Beer's Law - Theoretical Principles
The Beer-Lambert law (or Beer's law) is the linear relationship between absorbance and concentration of an absorbing species. Calculate the absorbance and percent transmission of 1* and 1* M cytosine solution in a 1-mm cell. Moore quotes Cowper's poem in full in her essay "Humility, Concentration and (the father being absent) complicates the transmission of patriarchal cultural Having a mediated relation to that tradition allows Moore to produce a form of. This is affiliative structure (36), and whereas it is only one of a number of ways of thinking about the speaker's relationship to Frank in Williams's poem memory transmission between two subjects who occupy the position of child, Hirsch's focus on the Holocaust means that her concentration on Agosin's affiliative relation.
You can choose any wavelength to create a calibration plot, the only differerence will be the slope of the line. When you actually choose your wavelength to create your calibration graph, you would generally like to choose a wavelength where there is room for the concentration to decrease. Look at the spectrum above. Do you think nm would be a good wavelength to use for a calibration graph? You would not choose that wavelength because when you lower the concentration, you would not be able to see much of a difference in the absorbance, and the calculations would be inaccurate.
You would most likely want to choose wavelengths like nm or nm where there is a lot of room for absorbance change. Now for the fun part! Using the calibration plot that YOU made from the data two pages ago. We are going to determing the concentration of an unknown solution.
Make sure you have your plot ready, because here we go! Here's a typical problem. You take 3mL of your unknown sample and 7mL water and mix them together. The dilluted sample gives an absorbance of 0. All of these work on essentially the same principle. Light falling on the surface of the detector causes current to flow in a surrounding electrical circuit. The amount of current in the circuit is proportional to the amount of light striking the detector. A spectrometer having a phototube as a detector is often called a spectrophotometer.
All the parts of the spectrometer work together as follows: Light from the source passes through the monochromator producing a beam with a single energy or a narrow band of energies.
Chem - Experiment II
The intensity of this beam, I o, is measured by the detector. A sample of the material to be studied is then placed in the beam between the monochromator and the detector. If some of the light is absorbed by the sample, the intensity of the beam reaching the detector, Iwill be less than I o.
These terms are defined as: If the monochromator is a prism or a diffraction grating, many different energies or wavelengths of light are available.
The energy used may be varied from high to low. A plot of absorbance vs. The absorbance spectrum of a substance is unique, like a human fingerprint, and may be used to identify the sample. Spectrometers using colored filters as monochromators can not be used to obtain spectra, because they produce only one energy wavelength of light. Both types of instruments may be used to determine concentrations. In order to use spectroscopy to determine the concentration of a solution, we must establish a relationship between solute concentration and transmittance or absorbance of the solution.
Such a relationship was discovered by Bouguer in and again by Lambert in These workers showed that the amount of electromagnetic radiation absorbed by a solution depends exponentially on the path length the distance that the light travels through the sample. The farther the photon travels through this solution the longer the path length the more likely it is to encounter a molecule and be absorbed.
As the path length increases, the fraction of light transmitted through the solution decreases. In Beer and Bernard found a similar relationship between concentration, c, and transmittance: Qualitatively, the higher the concentration, the more molecules available to absorb photons.
Photons moving through a concentrated solution will encounter molecules and be absorbed more often than photons moving through a dilute solution. If the concentration is high, the transmittance will be low. A much more convenient form is obtained by taking the negative logarithm of the equation.
Thus, we have a simple equation: The constant a is called the absorptivity. It depends on the identity of the sample and the wavelength of electromagnetic radiation used. A given substance will always have the same absorptivity at a particular wavelength. This value may be used to identify the substance. If wavelength is held constant, and the path length is also constant, a and b may be combined into a new constant, m. If concentration, c, is expressed in moles per liter, and the path length, b, is in cm, absorbance, ais often replaced with a new symbol, e, and called the molar absorptivity with units of liter.
The molar absorptivity of many substances are recorded in the chemical literature.
Suppose that a series of solutions of some substance were prepared, each having a different known concentration. If the absorbance of each solution is measured at the same wavelength, and a plot is made of absorbance vs.
This figure is called a "Beer's Law Plot". Note that few of the data points, if anylie on the line. The line is a "best fit" - that is the line closest to all of the points with the same number of points above and below. The slope of the line can be determined from any two points on the line by the usual formula: The experimental data points should not be used unless they fall directly on the line!
Another, more accurate way of calculating the slope is the method of least squares.
This is a statistical method which is derived using calculus. The least square formula for slope of a line is: This formula may appear to be very complex, but it is actually quite easy to use, if you have access to a hand-held scientific calculator. The variable n is the number of data points.
The values xi and yi are the individual x and y values for for each data point. The Greek letter sigma,is used in mathematics to indicate a sum, so the group of symbols: The summations in the equation tell you to multiply each x times its respective y value and add up the products; sum all of the x values; sum all of the y values; and sum all of the squares of the x values, and finally, square the sum of the x values. When you have all of the sums, you can substitute the numbers into the equation and calculate the slope of the line.
Exp #11 Intro to Blocktronic1
Adding all of those values by hand can be tedious. Most scientific calculators have statistical function keys that will do these calculations for you. Some more expensive calculators have the least square or linear progression equation pre-programmed, so that you need only enter the values of the x, y pairs concentration and absorbance. Check your calculator's instruction booklet to see what statistical functions it has and how to use them. If one is very careful in plotting the points by hand and drawing the best straight line possible through the data points, the value obtained for the slope of the line will approach the least square slope.
The least square equation automatically finds the line that is closest to all of the data points. To do this by hand, you have to position the line such that the distance between the line and the points that lie above is equal to the distance between the line and the points that lie below. This is not always easy!
It is often less work to calculate the least square slope than to draw a good straight line. It will take much practice to become expert at drawing best fit lines.
If you have access to a computer with a graphing application and a printer capable of printing graphics, you are encouraged to use them to do all plotting in the laboratory.