### ﻿Beer’s Law Lab Report

Abstract:
The Beer’s law lab was conducted to determine the optimal wavelength of Co(NO3)2·6H2O with the use of spectrometry. The results determined that the optimal wavelength to study the absorbance of this salt was 500nm. It also demonstrated how transmittance of light and absorbance of light are inversely proportional because absorbance is calculated by multiplying transmittance by a negative log. Introduction:

When one is studying chemicals, there are many important factors of significance. The color of a chemical is a useful tool in its study. The light one sees produced by a chemical is the result of both reflection and absorbance of wavelengths. The wavelengths that are absorbed by a chemical are not visualized. The wavelengths that are reflected back are the colors that one sees. When chemicals are diluted in water, their colors also become diluted. As the chemical is diluted, the molecules spread apart. The more dilute the solution, the further apart the molecules. As the molecules spread, the color that is reflected becomes less intense because some of the wavelengths are able to pass through the solution without encountering any of the solute.

The more wavelengths that are able to pass through a solution without encountering any of the solute, the greater the transmittance. The transmittance can be mathematically calculated by dividing the amount of light that exited the solution (IT) by the amount of original intensity (IO). That value is then multiplied by 100 to give the percent transmittance (%T)

Beer’s Law is used to relate and compares the amount of light that has passed through something to the substances it has passed through. The Law is represented by A=abc. “A” is the absorbance of a solution. The “a” represents the absorption constant of the solution being tested. The “b” represents the thickness of the solution in centimeters, and “c” represents the solution’s molarity or concentration. The “A” can be calculated by using the negative log of the transmittance (T).  The lab experiment conducted used the salt Co(NO3)2·6H2O. The Co(NO3)2·6H2O was diluted in distilled water to four different molarities. The most concentrated solution was used to determine the optimal wavelength to study the salt by measuring the transmittance of the Co(NO3)2·6H2O with twenty different wavelengths of light. Once the optimal wavelength was concluded, the transmittance of the less concentrated Co(NO3)2·6H2O solutions was also measured. The measurements of the less concentrated solutions was to determine the absorbance constant, “a”. Finally, the transmittance of an unknown concentration of Co(NO3)2·6H2O solution was measured and molarity was determined based on the absorbance constant determined earlier in the experiment.

Procedure:
A test tube was prepared with 0.1 M solution of Co(NO3)2·6H2O in 10mL of distilled water. Half of the .1M solution, 5mL, was drawn up into a pipette and put into another test tube with 5mL of deionized water to make a 0.05 M solution. Half of the 0.05 M solution, 5mL was drawn into a pipette and put into a test tube with 5mL of deionized water to make 0.025 M solution. Half of the 0.025 M solution, 5mL, was drawn into a pipette and put into a test tube with 5mL of deionized water to make 0.0125 M solution. A test tube of 10mL of deionized water was also prepared. The bubbles on all test tubes were removed by tapping on the outside of the test tube. The outside of the tubes were dried off and any fingerprints were removed with paper towels and placed into a test tube rack.

An absorbance spectrometer was zeroed by measuring the transmittance at 400nm with no test tubes in the spectrometer. The spectrometer was then calibrated to 100 percent transmittance with the test tube of deionized water. The deionized water was removed from the spectrometer and the 0.1 M solution was put inside the spectrometer. The transmittance of the solution was recorded and the solution was removed. The wavelength on the spectrometer was changed to 410nm and the deionized water was placed back into the spectrometer and the transmittance was calibrated to 100 percent.

The deionized water was replaced with 0.1 M solution and the transmittance was recorded. This process was repeated twenty times with the wavelength increasing by 10nm consecutively until the last wavelength, 600nm, was measured. It was necessary to calibrate the spectrometer between each change in wavelength. Every change in nanometers had to be measured and calibrated at 100 percent with the control of deionized water. This maintained accuracy when the transmittance of Co(NO3)2·6H2O solutions measured.

Based on the data gathered, the optimal wavelength was determined and the spectrometer was set to that wavelength. The transmittance was set to 100 with the deionized water. The 0.1 M solution replaced the deionized water in the spectrometer chamber and the transmittance was recorded. This process was repeated with 0.05 M, 0.025 M, and 0.0125 M solutions and the transmittance was calibrated to 100 between each solution with the deionized water.

