May 2017

# Icebergs and Avogadro’s constant

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Bob Perkins (retired) Port Alberni BC

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One of the desired student outcomes of the chemistry courses at our institutions is the ability to be able to use a variety of information sources to propose a solution to a given situation. Cooperative learning is also important; being able to work as part of a team is a necessary requirement for joining the work force after leaving a post-secondary institution. Most instructors will set thought-provoking problems1 that will require information from a number of sources, and will then often encourage their students to work in small groups to come up with a solution. Over the years there have been many published notes in the Journal of Chemical Education2 and Chem 13 News3-5 in regards to ways in which the magnitude of Avogadro’s constant can be conveyed to students. I would like to present another one which combines several aspects of introductory chemistry, and makes use of the concepts discussed above.

There have been a number of recent reports in the news regarding the eventual collapse of a portion of the Larsen C ice shelf in Antarctica, currently hanging on by a small frozen thread. Various estimates of the size of the

eventual calved iceberg include: 80 times the size of Manhattan, roughly the size of Delaware, area of 5000 square kilometres, thickness of 1000 feet. These reports have drawn attention to the reduced levels of ozone over the South Pole, as well as the warming trend leading to the breakup of some of the continental ice-sheet covering Antarctica. Massive quantities of ice have broken off into the ocean, and concerns have been raised regarding the possible hazards to shipping as the “country-sized” bergs move north. All one needs is a source of thermal energy to melt the icebergs and the problem would be solved.

If one had an unlimited supply of Life Savers, would the combustion of a mole of them be sufficient to melt the iceberg that is likely to be formed by the collapse of the portion of the Larsen C ice shelf mentioned above?

The following is a summary of the information required, along with the results of the calculations necessary to obtain a final answer. Instructors may decide to provide all, or only a portion, of the following information to their students. The caculated answers are rounded to three signifciant digits for simplicity.

To melt that enormous block of ice, a total of “only” 20 nanomoles of Life Savers would be required.

Students should find this exercise to be extremely effective in conveying the magnitude of Avogadro’s constant, as well as giving them additional practice in unit conversions and searching for physical constants. I hope that other instructors will be able to make use of this exercise with their students.

References

1. M. Naji, Chem 13 News, September 1993, 223, page 14.
2. D. Todd, Journal of Chemical Education, 62, 76, 1985.
3. A. Last, Chem 13 News, May 1990, 195, page 6.
4. R. DeLorenzo, Chem 13 News, September 1992, 214, page 1.
5. K. Brody, Chem 13 News, November 1994, 234, page 7. (Email Jean Hein, @ jhein@uwaterloo.ca if you would like copies of these Chem 13 News articles.)

## Data required

Area of the calved iceberg: | 5000 km2
Thickness of the ice: | 1000 ft
Mass of a Life Saver (assumption made that it is pure sucrose): | 2.36 g
Molar mass of sucrose (C12H22O11): | 342.3 g/mol
delta Hcomb of sucrose: | - 5642 kJ/mol
Density of ice: | 0.917 g/cm3
delta Hfusion of ice: | 6.00 kJ/mol

## Calculated Values

Energy released per Life Saver: | 38.9 kJ
Volume of ice: | 1.53 x 103 km3
Mass of ice: | 1.40 x 1018 g
Amount of ice: | 7.78 x 1016 mol
Energy needed to melt ice: | 4.67 x 1017 kJ
Number of Life Savers required: | 1.20 x 1016
Amount of Life Savers: | 1.99 x 10-8 mol

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