Question

Strain, Thomas and Katz measured the molar absorptivity of chlorophyll a in 1963 and obtained a value of 111700.0 ± 0.4 liter/cm-mole at 427.75 nm. Calculate the concentration of a solution which exhibits an absorbance of 3.267 ± 0.003 in a 10.004 ± 0.002 cm path length cell. It should be obvious that you must propagate the uncertainty onto your final result.

Answer 1

Beer-Lambert's Law is expressed as

A = c l

Where

A = Absorbance = 3.267 ± 0.003

= Molar absorptivity = (111700.0 ± 0.4) liter/cm-mole

c = concentration = ?

l = path length = (10.004 ± 0.002) cm

So,

(3.267 ± 0.003) = (111700.0 ± 0.4) liter/cm-mole * c *  (10.004 ± 0.002) cm

c = (3.267 ± 0.003) / [ (111700.0 ± 0.4) x (10.004 ± 0.002) ] liter/mole

= (3.267 ± 0.09%) / [ (111700.0 ± 0.0004%) x (10.004 ± 0.02%) ] liter/mole

= (3.267 ± 0.09%) / (1117446.8 ± 0.0204%) liter/mole

= (0.0000029 ± 0.1104%) mole/liter

= (0.0000029 ± 0.0000000032) mole/liter

= (2.9 x 10^-6) ± (3.2 x 10^-9) mole/liter