Quantitative science

Analytical chemistry is inherently a quantitative science. Whether determining the concentration of a species in a solution, evaluating an equilibrium constant, measuring a reaction rate, or drawing a correlation between a compound s structure and its reactivity, analytical chemists make measurements and perform calculations. In this section we briefly review several important topics involving the use of numbers in analytical chemistry. 

Catalyst preparation is more an art than a science. Many reported catalyst preparations omit important details and are difficult to reproduce exacdy, and this has hindered the development of catalysis as a quantitative science. However, the art is developing into a science and there are now many examples of catalysts synthesi2ed in various laboratories that have neady the same physical and catalytic properties. 

Chemistry is a quantitative science. The experiments that you carry out in the laboratory and the calculations that you perform almost always involve measured quantities with specified numerical values. Consider, for example, the following set of directions for the preparation of aspirin (measured quantities are shown in italics). 

To this point, our study of chemistry has been largely qualitative, involving very few calculations. However, chemistry is a quantitative science. Atoms of elements differ from one another not only in composition (number of protons, electrons, neutrons), but also in mass. Chemical formulas of compounds tell us not only the atom ratios in which elements are present but also the mass ratios. 

You ve probably already heard a lot about your general chemistry course. Many think it is more difficult than other courses. There may be some justification for that opinion. Besides having its very own specialized vocabulary, chemistry is a quantitative science, which means that you need mathematics as a tool to help you understand the concepts. As a result, you will probably receive a lot of advice from your instructor, teaching assistant, and fellow students about how to study chemistry. We hesitate to add our advice experience as teachers and parents has taught us that students do surprisingly well without it We would, however, like to acquaint you with some of the learning tools in this text. They are described in the pages that follow. 

Chemistry is a quantitative science. This means that a chemist wishes to know more than the qualitative fact that a reaction occurs. He must answer questions beginning How much. . . The quantities may be expressed in grams, volumes, concentrations, percentage composition, or a host of other practical units. Ultimately, however, the understanding of chemistry requires that amounts be related quantitatively to balanced chemical reactions. The study of the quantitative relationships implied by a chemical reaction is called stoichiometry. 

Chemistry is a quantitative science, and chemists frequentiy measure amounts of matter. As the atomic theory states, matter consists of atoms, so measuring amounts means measuring numbers of atoms. Counting atoms is difficuit, but we can easiiy measure the mass of a sampie of matter. To convert a mass measurement into a statement about the number of atoms in a sampie, we must know the mass of an individuai atom. 

Over the next 30 years, Patterson used mass spectroscopy and clean laboratory techniques to demonstrate the pervasiveness of lead pollution. He traced the relationships between America s gas pump and its tuna sandwiches, between Roman slaves and silver dimes, and between Native American Indians and polar snows. He forged as close a connection between science and public policy as any physical scientist outside of medical research. He made the study of global pollution a quantitative science. And marrying his stubborn determination to his passionate conviction that science ought to serve society, Patterson never budged an inch. 

Francis Albarede has been a very active actor in this evolution towards quantitative science. His abundant scientific contributions published in the best international journals are all focussed on the goal of building a quantitative science. He is one of the leading scientists in this area and has now decided to broaden his approach by writing a book on geochemical modeling. This book has no equivalent in the present literature. It explains how we can build mathematical models to explain geochemical observations. 

At the time of the first syntheses of the pharmaceutically active ingredients of natural products, the pioneers of pharmacology, Ehrlich, Langley, and Hill among others, were engaged in turning the study of the mode of action of drugs into a quantitative science. By... 

The aim of the book is to describe in all simplicity the combinatorial and quantitative science of nucleosynthesis, a pure stellar arithmetic, chaste and contemplative, cloaked in the ironic reticence of nnmbers. It is so penetrating and revealing that it may be considered as our most powerful tool for divulging the material history of the Cosmos. 

When Dalton propounded his theory, chemistry was not yet a quantitative science. Chemists did not know how elements combined or whether they always combined in the same proportions. Indeed, many chemists believed that the ratio of different elements in a... 

Perhaps it is worth emphasizing again that the importance of Dalton s theory didn t lie in the assumption that matter is composed of indestructible atoms. That was a very old idea. On the contrary, his idea was significant because it was a theory that explained how chemical compounds are formed and because the idea of atoms with different relative weights made it possible to turn chemistry into a quantitative science. As long as chemists held on to the old idea that elements could combine with one another in a variety of different proportions, they could describe chemical reactions only in a qualitative manner. It was Dalton who changed all this. 

Modern inorganic chemistry is a quantitative science. Consequently, when performing experimental work, students must determine the yield of the substances obtained and certain constants such as the boiling points, solubility, and cryohydrate points, and also perform the required calculations with the use of the fundamentals of thermodynamics. 

