Beers Law & Colorimetry

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.

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

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.

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

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.

Colorimeters

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.

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.

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

%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) = if %T = 45%, A = -log (45/100) = Make sure you can duplicate these calculations on YOUR calculator!

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

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