I've been given this biochemistry question, and I just keep getting the answer wrong and I don't know why. It would be great if someone could work through the calculation step by step to help me see where Im going wrong. here it is:
A 4-fold dilution of plasma is assayed spectrophotometrically for cholesterol. Given the following spectrophotometic data, what is the concentration of cholesterol in the diluted plasma in micromol/mL? (DO NOT INCLUDE THE UNITS IN YOUR ANSWER)
A500 standard = 0.77 A500 sample = 0.28 C (standard) = 3.9mM
Using spectrophotometry to determine the unknown concentration of a certain molecule requires Beer's Law: A = ecl
Where A is absorbance at a certain wavelength, c is the concentration of the molecule, and l is the path length. e is an empirically determined constant known as the molar absorptivity or molar extinction coefficient usually in the units of 1/M*cm.
We can calculate the molar extinction coefficient from the standard with the given information. In this case, we can substitute in A and c, and assume the path length is 1cm to make the math simple. Since both samples are measured in the same instrument, the path length should remain the same and will not make a different in the calculation because the values will just cancel out in the end. (You can try using different numbers for the path lengths below and you will get the same answer)
So for the standard, we have 0.77 = e x 0.0039M x 1cm. Solving for this equation gives e = 197.4 (in units of 1/M*cm)
Now that we have e, we can calculate the concentration of cholesterol in the unknown sample by using e found from the standard the absorbance value found for the plasma sample, which will be 0.28 = 197.4 (1/M*cm) x c x 1cm. Solving for this equation gives 0.00142M, which is equivalent to 1.42 micromol per ml. The conversions are 10^6 micromol to 1 mol, and 10^3 ml to 1 L.