Molar absorptivity is also known as the molar extinction coefficient ( ε ). B EER ’ S L AW E QUATION Currently we know that molar absorptivity (a), path length (b), and concentration (c) are all directly proportional to absorbance (A). We can write a mathematical expression relating all of these variables called Beer’s Law (names sometimes include Bouguer and/or Lambert): ( 7 ) This should be an easy equation to remember, it’s as easy as your “abc’s.” The above dimensional-analysis equation shows that absorbance is unitless. Given that our cuvets have a 1 cm pathlength, if absorbances for a set of standards of known concentrations are measured by the spectrophotometer, then only the molar absorptivity of the solute at that wavelength is an unknown. Molar absorptivity can be determined by plotting a calibration curve. If we think of Beer’s Law as the general equation for a line as follows, b A µ l max l max I in I in I out  I out  l max l max I in I in I out  I out 
13 (“b” in Beer’s Law = pathlength; “b” in the equation of a line is y-intercept!) where “ y” is absorbance (measured by the spectrophotometer or colorimeter), “ x” is the solute concentration of the solution to which the absorbance corresponds. The slope of the calibration curve equals the molar absorptivity times the pathlength. Since pathlength (b) is 1 cm, the numerical value of the slope equals the molar absorptivity. The y-intercept of any graph is the y-value when x is zero. In the case of the calibration curve for this experiment an x-value of zero corresponds to a concentration of zero. A solution with zero solute should give you an absorbance (and y intercept) of zero. In practice, the y intercept of the fitted straight line may differ slightly from zero. The following equation results from the 6 example data points (including the blank) plotted in the calibration curve to the right: A unknown = 2.286c unknown + 0.0286 The slope of the standard curve is 2.286 and its y-intercept is 0.0286 . From this equation we can calculate the concentration of the unknown once we have measured its absorbance. If, for example, the absorbance is 1.100, the concentration would be 0.468 mol/L.: As you can see we get the same result graphically (dashed line on sample graph). Therefore the concentration of the unknown solution is likely 0.468 M in solute “x.” T HE I NTERCEPT If the intercept is not zero, does this mean that our graph is wrong? No, not necessarily. The intercept of 0.0286 is close to zero. Reasons for not having a y-intercept of zero may include: random and systematic errors associated with solution preparation, instrumental drift, smudged or mismatched cuvets, etc. Also a result of these errors and variations, the 6 data points do not fall exactly on the line. Some are above and some are below. The line represents the “best average” of the 6 data points. If the concentration that you calculated for each dilution wasn’t matched by the sample used in the cuvet (perhaps you didn’t mix
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