absorbance of the sample at a wavelength
(a) A sample absorbs 80% of the light passed through it at a certain wavelength. What is the absorbance of the sample at this wavelength?
(b) What would the absorbance be at the same wavelength if the sample were diluted by half? Assume the same size sample cell was used.
The relationship between absorbance and percent transmittance is given by the following equation
Absorbance = -log (percent transmittance/100)
Since we are given the percent of light that is absorbed, we first must find the percent of light that was transmitted. If 80% was absorbed, then 20% was transmitted.
A = - log (20/100)
A = 0.70
If the sample were diluted to half the concentration (with the same path length), then the absorbance would also be reduced by half. There is a linear relationship between absorbance and concentration as given by Beer's Law
A = Elc
where A is the absorbance, E equals the molar absorptivity constant, l is the path length and c is the concentration.
Since E and l will be constants in this situation, if c is cut in half, then A will be reduced by half as well.