Spectrophotometry and a Beer's Law plot were applied to determine the concentration of a solution of chromium(III) nitrate with unknown concentration supplied by the company Pest Eliminator. A quadratic data set was re-expressed into a linear data set, which was then analyzed with a linear model; this model was then used to predict the molarity of the unknown solution from its absorbance. This calculated molarity was only slightly less than 0.100M, but the error of the measurement makes it far less certain, and so one cannot conclusively state whether the product is safe. Pest Eliminator is recommended to put less chromium(III) nitrate into their product, for the sake of safety.
A pest control company, "Pest Eliminator", has asked the Chemical Magicians to test their solution for concentration. If the solution is within a certain range, it will be toxic to pests but harmless to other animals. It is best if their solution is within an optimal molarity, since if it is too concentrated, it will be too effective on people and pets, while if it is not concentrated enough, it will be utterly ineffective even against pests. It is imperative, however, that the solution is not too strongly concentrated, as it is infinitely more preferable to have the pesticide not work than to have to deal with the effects of severe environmental contamination.
Their desired solution is a solution of chromium(III) nitrate nonahydrate, and the concentration must be lower than 0.100M. Spectrophotometric analysis of absorption will be used to calculate the unknown concentration since it is most efficient and economical.
[...] Fill six other spectrophotometer cuvettes, one with each test tube. Be sure to carefully mark which cuvette contains which sample! 6. One by one, place each cuvette into the (calibrated) spectrophotometer. Record the absorbance of the sample, and whether this was distilled water, one of the known samples, or the unknown Calculate a regression model for the data in order to predict the molarity of the unknown solution from its absorbance Results Observations Quite intuitively, as the molarity of the solution increased, the solution looked visibly darker, to the point that the 0.040 M solution was clear and the 0.200 M solution was nearly opaque. [...]
[...] spectrophotometer, this should not be a problem. It is, however, worth noting, just in case. What is important to note is that the dark purple/black nonahydrate should not be heated. The nonahydrate melts at around 30°C1 and completely decomposes at 100°C. It is recommended1 that it be stored below 24°C. Cr(NO3)3 9H2O is also an oxidizing agent. In fact, it is quite a strong oxidizing agent1. This should be taken into consideration when storing it in a container; some types of containers fare extremely poorly against strong oxidizing agents. [...]
[...] Multiplying both sides by the molarity, yields A = 16.124 c 45.2 c2. This equation can be used to find the molarity of a solution with known absorbance. Substituting the value of 1.16 the absorbance of the unknown solution for A and solving for c yields the result c = { 0.0999 M M}. Since there obviously cannot be two different values for molarity of the solution, one of these must be incorrect. The incorrect value is c = 0.257 M. [...]
[...] absorbance, there was a distinct bend. Beer's Law does not predict this, since plots of Beer's Law should be linear2. However, the first three data points are actually very nearly linear (and a quick linear regression with only these points, yielding R2 = dddddddddddddddddddddddddddd confirms this). It turns out that Beer's Law breaks down at high concentrations of solute2, when the solute particles begin to interact with each other. This causes a curved pattern to the graph for higher values of molarity. [...]
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