The absorbance of a protein solution measured in a 1.0 cm cuvette at 278 nm was 1.145. The protein content of that solution, calculated from quantitative amino acid analysis, was 256 micrograms/mL. Calculate the extinction coefficient of the protein in unitsbof mL/mg/cm. Assume that the molecular mass of the protein was 13,000. Calculate the molar extinction coefficient.
To calculate the extinction coefficient of the protein in units of mL/mg/cm, you can use the following formula:
Extinction Coefficient (ε) = (Absorbance / Path Length) / Protein Concentration
Given:
Absorbance (A) = 1.145
Path Length (b) = 1.0 cm
Protein Concentration (C) = 256 μg/mL
First, convert the protein concentration from micrograms/mL to mg/mL:
Protein Concentration (C) = 256 μg/mL * 0.001 mg/μg = 0.256 mg/mL
Now, you can calculate the extinction coefficient:
Extinction Coefficient (ε) = (1.145 / 1.0) / 0.256 = 4.472 mL/mg/cm
To calculate the molar extinction coefficient, you need to account for the molecular mass of the protein:
Molar Extinction Coefficient (ε') = Extinction Coefficient (ε) * Molecular Mass
Given:
Molecular Mass (M) = 13,000
Molar Extinction Coefficient (ε') = 4.472 mL/mg/cm * 13,000 mg/mol = 58,136 mL/mol/cm
Therefore, the extinction coefficient of the protein in units of mL/mg/cm is 4.472 mL/mg/cm, and the molar extinction coefficient is 58,136 mL/mol/cm.
To calculate the extinction coefficient of the protein in units of mL/mg/cm, you can use the Beer-Lambert Law, which states that absorbance (A) is proportional to the concentration (C) of the absorbing species and the path length (L) of the cuvette.
The formula is given as:
A = ε * C * L
Where:
A = Absorbance
ε = Extinction coefficient
C = Concentration
L = Path length
Now let's solve the problem step by step:
Step 1: Calculate the concentration of the protein in mg/mL.
The protein content given is in micrograms/mL, so we need to convert it to milligrams/mL. Since 1 microgram (μg) is equal to 0.001 milligrams (mg), we can convert as follows:
256 μg/mL = 256 * 0.001 mg/mL = 0.256 mg/mL
Step 2: Calculate the concentration of the protein in Molarity (M).
To calculate the molar concentration, we need to convert the concentration in mg/mL to molarity (mol/L). To do this, we need the molecular mass and assume the protein is composed of one peptide chain.
Given:
Concentration in mg/mL = 0.256 mg/mL
Molecular mass of the protein = 13,000
We can use the following formula:
Concentration M (mol/L) = (Concentration mg/mL) / (Molecular Mass g/mol)
Concentration M = (0.256 mg/mL) / (13,000 g/mol)
Note: We convert mg to g by dividing by 1000.
Concentration M = 0.256 / (13,000 * 1000) mol/L = 1.966e-8 mol/L
Step 3: Calculate the path length in cm.
Given: Path length = 1.0 cm
Step 4: Calculate the extinction coefficient (ε) in units of mL/mg/cm.
We rearrange the Beer-Lambert Law formula to solve for the extinction coefficient (ε):
ε = A / (C * L)
Given:
Absorbance (A) = 1.145
Concentration (C) = 0.256 mg/mL
Path length (L) = 1.0 cm
ε = 1.145 / (0.256 * 1.0) = 4.480 mL/mg/cm
So, the extinction coefficient of the protein is 4.480 mL/mg/cm.
Step 5: Calculate the molar extinction coefficient (ε) in units of M-1 cm-1.
To convert the extinction coefficient from mL/mg/cm to M-1 cm-1, we need to divide it by the molecular mass in g/mol.
Given:
Molecular mass of the protein = 13,000 g/mol
Molar Extinction Coefficient = ε / Molecular mass
Molar Extinction Coefficient = 4.480 mL/mg/cm / 13,000 g/mol
Note: We convert mL to L by dividing by 1000 and mg to g by dividing by 1000.
Molar Extinction Coefficient ≈ 4.480 / (13,000 * 1000) M-1 cm-1 ≈ 3.446e-7 M-1 cm-1
So, the molar extinction coefficient of the protein is approximately 3.446e-7 M-1 cm-1.