This experiment combines published procedures for the generation of three gases (hydrogen, nitrogen, and oxygen) and adapts them so that they can be used with a single gas-generation and collection apparatus. Working in collaborative groups, students determine density and number density for each gas. By comparing values for these two quantities in a post-lab discussion, students "discover" Avogadro's assertion that equal volumes contain equal numbers of particles and demonstrate that R has a single value for all three gases under consideration and so is truly a universal constant.