# Concentration from Absorbance vs Time

I am given a protein, BAPNA, and the initial concentration of the protein. The experiment involves reaction rates of varying protein concentrations. Each sample cuvette is inserted into a spectrometer, 100% transmittance is set, has the enzyme inserted, and then has transmittance measured every 20 s for 600 s.

I understand absorbance is given as: $A = 2 - \log (T\%)$ and that's no issue.

The problem I run into is trying to solve for the concentration or molar extinction constant. I understand that Beer-Lambert law, $A = \epsilon bc$ is used for this purpose. The only given concentration is the initial concentration. Assuming $b = 1$, we can solve for $\epsilon$ or $c$, but having 100% set in the beginning causes $A = 0$, meaning initially $\epsilon = 0$ if $c \neq 0$.

This is where my calculations run into a dead end. I'm not given $\epsilon$ or concentration at any other point, but I'm supposed to be able to calculate the final concentration and maximum reaction rate. I've only a set of transmittance numbers over time, and that initial concentration.

Is there something I am misunderstanding or not seeing?

The only given concentration is the initial concentration [...]

Unless there is a major misunderstanding on my side, you have all the data you need.

Given the initial concentration $c_0$ and knowing the path length $d$ of your cuvette, you measure the extinction $E$ at this point and use - as you have correctly stated in your question - the Lambert-Beer law to calculate the molar extinction coefficient $\epsilon$.

$$E = \epsilon\cdot c\cdot d$$ $$\epsilon = \frac{E}{c\cdot d}$$

Did I mention units? Units are your friend!

• Write the Lambert-Beer law with units!

• Percent (%) is NOT a proper unit for the initial concentration of your protein.

but I'm supposed to be able to calculate the final concentration and maximum reaction rate

Having determined $\epsilon$, you can now correlate at any point along your reaction the measured extinction with the actual concentration of your sample, including the final concentration.

From the slope of the curve of extinction $E\$ vs concentration $c$, the rate of your reaction can be obtained.

If the relation is not a straight line, logarithms are your friend.

• The problem I run into is that the experimental procedures do not call for a measurement of Extinction before the enzyme is added. Transmittance is set to 100 at that point, giving Extinction = 0. The equation becomes unsolvable at that point. – Ray N. Mar 25 '14 at 23:02