a constant that measures how strongly a substance absorbs light at a given wavelength.
Key Formula or Approach:
The Beer-Lambert Law is expressed as:
\[ A = \epsilon \cdot c \cdot l \]
where $A$ is absorbance (dimensionless), $\epsilon$ is the molar extinction coefficient, $c$ is the concentration of the absorbing solute, and $l$ is the path length of the cell ($1\text{ cm}$).
Rearranging to solve for the extinction coefficient:
\[ \epsilon = \frac{A}{c \cdot l} \]

Step 2: Detailed Explanation:
Given values from the problem:
Absorbance, $A = 0.62$.
Path length, $l = 1\text{ cm}$.
Concentration, $c = 100\text{ }\mu\text{M} = 100 \times 10^{-6}\text{ mol L}^{-1} = 10^{-4}\text{ mol L}^{-1}$.
First, let us calculate the extinction coefficient in standard biochemical units ($\text{L mol}^{-1}\text{ cm}^{-1}$):
\[ \epsilon = \frac{0.62}{10^{-4}\text{ mol L}^{-1} \times 1\text{ cm}} \]
\[ \epsilon = 0.62 \times 10^4\text{ L mol}^{-1}\text{ cm}^{-1} = 6200\text{ L mol}^{-1}\text{ cm}^{-1} \]
Next, we must convert liters ($\text{L}$) into cubic centimeters ($\text{cm}^3$) to match the units used in the options ($\text{cm}^2\text{ mol}^{-1}$):
Since $1\text{ Liter} = 1000\text{ cm}^3$:
\[ 1\text{ L mol}^{-1}\text{ cm}^{-1} = 1000\text{ cm}^3\text{ mol}^{-1}\text{ cm}^{-1} = 1000\text{ cm}^2\text{ mol}^{-1} \]
Now, substitute this conversion factor into our calculated value of $\epsilon$:
\[ \epsilon = 6200 \times 1000\text{ cm}^2\text{ mol}^{-1} \]
\[ \epsilon = 6.2 \times 10^6\text{ cm}^2\text{ mol}^{-1} \]
This value matches Option (D).

Step 3: Final Answer:
The molar extinction coefficient of NADH is $6.2 \times 10^6\text{ cm}^2\text{ mol}^{-1}$, which corresponds to Option (D).