beer lambert law

[proteinz]

hi all im using the beer law to find my protein's concentration at A280.
c= A/(epsilon)(c)
i have found a paper which says the concentration of CS was determined using molar absorption coefficent of 1.78 for a 1mg/ml solution. WHAT DOES THIS 1MG/ML SOLUTION MEAN. IS BELOW CORRECT

is this correct then i found A280 = 1.157

c= 1.157/ 1.78(1)
c= 0.65M

my stock is therefore 0.65M concentration.

[blcr11]

The stated coefficient is in the wrong units to be a molar absorptivity (or molar extinction coefficient). That would be in units of A per M (per 1 cm pathlength, but a 1 cm pathlength is usually assumed). If I understand what you said, a 1 mg/ml solution (in a 1 cm pathlength) has an A280 of 1.78 (epsilon = 1.78 A280/1mg/ml/cm), and that will be the extinction coefficient, but not the molar extinction coefficient. You’ve used the coefficient correctly, but the concentration will be 0.65 mg/ml, not M.

[jonmoulton]

Your units are not correct based on the given information.

First, the Beer's law equation is A=c(epsilon)l. I assume that you have a 1cm light path length through your cuvette and that your figure for epsilon (the absorbance of a 1 mg/ml solution) is calibrated for a 1 cm path length and so epsilon has units of (mg/ml)^-1 cm^-1. Watch out, you were not given the molar absorption coefficient! Instead, you were given an absorbance in units of mg/ml.

Solving for c (the concentration) gives:

c=A/(epsilon * l)

For your setup,
A = 1.157
epsilon = 1.78 (mg/ml)^-1 cm^-1 (I must assume that was measured in the same solvent systemyou are using and at 280 nm, but you should check)
l = 1 cm

c = A/(epsilon * l) = 1.157/(1.78 * 1) = 0.65 mg/ml

For units, note that A has no units (dimensionless), epsilon is in (mg/ml)^-1 cm^-1 and l is in cm. Plug these into the Beer's law eq'n: c=A/(epsilon * l)
The cm unit cancels, so the units of the concentration are 1/(mg/ml)^-1 = mg/ml

If you need the result as a molarity, you will need to get the molecular mass of the protein you are measuring and convert mg/ml to moles/l.

[proteinz]

thanks so much guys! you've cleared it up completely.
have a nice day!