This problem highlights the importance of modelling rate laws

Problem Statement

“I am curious how long I should let my coffee brew in my percolator. I also want the most accurate answer.”

Mathematical Background

A laboratory experiment was conducted to measure the rate law of the formation of dark brown rings and the diameter of cups made by percolation with pure water or coffee-water mixtures at various concentrations. The desired volume of solution (in ml) was put into the bottom of each of three beakers. There were 3 or 4 strips of filter paper placed vertically in the beakers. Then, water was poured over the top of the filter paper until the solution was level with the top of the paper. This process was repeated for all beakers. Next, each beaker was fitted with a rubber cork stopper, and the beaker was placed on a laboratory stirrer. A suitable metal rod was dipped into the solution and stirred with a magnetic stirrer. After all of the beakers were on the stirrer, they were allowed to stand for 15 minutes. At the end of the 15 minutes, all of the stoppers were removed, and the rods were put back into the beakers and swirled with the stirrer. After 30 seconds, all of the rods were returned to the beakers, and the beakers were left standing for another 15 minutes. At the end of 15 minutes, the rods were put back in the beakers, and stirring was continued for 30 seconds. After 30 seconds, the rods were returned to the beakers, and stirring was continued for 15 minutes. After 15 minutes, all of the rods were put into the beakers, and the beakers were left standing overnight. The following morning, the experiment was over, and the rods were inspected to determine the diameter of the cup made by the coffee-water mixture. The experiment was conducted with samples of pure water and 8 coffee-water mixtures.

Findings

The data were analyzed to obtain the rate law for percolation.

Conclusion

Using the data collected during the experiment, the rate law for percolation of coffee-water mixtures was obtained. The resulting equation was n = -0.05(t)^2nt