Homework #1 Humphrey Geology 4888/5888 Fall 2008 GLACIOLOGY

These are due next Tuesday (Sept 8). .

Notes:

Try to couch your answers at the appropriate level of accuracy that is implied by the question. You are free to use data from any source or to make reasonable assumptions, but state what you assume, or show the data you use and give the source of the data. Be aware that data and ideas from the Web are of highly variable quality, so if you use web sources you must included the URLs. To do the homework you will have to take 4 steps: figure out how to do the problem, decide on the data you need (if any), collect the necessary information, and finally produce the answer.

This should take you 1-2 hours. Your work must be neat, legible, and organized. I am not willing to wade through a mess and I will just give it back to you to re-do. You can work with others, but be aware that you will have to do similar questions on exams and quizzes, by yourself.

1 Sketch neatly by hand(!) a side view of an IceIh crystal, showing the arrangement of Oxygen atoms. Include the Hydrogen atoms, but include some Bernal-Fowler defects. You will need to include 20 or more Oxygen atoms in your sketch for it to make sense. (Feel free to copy any sketches you find, but I want yours done by hand)

2 (hard) Water is interesting stuff, and we have explored some of its properties. This question is designed to explore this more, and to get you to work with ‘orders of magnitude’ and with thinking in 3D.

a) Estimate the percentage of empty space in liquid water (i.e. space that is not occupied by molecules, assume the molecules are effectively solid inside the space defined by the component atoms)

b) Based on your answer to part a, explain why water expands on freezing?

Useful info. Water molecules are made up of two hydrogen atoms and one oxygen, roughly in a triangle. Water has a density of 1 gram per cubic centimeter, every 18 grams of water has Avogadro's number (6.02 x 10²³) water molecules, and small atoms have a size of about 1 angstrom with inter atom spacings (center to center) inside molecules of about 2.5 angstrom.

Hint: Try this question in two steps: first assume the molecules are spheres or cubes, with the size needed to enclose the ‘triangles’ of water. This should be fairly easy, and will give you the result that there isn’t much extra room in liquid water.

Hint: (this is the hard part) Then attempt to take into account the shape of the water molecule... basically an equilateral triangle with the atoms at the corners. If you want to get very fancy you can try looking at the water molecules as tetrahedra, with sides of ~3.5 angstrom, unfortunately tetrahedral do not tessellate space.

Hint: part b If you do 5a reasonably well, you may be able to see why water has the unusual property of expanding on freezing. The crux is that water bonds only at the tips of the tetrahedrons (or triangles) to a different molecule at each tip. Visualize that, and then answer part b.