If the calibration curve for a Beer's Law plot of a protein assay had a slope of 0.433 when absorb acne, A, was plotted as a function of protein concentration, c, in mg/mL. The absorbance of an unknown protein sample was 0.345. What is the concentration of protein in this sample in mg/mL?
To find the concentration of protein in the unknown sample, we can use the equation for Beer's Law:
A = εcl
Where A is the absorbance, ε is the molar absorptivity (also known as the slope of the calibration curve), c is the concentration of the protein, and l is the path length of the cuvette (which is typically 1 cm).
Plugging in the values we have:
0.345 = (0.433) * c * 1
To isolate the concentration, divide both sides of the equation by 0.433:
0.345 / 0.433 = c
Calculating this, we find that the concentration of protein in the sample is approximately 0.796 mg/mL.
To determine the concentration of protein in the unknown sample, we need to utilize Beer's Law equation, which is:
A = εlc,
where:
- A is the absorbance of the sample,
- ε is the molar absorptivity (slope of the calibration curve),
- l is the path length of the cuvette (usually 1 cm),
- c is the concentration of the sample.
From the question, we are given:
- The slope of the calibration curve (ε) = 0.433,
- The absorbance of the unknown sample (A) = 0.345.
Now, we rearrange the equation to solve for c:
c = A / (εl).
We substitute the given values into the equation:
c = 0.345 / (0.433 * 1).
Simplifying the equation gives us:
c = 0.345 / 0.433.
Using a calculator, we can now evaluate the expression:
c ≈ 0.797 mg/mL.
Therefore, the concentration of protein in the unknown sample is approximately 0.797 mg/mL.