The extinction coefficient for NADH is 6220 M^-1 cm^-1 at 340 nm. Calculate the following.
a. The absorbance of a 2.2 times 10^-5 M sample in a 1-cm cuvette at 340 nm
b. The absorbance of a 2.2 times 10^-5 M sample in a 1-mm cuvette at 340 nm
c. The absorbance of a 1 mM sample in a 1-cm cuvette at 340 nm
The Correct Answer and Explanation is :
The absorbance of a solution is calculated using Beer-Lambert Law:
[
A = \varepsilon \cdot c \cdot l
]
Where:
- ( A ) is the absorbance
- ( \varepsilon ) is the molar extinction coefficient (given as 6220 M(^{-1}) cm(^{-1}) at 340 nm)
- ( c ) is the concentration of the solution in moles per liter (M)
- ( l ) is the path length of the cuvette in centimeters (cm)
a. The absorbance of a 2.2 × 10(^{-5}) M sample in a 1-cm cuvette at 340 nm:
We can substitute the known values into the Beer-Lambert equation:
- ( \varepsilon = 6220 \, \text{M}^{-1} \, \text{cm}^{-1} )
- ( c = 2.2 \times 10^{-5} \, \text{M} )
- ( l = 1 \, \text{cm} )
Substitute into the equation:
[
A = 6220 \cdot (2.2 \times 10^{-5}) \cdot 1
]
[
A = 0.137 \, \text{(no units)}
]
Thus, the absorbance is 0.137.
b. The absorbance of a 2.2 × 10(^{-5}) M sample in a 1-mm cuvette at 340 nm:
For this case, the path length ( l = 1 \, \text{mm} = 0.1 \, \text{cm} ).
Now, substitute the values into the Beer-Lambert equation:
[
A = 6220 \cdot (2.2 \times 10^{-5}) \cdot 0.1
]
[
A = 0.0137
]
Thus, the absorbance is 0.0137.
c. The absorbance of a 1 mM sample in a 1-cm cuvette at 340 nm:
Here, the concentration ( c = 1 \, \text{mM} = 1 \times 10^{-3} \, \text{M} ), and the path length remains ( l = 1 \, \text{cm} ).
Substitute the values:
[
A = 6220 \cdot (1 \times 10^{-3}) \cdot 1
]
[
A = 6.22
]
Thus, the absorbance is 6.22.
Explanation:
- In all calculations, the relationship between absorbance, concentration, path length, and the extinction coefficient is fundamental. A higher concentration and a longer path length result in a higher absorbance.
- The extinction coefficient (( \varepsilon )) is a constant for a given substance at a specific wavelength, indicating how strongly the substance absorbs light at that wavelength.
- The path length (( l )) is the distance that light travels through the sample, and typically the longer the path length, the more light will be absorbed.
- The molar concentration (( c )) directly affects absorbance; higher concentration increases absorbance.
In practice, these calculations help in determining concentrations of substances based on the amount of light absorbed at a specific wavelength.