Finally, a Co(NO3)2·6H2O solution with an unknown molarity was provided (unknown “B”). The wavelength of the spectrometer was not changed. The deionized water was placed in the chamber and calibrated to 100 percent transmittance. The deionized water was removed and replaced with a test tube containing unknown “B”. The transmittance was recorded to determine what the molarity was. Data:

After the solutions had been completed, the transmittance was measured at 10nm intervals from 400nm to 600nm. The measurements were determine the wavelength to best study Co(NO3)2·6H2O. Higher transmittance demonstrated less absorption of the wavelength and lower transmittance demonstrated higher absorption of the wavelength.

Discussion:
Beer’s Law is a law that demonstrates that the absorbance of light at a certain wavelength is directly proportional to the concentration or molarity of a solution. This was apparent with the naked eye. When making the solutions, 0.291 moles of was added to a test tube with 10mL of deionized water to make a 0.1 M solution. By taking 5mL out of the solution and mixing it with 5mL of deionized water, the number of moles was halved which made the second solution a 0.05 M solution. When the process had been repeated, it was apparent that the solutions had been diluted based on the color of the solutions in the test tubes. The 0.1 M solution was absorbing more light and was a deep rose color. As the solutions became more dilute, the concentration of the visible color diminished as less light was absorbed to a very pale translucent pink in the 0.0125 M solution.

For the first part of the lab, the wavelengths 400-600nm were used. These wavelengths were used to determine the optimal wavelength when the most light was absorbed by the solution. It was important to calibrate the transmittance to 100% on the spectrometer with the deionized water because there were no solutes to absorb light. The spectrometer was then able to use that calibration to determine how much of the light was absorbed by the solution containing Co(NO3)2·6H2O by comparing the difference in how much light was absorbed by the detectors in the spectrometer.

The spectrometer than calculated the percent transmittance (%T) and displayed the data in a percent. As was shown above in table 1 and graph 1, the %T started high and ended high with percentages over 90. The higher %T demonstrate less light was absorbed by the solution and therefore not the wavelength of light that is absorbed by Co(NO3)2·6H2O. Toward the middle of the data, 500nm and 510nm, the %T became substantially lower. This demonstrates that Co(NO3)2·6H2O absorbs wavelengths about 500nm.

In the second part of the lab, the different molarity, or concentrations, of solution were measured for %T with a 500nm wavelength. The absorbance was calculated by using the negative log of T. This was done because T and A are inversely proportional. This was demonstrated in table 2 and table 3. These tables confirmed that as T decreases, A increases.

The third part of the experiment used the point slope formula to determine a molarity based on an absorbance.

The absorbance of light was dependent on the concentration of solute. The variables “A” and “y” are both dependent variables and were comparable to one another. The variable “x” and “c” were the independent variables. The variable “a” was the absorption constant and “b” was the thickness of the solution. In this case, “b” was equal to 1 cm. Graphs 2 and 3 demonstrated the plotted points and from that, excel calculated a trend line based on the point-slope formula. Graph 3 demonstrated how the estimated molarity of unknown “B”, based on the point-slope formula, fits the trend line. Conclusion:

Beer’s Law was studied in this lab. The goals of this were to determine optimal wavelength absorption by Co(NO3)2·6H2O and determine transmittance and absorption from the data collected. The optimal wavelength absorption for Co(NO3)2·6H2O occurred at 500nm. The data also showed that while the transmittance and absorbance were indirectly proportional from one another, both variables were dependent on the concentration of the solution. Once the data had been collected and understood, an unknown concentration of solution was tested for transmittance. Based on the trend line formed from other concentrations of Co(NO3)2·6H2O solutions, the molarity was easily calculated to be 0.048.

Possible errors that may have occurred during this lab have to do with calibration of the spectrometer. The transmittance values changed second to second so if the timing was not perfect in measuring the samples, the transmittance would have been erroneous. The transmittances would have been too high (based on experimentation) so the absorbance rates would have been too low. This in turn would have caused the absorbance constant to be too low. If the absorbance constant was too low, the concentration of unknown “B” would have been calculated too high.