Float or Sink? An at-home lab on density

There is a classic chemistry demonstration that involves placing cans of soda pop in water to see if they float or sink.^1-8 Usually, sugared sodas sink in water while diet sodas float (video 1).

Video 1: Curious Cans: A Simple, yet Baffling Science Experiment, Tommy Technicium's YouTube Channel (accessed 3/2/2021)

The sinking of cans of sugared sodas can be explained by the fact that sugar water is more dense than pure water, and of course more dense fluids sink below less dense fluids. Yet as seen in Video 1, it is not always the case that cans of sugared soda sink in water (see the video in reference 7 for an explanation of how the regular Coke floated in Video 1).^4-8 To make sense of this behavior, it must be remembered that whether an unopened can of soda floats or sinks depends upon the density of the entire can. The entire can includes the aluminum can itself, the beverage contained in the can, and the gas in the headspace of the soda. Each contributes to the overall density. If the density of the entire unopened can is greater than that of water it will sink, if it is less than the density of water it will float.

An analysis of whether an unopened can will float or sink can be made quantitatively. The method of doing so is simple enough to carry out in your own kitchen if one has access to a digital balance.⁹

Background

The density (D_full) of a full, unopened can of soda is equal to the total mass of the unopened soda (m_ror) divided by its total volume (V_ror):

               Equation 1

The total mass of the unopened can is easy enough to find: just place the unopened can on a balance! Finding the volume of the unopened can is a bit trickier (see reference 8 for a slightly different method than presented here). Notice that the total volume of the unopened can of soda pop is the sum of the volume of the space in the interior of the can (V_i), and the volume of the metal that makes up the empty can (V_can):

                    Equation 2

It is instructive to point out that V_i is the sum of the beverage volume and the gas headspace in the enclosed can.  can be estimated by first finding the mass of water (m_w) required to completely fill the empty space in the can. This mass is then converted to volume using the density of water (D_H2O = 1.0 g mL^-1):

                                Equation 3

It is possible to find V_can in a similar manner. First, the mass of the completely emptied can (m_can) is found. This mass is converted to volume using the density of aluminum (D_Al = 2.7 g mL^-1):

                             Equation 4

Substitution of Equations 3 and 4 into Equation 2 allows for the calculation of the volume of the unopened can:

              Equation 5

Finally, substitution of Equation 5 into Equation 1 allows us to see how to calculate the density of the unopened can from measured values and the known densities for water and aluminum:

                   Equation 6

Results

I had students in my non-majors science course (see supporting information for the labsheet I used) test out this method of determining the density of unopened cans of various brands of soda; a total of 37 cans were tested (Table 1). Students first tested the unopened cans of soda to see if they floated or sunk in water. After doing so, they used the method outlined above to determine the density of the unopened can. In 34 of the cans tested, the calculated density was found to be consistent with the observed floating and sinking behavior of the can. For these cans, if the measured density of the can was greater than 1.00 g mL^-1 the can sunk, while if the measured density was less than 1.00 g mL^-1 the can floated. Of note, cans of Diet Coke, Diet Pepsi, and regular Pepsi all displayed floating and sinking behavior that was consistent with the density that students measured. However, the same was not true for cans of regular Coke. Of the 8 cans of regular Coke tested, 5 cans showed floating and sinking behavior that was entirely consistent with the calculated density. One can of regular Coke exhibited behavior inconsistent with its calculated density: it floated in water, but its calculated density was 1.01 g mL^-1. The remaining two cans of regular Coke had a calculated density that was the same as water: 1.00 g mL^-1. Of these two cans, one floated, while the other sunk. Overall, cans of Diet Pepsi had an average density of 0.975 g mL^-1, cans of Diet Coke averaged 0.980 g mL^-1, cans of regular Coke averaged 1.009 g mL^-1, and cans of regular Pepsi averaged 1.021 g mL^-1.

Table 1: Experimentally determined densities of cans of soda

Discussion

The method presented here is a variation on a previously published method for determining the density of unopened beverage cans.⁸ In this previous method, water displacement was used to determine the volume of the unopened can. The method used herein makes use of mass measurements, which are subsequently converted to the necessary can volume. An advantage of this new method is that it can be accomplished in an at-home setting if a kitchen scale.⁹ In my non-majors class we used balances that could measure to the nearest 0.01g, but I surmise one could get good results with a balance that measures to the nearest 0.1g, and fair results with a balance that measures to the nearest gram.

In the experiments presented here, cans of Diet Coke and Diet Pepsi consistently floated, whereas cans of regular Pepsi consistently sunk. Thus, these beverages are preferred if one wishes to demonstrate differences in density between sugared and diet sodas by way of floating and sinking behavior. On the other hand, regular Coke displays differential floating and sinking behavior. Sometimes cans of regular Coke float in water, and sometimes they sink. Therefore, unopened cans of regular Coke have densities that are very close to the density of water. As a result, small changes in the manufacturing of a can of regular Coke (amount of beverage, amount of metal in can, amount of gas in headspace) or experimental conditions (temperature of the water into which the can of Coke is placed) will have noticeable effects on whether a can of regular Coke floats or sinks. Perhaps this is something my students and I will study in the future. I'm also curious about how other beverage brands behave. If you happen to look into the densities of cans of other beverages – or anything else related to this experiment - please let us know. I'd be very inerested to hear what you migth learn.

Happy experimenting!

References

1. Toepker, T. P. Phys. Teach. 1986, 24, 164.
2. Measure density of the fluid: J. Chem. Educ. 1999, 76, 1411.
3. J. Chem. Educ. 2006, 83, 1632A.
4. J. Chem. Educ. 2008, 85, 18-19.
5. J. Chem. Educ. 2011, 88, 272–273.
6. https://www.chemedx.org/blog/solution-chemical-mystery-7-curious-cans
7. https://www.chemedx.org/blog/chemical-mystery-7-curious-cans
8. J. Chem. Educ. 2009, 86, 209.
9. A balance with a capacity of 500 g and precision of 0.01 g is recommended – but perhaps not entirely necessary. At the time of this writing, balances with these specifications can be purchased at retail stores or on Amazon for $10 - $40.