1.4: Beer's Law
A = abc or A = εbc or even occasionally A = εℓc
(The first is the form the AP test uses, but you will see the other symbols elsewhere. They all mean the same thing)
A: Absorbance. The amount of light absorbed by a sample. It's an odd logarithmic scale that is unitless, but higher A is more light absorbed (or less going through).
a (or ε): the 'molar absorptivity' or 'extinction coefficient'. This is just a number that says how well a given compound absorbs light. The higher the value, the more light it absorbs. Note that this value is only good for one specific wavelength (color) of light, so it's often given in the form 'a=0.00526 at 475 nm'. You don't use the 475 nm anywhere in the math; it's just to tell you what color light we're using.
b (or ℓ): pathlength through the sample. The more stuff the light has to go through, the more will be absorbed. For almost all instruments used, the pathlength is 1 cm.
c: concentration. The more concentrated a sample is, the more light it will absorb.
Using Beer's Law: typically this is used to measure the concentration of a sample.
Option 1: you know the value of a. In this case, just plug in your numbers and solve for c.
Option 2: you don't know the value of a, but you do have some samples with known concentrations. In this case, you need to make a calibration curve. Make up a couple different samples with known concentrations, and plug them in the machine. You'll get something like this:
(The first is the form the AP test uses, but you will see the other symbols elsewhere. They all mean the same thing)
A: Absorbance. The amount of light absorbed by a sample. It's an odd logarithmic scale that is unitless, but higher A is more light absorbed (or less going through).
a (or ε): the 'molar absorptivity' or 'extinction coefficient'. This is just a number that says how well a given compound absorbs light. The higher the value, the more light it absorbs. Note that this value is only good for one specific wavelength (color) of light, so it's often given in the form 'a=0.00526 at 475 nm'. You don't use the 475 nm anywhere in the math; it's just to tell you what color light we're using.
b (or ℓ): pathlength through the sample. The more stuff the light has to go through, the more will be absorbed. For almost all instruments used, the pathlength is 1 cm.
c: concentration. The more concentrated a sample is, the more light it will absorb.
Using Beer's Law: typically this is used to measure the concentration of a sample.
Option 1: you know the value of a. In this case, just plug in your numbers and solve for c.
Option 2: you don't know the value of a, but you do have some samples with known concentrations. In this case, you need to make a calibration curve. Make up a couple different samples with known concentrations, and plug them in the machine. You'll get something like this:
Now take your sample with unknown concentration and put it in the machine to measure absorbance.
You can use the graph to get the concentration
You can use the graph to get the concentration
