when calculating the Molar absorptivity using a standard curve graph (line equation) , the value obtained is lower than the value obtained when using just beer's law. what is the reason for this?
I am not sure if I understand you correctly. Do you want to say that you prepared a number of solutions, measured the transmittance, calculated absorbance A from A = - log10T, and determined for one particular wavelength the molar absorptivity by fitting a line and determining the slope? This is actually to use Beer's law, so what do you mean by "using Beer's law"? Please provide more details so that we can help you.
There is no difference between absorptivity and molar absorptivity because the two terms express the same idea. Absorptivity, or molar absorptivity, is the absorbance of a solution per unit path length and concentration. The molar absorptivity can be determined when using the Beer Lambert Law.
The higher the molar absorptivity, the higher the absorbance. Therefore, the molar absorptivity is directly proportional to the absorbance.