Now we use Solver to find K for the previous problem. The only absorbing species at 332
Question:
Now we use Solver to find K for the previous problem. The only absorbing species at 332 nm is the complex, so, from Beer's law, [complex] = A/ε (because pathlength = 1.000 cm). I2 is either free or bound in the complex, so [I2] = [I2]tot - [complex]. There is a huge excess of mesitylene, so [mesitylene] [mesitylene]tot.
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The spreadsheet shows some of the data. You will need to use all the data. Column A contains [mesitylene] and column B contains [I2]tot. Column C lists the measured absorbance. Guess a value of the molar absorptivity of the complex, ε, in cell A7. Then compute the concentration of the complex (= A/ε) in column D. The equilibrium constant in column E is given by E2 = [complex]/([I2][mesitylene]) = (D2)/((B2-D2)*A2).
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What should we minimize with Solver? We want to vary in cell A7 until the values of K in column E are as constant as possible. We would like to minimize a function like Σ(Ki - Kaverage)2, where Ki is the value in each line of the table and Kaverage is the average of all computed values. The problem with Σ(Ki - Kaverage)2 is that we can minimize this function simply by making Ki very small, but not necessarily constant. What we really want is for all the Ki to be clustered around the mean value. A good way to do this is to minimize the relative standard deviation of the Ki, which is (standard deviation)/average. In cell E5, we compute the average value of K and in cell E6 the standard deviation. Cell E7 contains the relative standard deviation. Use Solver to minimize cell E7 by varying cell A7. Compare your answer with that of Problem 18-12.
Step by Step Answer:
After running Solver the average value of K in cell E10 is 0464 and s 1073 ...View the full answer
