Earth, a planet teeming with life, is seen here in a satellite photograph.
Download Free PDF View PDF
183 philosophical implications of quantum mechanics and develop a new way of thinking about nature on the nanometer-length scale. This was undoubtedly one of the most signiicant shifts in the history of science. The key new concepts developed in quantum mechanics include the quantiza-tion of energy, a probabilistic description of particle motion, wave–particle duality, and indeterminacy. These ideas appear foreign to us because they are inconsistent with our experience of the macroscopic world. Nonetheless, we have accepted their validity because they provide the most comprehensive account of the behavior of matter and radiation and because the agreement between theory and the results of all experiments conducted to date has been impressively accurate. Energy quantization arises for all systems whose motions are connned by a potential well. The one-dimensional particle-in-a-box model shows why quantiza-tion only becomes apparent on the atomic scale. Because the energy level spacing is inversely proportional to the mass and to the square of the length of the box, quantum effects become too small to be observed for systems that contain more than a few hundred atoms. Wave–particle duality accounts for the probabilistic nature of quantum mechanics and for indeterminacy. Once we accept that particles can behave as waves, we can form analogies with classical electromagnetic wave theory to describe the motion of particles. For example, the probability of locating the particle at a particular location is the square of the amplitude of its wave function. Zero-point energy is a consequence of the Heisenberg indeterminacy relation; all particles bound in potential wells have nite energy even at the absolute zero of temperature. Particle-in-a-box models illustrate a number of important features of quantum mechanics. The energy-level structure depends on the nature of the potential, E n n 2 , for the particle in a one-dimensional box, so the separation between energy levels increases as n increases. The probability density distribution is different from that for the analogous classical system. The most probable location for the particle-in-a-box model in its ground state is the center of the box, rather than uniformly over the box as predicted by classical mechanics. Normalization ensures that the probability of nding the particle at some position in the box, summed over all possible positions, adds up to 1. Finally, for large values of n, the probability distribution looks much more classical, in accordance with the correspondence principle. Different kinds of energy level patterns arise from different potential energy functions, for example the hydrogen atom (See Section 5.1) and the harmonic oscil-lator (See Section 20.3). These concepts and principles are completely general; they can be applied to explain the behavior of any system of interest. In the next two chapters, we use quantum mechanics to explain atomic and molecular structure, respectively. It is important to have a rm grasp of these principles because they are the basis for our comprehensive discussion of chemical bonding in Chapter 6.
Download Free PDF View PDF
Polyfunctional acids and bases play important roles in many chemical and biological systems. The human body contains a complicated system of buffers within cells and within bodily fluids, such as human blood. Shown here is a scanning electron micrograph of red blood cells travel-ing through an artery. The pH of human blood is controlled to be within the range of 7.35 to 7.45, primarily by the carbonic acid-bicarbonate buffer system: CO 2 (g) 1 H 2 O(l) 8 H 2 CO 3 (aq) H 2 CO 3 (aq) 1 H 2 O(l) 8 H 3 O 1 (aq) 1 HCO 3 2 (aq) This chapter describes polyfunctional acid and base systems including buffer solutions. Calculations of pH and of titration curves are also described. I n this chapter, we describe methods for treating complex acid/base systems, including the calculation of titration curves. We define complex systems as solutions made up of (1) two acids or two bases of different strengths, (2) an acid or a base that has two or more acidic or basic functional groups, or (3) an amphiprotic substance, which is capable of acting as both an acid and a base. For more than one equilibrium, chemical reactions and algebraic equations are required to describe the characteristics of any of these systems. Each of the components in a mixture containing a strong acid and a weak acid (or a strong base and a weak base) can be determined provided that the concentrations of the two are of the same order of magnitude and that the dissociation constant for the weak acid or base is somewhat less than about 10 24. To demonstrate that this statement is true, Example 15-1 shows how a titration curve can be constructed for a solution containing roughly equal concentrations of HCl and HA, where HA is a weak acid with a dissociation constant of 10 24 .
Download Free PDF View PDF
