The molar absorptivity can be determined by plotting a graph If we arrange

The molar absorptivity can be determined by plotting

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The molar absorptivity can be determined by plotting a graph . If we arrange Beer’s Law into a linear equation for a line as follows, b mx y bc A where y is absorbance (measured by the spectrophotometer), and x is the concentration of the solution to which the absorbance corresponds. The slope of the straight line is then equal to the molar absorptivity times the pathlength, m = b. Remember that pathlength (b) is always equal to 1.00 cm, which leaves the slope of the straight line equal to the molar absorptivity, m = . The y-intercept of any graph is the corresponding y-value when the value for x is equal to zero. In t he case of the Beer’s Law plot for this experiment an x-value of zero corresponds to a concentration of zero. A solution with zero solute should give you an absorbance value of zero. In practice, this may not be the case, since the solvent which is used to make the solution may give a minimal absorbance reading. In any case, the y-intercept for the plot should theoretically be zero. The following equation results from the example data that is plotted in the graph on the right: 0.0286 c 2.286 A Unknown Unknown The slope of the straight line 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 1.1, the concentration would be 0.47 mol/L: mol/L 0.47 ~ 0.468 c 2.286 0.0286 1.1 2.286 0.0286 A c Unknown Unknown Unknown As you can see we get the same result graphically (dashed line on sample graph). Therefore the concentration of the unknown solution is likely 0.47 M in this example. As stated previously, the y-intercept for the graph should be zero, due to the fact that at zero concentration of solute there is zero absorbance. If the intercept is not zero, does this mean that our graph is wrong? No, not necessarily. Our intercept of 0.0286 mol/L is very close to zero. The reason for not getting exactly zero has to do with random and systematic errors associated with variance in solution preparation and instrumental drift. As a result of these errors, 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 points. If the concentration that you reported for the first solution is not exactly 0.1 M, random error has been introduced into the experiment and that data point would not fall within the linear response expected for the plot. However, even if the solutions were prepared with minimum random error, there is systematic error that is associated with any given absorbance reading. If you re-measure a sample some time later the same exact absorbance value would not result. There are simply limitations on how precisely you can make a measurement.
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