Solutions to General Chemistry (Linus Pauling)/The Atomic and Molecular Structure of Matter

1. What are the differences between a hypothesis, a theory, a law, and the fact? Classify the following statements as hypotheses, theories, laws, or facts:
   1. The interior of the moon consists of granite and similar rocks.

      This can be considered a fact. The Apollo missions brought back hundreds of kilograms of diverse lunar rocks, including some with a composition not unlike granite.

   2. Hydrogen, nitrogen, oxygen, and neon are all gases under ordinary conditions.

      This statement is a conjunction of directly observed experimental facts.

   3. The force f acting on a body with mass $m$ causes it to be accelerated by the amount fm^-1.

      This statement is an inductive generalization over all forces acting on bodies with mass, which have been borne out by many observations from the seventeenth century onwards. It does not explain why this happens.

   4. The properties of gases can be explained by considering the motion of molecules comprising them.

      The keyword in this statement is 'explain'. Hypotheses and theories aim to explain observations, with the distinction being that theories are supported by a large body of empirical evidence. Specifically, the term 'theory' is ostensibly being used in the second sense given in the text, "a systematic body of knowledge, compounded of facts, laws, theories in the limited sense [of a hypothesis borne out], deductive arguments, and so on." This "systematic body" would encompass areas of physics and chemistry, such as thermodynamics.

   5. All crystals contain atoms or molecules arranged in a regular way.

      On the surface, this statement seems to be a definition, true de facto. However, Pauling appears to imply early on in the chapter that he is referring to the atomic theory of crystals, which explains why crystals have readily apparent regular, highly ordered structures. (Remember that the distinction between a law and a hypothesis or theory is that a law does not explain the facts it summarizes, while a hypothesis or theory does.)

2. Discuss some of the evidence for the atomic nature of matter.

   open-ended

3. The metal indium forms tetragonal crystals. The unit of structure is a rectangular parallelepiped, with edges a = 3.24 Å, b = 3.24 Å, and c = 4.94 Å... TODO

Problem 3 (as written) appears to have no solution. The positions of the atoms are given in the problem as 0,0,0, and 1/2, 1/2, 1/2 which implies a body-centered structure. Indium has a face-centered (not body-centered) tetragonal structure that can be solved. Each atom then has 4 closest neighbors and 8 more a little farther away. Do the math.