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# Macromolecules

### Assignment 3, due on Oct. 13 before 4:30 pm

Inorganic macromolecules are present in elements and compounds. They are present in diamond, graphite, fullerenes, sulfur, phosphorus, silicate, and boron nitride.

Since vague questions asking you to describe or discuss these structures have caused a considerable frustration in some members of the class, the following questions have changed to demand specific information. The wording put in here is for the purpose of directing your thought, because you may not see the purpose of the assignment. However, if you feel that you have a better way to write up your assignment, please feel free to change some parts as suggested here.

The format of the discussion is suggested, and please provide the information in the blank (__) spaces. You may down load this file and use a word processor to do your assignment, leaving spaces for your diagrams, which must be hand drawn not by photo-copying or electronic images from other source.

## Problems

1. Discuss the structure of diamond, a metastable allotrope of carbon at room temperature.

• The carbon nuclei (of the atom) have a radius approximately __ m whereas the atomic radius is about __m. All carbon nuclei have __ protons, and natural isotopes of carbon have mass number of __, __, and __; and their atomic nuclei have __, __, and __ neutrons respectively.

• The abundances of the natural carbon isotopes are 98.89% and __ respectively for 12C, and 13C respectively, and only traces of radioactive (beta emitting) 14C is present. The mass of 13C is 13.003355 based on the standard 12C, whose mass is defined as 12 exactly. From these values, the average atomic weight of carbon is __, calculated using the formulation:

__

• The electronic configuration of carbon is __. The quantum numbers for the orbitals are:
```Orbital n   l  m
------- -- -- --
1s   __ __ __          __                    __
2s   __ __ __
2p   __ __ __       a 2s orbital and a 2p orbital (any of three)
```
Draw a diagram (free hand in any fashion) of the 2s, and 2p orbitals.

• A single bond between carbon atoms (C-C) is due to the overlaps of hybrid orbitals, __. These 4 orbitals of each carbon can be represented by diagrams as shown below:

__ __ __ __
And a diagram putting all 4 orbitals together is shown below:

__
And the overlap of orbitals in the formation of single bonds are shown below:

__

• A double bond between carbon atoms (C=C) consists of a sigma bond, which uses a hybrid orbital of __, and a pi bond, which are due to overlap of hybrid orbitals of __. These hybrid orbitals are shown below:

__, __

• The overlap of atomic orbitals in the formation of C=C double bonds are shown below:

__
This diagram shows the overlap of orbitals in both bonds in the C=C.

• The structure of graphite consists of sheets of six-membered rings. The bonding on these rings are similar to __ (one or some organic compounds). The structure of diamond consists of a three-dimensional network in which every carbon is connected to 4 neighbouring carbons by single bonds. The C-C bond distance is 1.5445x10-10 m, approximately the same as that of __ (one or some organic compounds).

• Using the bond distances, we can calculated the edge length of the unit cell (as outlined by the cube in this diagram) of diamond to be __. This value is derived in the following way:

__

• The number of carbon atoms in the unit cell is __. Thus, using the average atomic weight and the cell edge calculated above, the density of diamond can be calculated to be __. The formulation is:

__

The observed value tabulated in __(give reference) is __.

• The number of carbon atoms in a 5.0-carat diamond is __, and despite the existence of some defects, the whole crystal is a molecule due to the extensive bonding. The volume occupied by this molecule is __, calculated from the density given earlier. Thus, the average volume occupied by an atom is __. If this volume is spherical, the radius of this volume is __.

2. Silicon is perhaps the most important element in information technology (IT), and its crystal and electronic structures form the basis of its application in the electronic industry. Discuss the bonding and structure of this key element.

• Silicon is in the same group as carbon (Problem 1), and its electronic configuration is __. The atomic orbitals occupied by the valance electrons are: __, and __.

• Elemental silicon has the same structure as __, but silicon does not have any allotrope with graphite-like structures. This is mainly due to the inability of silicon to form __ bonds. Some other factors are: __.

• From the silicon density of 2.33 g cm-3, the edge length of the cubic unit cell (similar to that of the diamond structure) can be shown to be __, as follows.

__

The diamond structure is common to not only group IV (or 14 in IUPAC convention) elements but to many other compounds such as zinc blend (c-BN, GaAs, ZnS, CdS etc). Thus, the skills you have developed in this assignment will enable you to solve other problems involving some cubic structures.

3. What are the allogropes of sulfur? At what temperature will one transform into another? How do atomic orbitals overlap in the formation of sulfur molecules and chains? How are the properties of sulfur related to the structure and bonding of sulfur?

• Rhombic and monoclinc sulfur are allotropes of sulfur, with the former stable at room temperature, but monoclinc sulfur is stable above 368 K. In both allotropes, the molecules S8 are present. This molecule has the structure as shown:

__

When heated, sulfur molecules breakup and long chains are formed. This chain has a structure as shown:

__

• In order to understand the structure of sulfur, we need to look at its electronic configuration. The __ valence electrons of sulfur has the electronic configuration (or occupy the atomic orbitals) of:

__

• The __ hybrid atomic orbitals are used in the formation of the sulfur molecules. These orbitals have the same orientation as those used in the formation of diamond. However, the number of valence electrons in sulfur is __, and two of the orbitals already have a pair of electrons.

Thus, the orbital overlap in the formation of sulfur molecules is shown as follows:

__

The same argument applies to the bonding for the molecule H2S, and the overlap of orbitals for H2S is shown below:

__

The viscous molten sulfur, when cooled suddenly, becomes an elastic sulfur. The viscosity and the elasticity can be explained this way. ________.

4. What are the allotropes of phosphorus? How are their properties related to their structures. Discuss the bonding for these structures. (No guide or hint is given here, and you are free to present your information in any format.)

______
______