Theories of Matter
There is a wide variety of chcmical and physical theories from which wc select as our example theories of matter (atoms, molecules, solids, nudci, and elementary particles). Wc can illustrate the ACP cpistcmology with the familiar ball-and-stick theory of molcculcs. This theory employs sticks and coloured balls with holes drilled in them at prescribed angles. The procedure consists of assembling the balls and sticks into figures in all possible ways. The predictions of the theory includc molccular geometry and the number of isomers cxpcctcd for the moleculc in question. Wc all feel comfortable with this ball-and-stick theory bccausc it operates in the three-dimensional, classical world of our senses and seems “real” to us. While it is a very useful theory, it has a number of significant failures. For example, it fails to predict both the geometry and the number of isomers of benzene. More seriously, it fails to predict the clcctronic, vibrational, and rotational spcctra of molcculcs. This failure to predict spcctra is common to all classical theories and has made ncccssary the development of a new theory which includes predictive powers in this area. The nonclassical quantum theory is a theory that predicts more diversely, more quantitatively, but not more simply than the ball-and-stick theory.
Quantum theory has two essentially equivalent versions: one concerned with wave mechanics (derived from Schrocdingcr’s work) and one concerned with matrix mechanics (due to Dirac-Hciscnbcig) which is our choice. The procedure of the matrix mechanics theory o fmatter (MMTM) is very interesting but is not relevant to the application of the procedure. It employs vector space and their bases, operators, matrices, secular equations, eigenvectors, eigenvalues, groups, group algebras, etc., conccpts that arc well known to mathematicians but essentially unknown, to beginning physicists and chcmists. In conscqucncc MMTM may seem less “real” to these beginners than the classical ball-and-stick theory. The MMTM procedure can be applied uniformly to atoms, molcculcs, solids, nuclci, and elementary particlcs. It is dear that the conccpt of structure is much simpler and more intuitive in the ball-and-stick theory than in the MMTM theory. The MMTM structure concept is that of a set of building blocks (basis vector of a vcctor space) that arc assembled under supervision of the Hamiltonian into a physically significant set of structures (eigenvectors to the Hamiltonian).
The numerical and algcbraic calculations required in the MMTM procedure can become quite tedious but fortunately many of them have been or can be programmed for personal computers. The calculations of MMTM then bccomc trivial and operational familiarity is quickly acquired. Consequently, the challenging part of MMTM bccomcs the selection of the vcctor spacc and the Hamiltonian and then the interpretation of the output.
Molccular Theory
Matrix mechanics theory of matter (MMTM) is a better molccular
theory than the ball-and-stick molccular theory. In the ab initio MMTM molecular theory the only parameters required by the procedure arc Planck’s constant, the charge and mass of the clcctron, and the number and kind of nuclci. This theory can for many molcculcs predict with high accuracy their equilibrium geometries and their forcc constants. Unfortunately it predicts other properties, c. g., dissociation energy,
clcctronic spcctra, etc., with a lower accuracy. The accuracy can be
increased by the use of larger vector spaces, a technique that can be very difficult, very expensive, and/or impossible with the currently available scalar computers. The problem bccomcs easier with supercomputers that employ vector and/or parallel processors and larger memories, but there will always be some upper limit to the size of a molcculc on which accuratc ab initio calculations can be made. A theory which is less strongly computcr-dcpcndcnt is the semiempirical molecular theory. Its procedure employs a smaller vcctor spacc and its parameters arc determined by comparison of predictions with a small number of observations.
An example of a scmicmpirical molccular theory is the л -electron theory of conjugated, unsaturatcd hydrocarbons. Here the size of the vcctor spacc is rcduccd by ignoring corc and 5-bondcd clcctrons and employing a single n-orbital for cach carbon site. The size of the vcctor spacc can be further rcduccd by the use of either of two more approximate theories: the n-HUckel molecular orbital theory, which resembles the Bohr theory of the atom, and the я-valence bond theory, which resembles the ball-and-stick theory.
Text 14
Differentiating between Primary,
Secondary, and Tertiary Alcohols
A primary or secondary aliphatic alcohol dissolved in pure glacial acetic acid decolourizes a water solution of KMnO.», while a tertiary alcohol fails to do so. A secondary alcohol will continue to rcact with KMn04 solution if a little concentrated sulphuric acid is added, while a primary alcohol docs not. By means of Uiosc reactions one may distinguish between primary, secondary, and tertiary alcohols of the paraffin series. Further, no more than one drop of the alcohol is ncccssary to make the test, which fact should make it especially interesting in investigations where only small quantities of alcohol arc available.
A convenient procedure is as follows: A 4-inch test-tube is fitted with a one-hole rubber stopper carrying a glass rod which rcachcs to the
bottom of the test-tube. Glacial acctic acid (3 ml.) is introduced into die test-tube, and then one drop of the pure unknown is added. A saturated, filtered solution of KMn04 in water is added, a drop at a time, to the contents of the tube, with stoppering and vigorous shaking between cach addition.
If no dccolourization of die KMn04 takes place, the alcohol is tertiary. If dccolourization takes place (best ascertained from time to time by spotting the mixture by means of the glass rod into filter paper), the addition of KMn04 is continued a drop at a time until the pink colour of KMnO< persists. When dccolourization has ccascd to take place, a drop of conccntratcd H2S04 is added and the addition of KMn04with shaking is continued. If the pink colour is not discharged under these conditions, the alcohol is primary. If dccolourization proceeds again after the addition of HjS0 4, followed by a final permanent pink colour, the alcohol is secondary.
It is advisable to run a blank test of the glacial acctic acid used, bccausc some glacial acid samples contain extraneous materials which react with KMn04 solution.
This method has been found reliable for all aliphatic alcohols through the amyl group. Whether it can be extended to other classes of alcohols has not been determined.
To the student in the laboratory it would seem that this different approach to the differentiation of the alcohols would be much more simple and direct than the Lucas test currently in manuals.
Text 15
A Brief History of Polypeptide Chemistry
Protein chcmistry really began in the 1830s with Mulder’s systematic investigation of nitrogenous biological materials, such as blood fibrin, egg white, gelatins, and silk. In 1840, Huncfcld was the first to ciystallizc a protein— viz., hemoglobin. During the following 90 years, amino acids, the building blocks of protein, were isolated by many investigators, but for many years it was not realized how amino acids were linked to form proteins. In fact, it was not until 1902 that Fisher and Hofmcister independently proposed that amino acids were joined together by peptide bonds (—CO—NH—).
It was not the early work on protein chcmistry, however, that led to the conccpt of enzymes as catalysts of biological reactions. Indeed, it was the early research on fermentation of Lavoisier in the later 1700s and the subsequent work by Schwann, Pasteur, and Buchner between 1830 and 1900 that led to the development of this conccpt. Oncc the role of enzymes was realized, scientists, uncluding Harden and Young, Embodcn and Meyerhof, Krebs, Lyncn and Lipmann, were eventually able to formulate die individual steps of most of the mctabolic processes in the body.
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