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PATHLENGTH (b)EFFECTSSince we now understand that more light will be absorbed as the amount of solute increases oncentratioakes sense that, in passing though a thicker sample, more light will be hat light travels through the sample is called e bottom in the deep end. The light reflected off the hort path length” (Iout) is greatly reduced. ed. (cn effect), it mabsorbed. The distance tmax max Iin Iout[1the pathlength. You may have noticed this looking for something lost in a swimming pool. Looking into the shallow end you can easily see the bottom. It’s harder to see thIin Iout]bottom encounters more solute particles passing though more liquid. See the figure to the right. Again the measurements are made at max, and the incident intensities are the same. Much more light passes throsample (Iout). In the longer pathlength case, the transmitted light ugh a “sYou can imagine that, at some pathlength, effectively no light is transmittBecause absorbance is directly proportional to path length (bA), in designing an experiment, you need to ensure that all measurements are made using the same pathlength. Fortunately, the cuvets we use the standard pathlength of 1 cm. MOLAR ABSORPTIVITY (a)EFFECTSDifferent substances absorb light of different wavelengths to different extents. Where chlorophyll sreen light least, the dye in strawberry Kool-Aid® absorbs green wavelengths the most. ependent on the particular substance, wavelength, and, to a absorbgMolar absorptivity, a, (aA) is dlesser degree, the instrument and concentration. Molar absorptivity is also known as the molar extinction coefficient (ε). BEER’S LAW EQUATIONCurrently we know that molar absorptivity (a), path length (b), and concentration (c) are all directly ortional t absorbance (A). We can write a mathematical expression relating all of these w (names sometimes include Bouguer and/or Lambert): propovariables called Beer’s LacbaA(7) This should be an easy equation to remember, it’s as easy as your “abc’s”. UnitlessolLcbaALmolcmm(cm)The above dimensional-analysis equation shows that absorbance is unitless. Given that our cuvets have a 1 cm pathlength, if absorbances set of standards of known r absorptivity of the ined by plotting a for aconcentrations are measured by the spectrophotometer, then only the molasolute at that wavelength is an unknown. Molar absorptivity can be determcalibration curve. If we think of Beer’s Law as the general equation for a line as follows,
bmxycbaA(“b” above is pathlength, “b” below is y-intercept!)where yis absorbance (measis the solute concentration of the solution to which the absorbance corresponds. The slope of the calibration ht: ured by the spectrophotometer or colorimeter), xcurve equals the molar absorptivity times the pathlength. Pathlength (b) is 1 cm, leaving the numerical value of the slope equal to the molar absorptivity.