Question

Beer’s law states that $ {\text{A = abc}} $ , where A is absorbance, a is the molar absorptivity constant, b is the path length and c is the molar concentration. Which of the following would be an incorrect application for the beer’s laws?
(A) The path length is irreverent, as long as it is inversely proportional to molar concentration when determining the concentration of unknown as compared to a standard curve.
(B) The molar concentration is directly related to absorption of light by the sample and is used to develop a standard curve.
(C) The concentration of an unknown sample can be easily determined from a standard curve of known concentration plotted against absorbance for a fixed path length.
(D) The use of Beer’s law and spectrophotometer for a colored sample is a better method of determining molar concentration than visual comparison.

Answer 1

Hint: In the above question, the definition of beer’s law is given. We have to find out the invalid application of beer’s law. Beer’s law is the direct relationship between absorbance and molar absorptivity constant or path length or molar concentration.

Complete step by step solution
Let us first elaborate Beer’s law:
Beer’s law states that $ {\text{A = abc}} $ , where A is absorbance, a is the molar absorptivity constant, b is the path length and c is the molar concentration. Beer's law stated that the transmittance of a solution remains constant if the product of concentration and path length stays constant.
Option a:
A standard curve is plotted when axes contain concentration and absorbance. The path length is always relevant so that we can easily find out molar absorptivity constant from the graph and Beer’s Law. So, this option is inappropriate which states that path is irrelevant.
Option b:
A standard curve is obtained between concentration and absorption of light of the curve and a straight line is obtained. So, this option is a correction application of Beer’s law which states that the molar concentration is directly related to absorption of light by the sample and is used to develop a standard curve.
Option c:
Since a graph is plotted between absorbance and concentration. So, for an unknown sample’s concentration can be obtained from the graph. Hence, this option is the correct application.
Option d:
The results obtained from Beer’s law are more accurate and hence, the use of Beer’s law and spectrophotometer for a colored sample is a better method of determining molar concentration than visual comparison. So, this is also a correct explanation.
Since, the only option is an inappropriate application of beer’s law.
So, the correct option is option A.

Note
-Beer’s law tends to break down at very high concentrations, especially if the material is highly scattering.
-Beer’s law is applicable only when absorbance is within the range of $ 0.2{\text{ to }}0.5 $ .