When morning rolls around an important element to starting the day on the right foot is a cup of coffee. But, did you know that every time you brew a cup of coffee you are essentially performing an extraction experiment? In this case, the extraction process is more specifically referred to as leaching. Leaching is a technique used to isolate a substance of interest from a solid by dissolving it in a liquid.
Coffee grounds (inert solid) contain caffeine molecules (solute). The coffee grounds are submerged in water (solvent) to obtain the caffeine molecules. In water, the coffee grounds are insoluble while the caffeine molecules are soluble. Over time the caffeine molecules dissolve and diffuse into the water. When brewing coffee, a filter captures what remains of the coffee grounds but allows the caffeine and other molecules that have dissolved into the water to pass through.
There was a study conducted to understand how time and water temperature affect the amount of caffeine obtained. The following charts were produced from data produced in the study for Coffea arabica beans:
Notice that the amount of dissolved caffeine in a solution increases over time and increasing temperature. Therefore, if completely disregarding taste, the longer and hotter you brew your coffee the more caffeine you will obtain.
 Nhan, Pham Puoc, and Nguyen Tran Phu. "Effect of Time and Water Temperature on Caffeine Extraction from Coffee". Pakistan Journal of Nutrition. 11. 2. (2012): 100-103. Web.