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Beers Law & Colorimetry

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Absorbance ABSORBANCE is the amount of light that gets stopped by a material Zero = a perfectly transparent material that lets all light through. Infinity = a completely opaque material that does not let any light through. Absorbance (A) is directly proportional to concentration (c) : A = kc. This is a mathematical model for something you already know: a darker solution is a more concentrated one.

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Path Length PATH LENGTH is the distance light travels through a solution. Note how the solution in the belly of this volumetric flask is darker than the solution in the neck. PATH LENGTH (b) is directly proportional to absorbance (A) : A = kb. less dark neck darker belly

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Beers Law A = abc absorbance path length concentration constant (nature of solute) Beers Law puts all the factors that affect absorbance together in one equation.

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If we are using only one solute, then a is a constant. If we are are careful to always use the same path length, then b is a constant, too. This simplifies Beers Law to: A = kc. Beers Law Graphs concentration absorbance

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Then, we can find the concentration of any unknown by measuring its absorbance and interpolating the concentration. Using Graphs concentration absorbance If we can measure the absorbance of several known concentrations of a solution, we can make a straight line graph.

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Colorimeters

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Transmittance 100% = a perfectly transparent material that lets all light through. 0% = a completely opaque material that does not let any light through Colorimeters actually measure TRANSMITTANCE: the amount of light that goes through a solution.

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A Comparison concentration absorbance concentration %Transmittance At c =0, A = 0. At c =, A =. A and c are directly proportional. At c =0, %T =100. At c =, A = 0. A and c are exponentially related.

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A %T Absorbance and transmittance are related exponentially. 10 -A = %T/100 so if A = 1: 10 -1 = 0.1 = T, or %T = 10% if A = 2, 10 -2 = 0.01 = T or %T = 1% We will usually deal with A < 1. if A = 0.5, 10 -0.5 = 0.316 = T or %T = 31.6% if A = 0.1, 10 -0.1 = 0.794 = T or %T = 79.4% Make sure you can duplicate these calculations on YOUR calculator!

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%T A Most of the time, we need to convert %T (from the colorimeter) to A (so we can plot the direct relationship between A and c. A = -log(%T/100) so if %T = 90%, A = -log (90/100) = -log(.90) = 0.045 if %T = 45%, A = -log (45/100) = 0.347 Make sure you can duplicate these calculations on YOUR calculator!

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Sample Problem 1.Calculate A for the transmittances in this data table. 2.Graph c vs. A and get a best fit straight line. 3.If an unknown K 2 CrO 4 (aq) solution was measured at 53.7%T, what would be its concentration? K 2 CrO 4 (aq) Concentration (M) %Transmittance 0.000100 0.12579.4 0.25063.1 0.37550.1

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Answer At 53.7% T, A = -log(0.537) = 0.270 From the graph, @ 0.270 for A, c = 0.338M

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