Procedure
Opener
Demonstrate, using the two water baths, that a can of co*kewill sink in water, while a can of the exact same size containing Dietco*ke will float. Ask the class how this might be explained.The students should know that this indicates that the can Dietco*ke is less dense than water, while the can of regular co*ke is moredense. Guide the students to realize that, given the formula fordensity, p = m/v, this means that the Diet co*ke can contains less massthan the regular co*ke can, since both cans are of equal volume.
Development
Explain tostudents that one potential source of the massdiscrepancy might be due to the differing compounds used as sweetenersin each soft drink; while co*ke uses high fructose corn syrup (55%fructose and 45 % glucose), diet co*ke uses aspartame. The students arethen asked to predict the mass ratios ofsweeteners in the twosodas, given the molecular formulae for each of these compounds,fructose = glucose = C6H12O6, aspartame = C14H18N2O5. The targetresponse is that, assuming equal molar quantities of each sweetener,the mass ratio of sweetener would be 294/180 aspartame : high fructosecorn syrup (HFCS), meaning the Diet co*ke would actually contain moresweetener mass. Under such a scenario, the Diet co*ke can shouldbe more dense than the co*ke can, which is contrary to observation.Ask the students to discuss how it might be possible that Dietco*ke, which contains a sweetening compound of larger molecular mass, is somehow less dense than regular co*ke.
Closure
After the students have brainstormed for a bit, givethem this piece of information: tests have indicated that aspartame isabout 200 times sweeter than sugar. Now have the students revisetheir mass ratio calculation. They should determine that,assuming one needs only about 1/200 of the molar quantity of aspartameto achieve the same sweetness as the high fructose corn syrup, it isreasonable to assume that the mass ratios of the sweeteners might be3/180, or 1/60 aspartame : HFCS. Given that there are 41 g ofHFCS in one can of co*ke (based on the nutritional facts label), havethe students caculate the expected mass of aspartame in Diet co*ke.They should find that there should only be about 700 mg ofaspartame in Diet co*ke, making for a mass discrepancy of about 40 gbetween the regular and diet cans. However, according to theCoca-Cola company, there are only 188 mg of aspartame in a can of Dietco*ke. Have students use this information to estimate the relativesweetness of aspartame and the HFCS used in co*ke.
Finally, have a volunteer come up and weigh the two cans on a balance.Knowing that the density of water is about 1g/mL, have thestudents calculate upper and lower boundaries for the volume of thesoda can, based on the observation that the co*ke can sinks and the Dietco*ke can floats.