# Beer's law

1. Oct 27, 2008

### prize fight

1. The problem statement, all variables and given/known data
IF I=15.0 mW (s=0.29), I0=75.6 mW (s=0.64), b=1.00 (s=0.02) and c= 2.32*10^-3 (s=0.05*10^-3), what is the molar absorptivity for the absorbing species? Calculate the result, the absolute standard deviation, and the relative standard deviation in parts per thousand of the result.

2. Relevant equations

log(I0/I)=abc

Sx/x =SQRT((Sp/P)2+(Sq/q)2+(Sr/R)2

Sx=0.434(Sp/P)

RSD = S/x *10^x

3. The attempt at a solution

Result:
(75.6/15) = 5.04

log(75.6/15.0)= 0.702

a=0.702/(1.0*2.32*10^-3)=302.77

Standard Deviation:

STD of log(I0/I) = 0.434((SQRT(((0.64/75.6)^2)+((0.29/15.0)^2))/5.04))=0.013

STD of bc = SQRT(((0.02/1.0)^2)+((0.05*10^-3/2.32*10^-3)^2)) = 0.03

STD of a = SQRT(((0.013/0.702)^2)+((0.03/(2.32*10^-3))^2) = 12.67

I am not sure about the standard deviation of the molar absorptivity (a) or what value to use to calculate the relative standard deviation I know it is the standard deviation divided by the average, but value is the average.