M. Bordons, F. Morulo, L Gomez, in Handbook of Quantitative Science and Technology Research (Eds. H. F. Moed, W. Glanzel, U. Schmoch), Dordrecht Kluwer, 2004, 437-456. 

Quantum electrodynamics (QED) is one of the most successful, unifying theories of physics.In fact, the theory of QED underlies all the experiments I have just Hsted. Eurthermore, with QED and the fine-structure constant, physicists can predict the values of many physical parameters to a high level of precision. For these reasons, QED is highly regarded by physicists. Nonetheless, QED, like all theories of physics, is always vulnerable. Since the theory of QED underlies all the various experiments shown above, the measured values of the fine-structure constant from these different experiments should be the same. If these experiments revealed different values of a, even slightly different values, questions as to the validity of QED would automatically follow. That s the way physics and other quantitative sciences work. 

This book is designed to help you leam the fundamentals of chemistry. To be successful, you must master the concepts of chemistry and acquire the mathematical skills necessary to solve problems in this quantitative science. If your algebra is rusty, you should polish it up. Appendix 1 reviews the algebra used in basic chemistry and also shows how to avoid mistakes while solving chemistry problems with your scientific calculator. The factor label method is introduced in Chapter 2 to show you how to use units to help with problem solutions. You can help yourself by using the standard symbols and abbreviations for various quantities (such as m for mass, m for meter, mol for moles, and M for molarity). Always use the proper units with your numerical answers it makes a big difference whether your roommate s pet is 6 inches long or 6 feet long ... 

Chemistry is a quantitative science, which means that it is concerned with measurements that involve quantities or numbers, such as the amount of space a substance takes up or how much it weighs. Those measurements, which analyze the quantity of matter, are of especial importance to chemists. 

Medicine is becoming increasingly an objective and quantitative science, and like other sciences demands a realistic appraisal of the value of the numerical data upon which its conclusions are based. No longer is it permissible to regard a result of a blood glucose estimation, for instance, as an absolute value beyond question. Instead, such a figure must... 

In this and the previous chapter we have emphasized least-squares methods. Because computers can facilitate their implementation, such methods have become part and parcel of quantitative science. The emphasis must now shift to the appropriate choice of functions to be fitted, and to a careful consideration of the nature of the experimental uncertainties. Unfortunately, the latter topic is beyond the scope of this short book. 

As mentioned, physical chemistry is a quantitative science, which implies that equations will frequently be given. It may be useful to point out that equations can be of various types. Some equations define a property, like pressure equals force over area. Such an equation is by definition exact. Generally, the sign for is defined as ( = ) is used rather than is equal to (=) ... 

The first mass spectrometer, developed in the 1920s by the English physicist F. W. Aston,1 was crude by today s standards. Nevertheless, it provided indisputable evidence of the existence of isotopes—neon-20 (atomic mass 19.9924 amu and natural abundance 90.92 percent) and neon-22 (atomic mass 21.9914 amu and natural abundance 8.82 percent). When more sophisticated and sensitive mass spectrometers became available, scientists were surprised to discover that neon has a third stable isotope with an atomic mass of 20.9940 amu and natural abundance 0.257 percent (Figure 3.4). This example illustrates how very important experimental accuracy is to a quantitative science like chemistry. Early experiments failed to detect neon-21 because its natural abundance is just 0.257 percent. In other words, only 26 in 10,000 Ne atoms are neon-21. The masses of molecules can be determined in a similar manner by the mass spectrometer. 

In the period 1775-1780, Lavoisier established chemistry as a quantitative science by proving that in the course of a chemical reaction the total mass is unaltered. The conservation of mass in chemical reactions proved ultimately to be a death blow to the phlogiston theory. Shortly after Lavoisier, Proust and Dalton proposed the laws of definite and multiple proportions. In 1803 Dalton proposed his atomic theory. Matter was made up of very small particles called atoms. Ever kind of atom has a definite weight. The atoms of different elements have different weights. Compounds are formed by atoms which combine in definite ratios of (usually small) whole numbers. This theory could give a satisfying interpretation of the quantitative data available at the time. 

Physics is a science that deals with matter and energy, and their interactions. It is a quantitative science of measurement, experiment, and systanatization of experimental results. The scientific method is used in its most classic sense to formulate principles or laws that can be widely applied in predicting results to be achieved in engineering applications. 

Heilbron, John. Weighing Imponderables and Other Quantitative Science around 1800. Berkeley University of California Press, 1993. 

Neither pugging nor degassing is amenable to a design methodology based upon quantitative science. However, the significance of the two effects is well known and practical means for performing these available. 

---