Problem 76 - Chemistry The Science in Context

Question

Ice under Pressure Kurt Vonnegut's novel Cat's Cradle describes an imaginary, high-pressure form of ice called "ice-nine." With the assumption that ice-nine has a cubic closest-packed arrangement of oxygen atoms with hydrogen atoms in the appropriate holes, what type of hole will accommodate the \(\mathrm{H}\) atoms?

Step-by-Step Solution

Answer

Answer: In ice-nine, hydrogen atoms are accommodated in the tetrahedral holes present in the cubic closest-packed arrangement of oxygen atoms.

Step 1: Understanding the cubic closest-packed arrangement

A cubic closest-packed (ccp) arrangement is a type of crystalline structure formed by arranging atoms in a way that they occupy the least possible space. In a ccp arrangement, the atoms are arranged in layers, with each layer being designated as either A or B, following an ABAB... pattern. The oxygen atoms in ice-nine are arranged in a ccp arrangement.

Step 2: Identifying the types of holes in a ccp arrangement

There are two types of holes present in a ccp arrangement - tetrahedral holes and octahedral holes. The tetrahedral holes are formed by four surrounding oxygen atoms, making a tetrahedron. The octahedral holes are formed by six surrounding oxygen atoms, making an octahedron. The size and shape of these holes can accommodate different types of atoms.

Step 3: Understanding the hydrogen atom's size and bonding

Hydrogen atoms are the smallest and lightest elements in the periodic table. Their size makes them suitable to fit into the smaller holes in a crystal structure. In the case of ice, hydrogen atoms bond with oxygen atoms through hydrogen bonds. To accommodate hydrogen atoms in ice-nine, we need to find holes that would allow hydrogen atoms to form hydrogen bonds with oxygen atoms.

Step 4: Determining the suitable hole for hydrogen atoms in ice-nine

Tetrahedral holes are smaller and more appropriate for hydrogen atoms to fit and form hydrogen bonds. In the ice-nine structure, hydrogen atoms can be accommodated into the tetrahedral holes formed by the ccp arrangement of oxygen atoms. This allows each hydrogen atom to form hydrogen bonds with the surrounding oxygen atoms in the structure.

Step 5: Conclusion

In the novel Cat's Cradle, ice-nine is a high-pressure form of ice in which oxygen atoms form a cubic closest-packed arrangement. Hydrogen atoms are accommodated in the tetrahedral holes present in the structure, allowing them to form hydrogen bonds with the surrounding oxygen atoms.

Key Concepts

Ice Structure

Ice is a fascinating form of water that exists in different structures, each with unique properties. The common ice we're familiar with, known as ice Ih, features a hexagonal structure. But under different conditions, such as temperature or pressure, ice can take on various other forms, each with its own distinct arrangement of atoms.
In the story "Cat's Cradle," the fictional "ice-nine" is described as having a cubic closest-packed (ccp) arrangement of oxygen atoms. The ccp structure is efficient, with the atoms packed tightly, minimizing the space they occupy. This form of ice is not found naturally and is a work of fiction, but it highlights the diversity of ice's structures in real life. Understanding these structures is crucial as they can affect the properties of ice, such as density and melting point.

Hydrogen Bonding

Hydrogen bonding is a critical concept in understanding ice and its structures. In water, hydrogen bonds form between the slightly positive hydrogen atoms of one molecule and the slightly negative oxygen atoms of neighboring molecules. This interaction gives water and ice their unique properties, such as high surface tension and lower density in its solid form.
An essential feature of hydrogen bonding is that it's not as strong as covalent or ionic bonds, but it's stronger than typical van der Waals forces. In ice, these hydrogen bonds link water molecules into a lattice, which is less dense than liquid water. Therefore, ice floats on water due to these bonds. In any form of ice, such as the fictional ice-nine, hydrogen bonding plays a key role in the stability and arrangement of its structure.

Tetrahedral and Octahedral Holes

In crystalline structures, like the cubic closest-packed arrangement, there are interstitial spaces or "holes" among the tightly packed atoms. These are the spaces into which smaller atoms, like hydrogen, can fit.

• Tetrahedral Holes: These holes are created by four atoms forming a tetrahedron shape around the interstitial space. They're smaller than octahedral holes and suitable for accommodating small atoms like hydrogen.
• Octahedral Holes: These are larger than tetrahedral holes, surrounded by six atoms forming an octahedral shape, and can hold larger ions or molecules.

In ice-nine's structure, as described in "Cat's Cradle," hydrogen atoms are believed to occupy the tetrahedral holes. Their small size makes it feasible for them to fit and participate in the hydrogen bonding with the surrounding oxygen atoms, contributing to the stability of the structure.

High-Pressure Ice Forms

Ice comes in several forms that occur under various conditions of temperature and pressure. While the typical ice we see in our freezers is known as Ice Ih, there are many other possible forms, each stable under different conditions.
These forms include Ice II, Ice III, Ice V, and Ice VI, among others. They exist at higher pressures and temperatures, where the molecules are forced into denser arrangements, altering their properties. These high-pressure forms of ice are incredibly fascinating for scientific research because they can simulate conditions found in the interior of icy planets and moons.
In the context of fiction, ice-nine exemplifies a high-pressure form that vastly differs from anything found naturally. Studying high-pressure ices helps us understand not only Earth's water but also the broader universe's water systems.