Working with Moles: Density of Coke vs. Diet Coke

 

Subject Area

  General Chemistry
Age or Grade

  Chemistry I: grades 10 or 11
Estimated Length

  one 45 minute class period
Prerequisite knowledge/skills

  Students will have already been introduced to the mole concept as part of the unit on chemical reactions and stoichiometry.
Description of New Content

  This lessons provides an opportunity for students to use their newfound understanding of the mole concept in order to explain and understand an observed phenomenon.
Goals

  Students will use concepts of molar mass, density, and buoancy to explain why a can of Diet Coke floats in water, while a can of Coke sinks.
Materials Needed
One can of Coke
One can of Diet Coke
 Two baths of water

Procedure

 

 

 

Opener

Demonstrate, using the two water baths, that a can of Coke will sink in water, while a can of the exact same size containing Diet Coke will float.  Ask the class how this might be explained.  The students should know that this indicates that the can Diet Coke is less dense than water, while the can of regular Coke is more dense.  Guide the students to realize that, given the formula for density, p = m/v, this means that the Diet Coke can contains less mass than the regular Coke can, since both cans are of equal volume.  

Development

Explain to students that one potential source of the mass discrepancy might be due to the differing compounds used as sweeteners in each soft drink; while Coke uses high fructose corn syrup (55% fructose and 45 % glucose), diet Coke uses aspartame. The students are then asked to predict the mass ratios of sweeteners in the two sodas, given the molecular formulae for each of these compounds, fructose = glucose = C6H12O6, aspartame = C14H18N2O5.  The target response is that, assuming equal molar quantities of each sweetener, the mass ratio of sweetener would be 294/180 aspartame : high fructose corn syrup (HFCS), meaning the Diet Coke would actually contain more sweetener mass.  Under such a scenario, the Diet Coke can should be more dense than the Coke can, which is contrary to observation.  Ask the students to discuss how it might be possible that Diet Coke, which contains a sweetening compound of larger molecular mass, is somehow less dense than regular Coke.

Closure

 After the students have brainstormed for a bit, give them this piece of information: tests have indicated that aspartame is about 200 times sweeter than sugar.  Now have the students revise their mass ratio calculation.  They should determine that, assuming one needs only about 1/200 of the molar quantity of aspartame to achieve the same sweetness as the high fructose corn syrup, it is reasonable to assume that the mass ratios of the sweeteners might be 3/180, or 1/60 aspartame : HFCS.  Given that there are 41 g of HFCS in one can of Coke (based on the nutritional facts label), have the students caculate the expected mass of aspartame in Diet Coke.  They should find that there should only be about 700 mg of aspartame in Diet Coke, making for a mass discrepancy of about 40 g between the regular and diet cans.  However, according to the Coca-Cola company, there are only 188 mg of aspartame in a can of Diet Coke.  Have students use this information to estimate the relative sweetness of aspartame and the HFCS used in Coke.

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 the students calculate upper and lower boundaries for the volume of the soda can, based on the observation that the Coke can sinks and the Diet Coke can floats.

Evaluation

  During the course of the lesson, students are to follow along and perform the calculations in their notebooks, which are collected and graded.
Extensions

  
References  Coke and Diet Coke Nutritional Information: http://www.thecoca-colacompany.com/mail/goodanswer/soft_drink_nutrition.pdf