Chapter 1 Problems
1, 2, 3 = straightforward, intermediate, challenging
Section 1.2 Matter and Model-Building
Note: Consult the endpapers, appendices, and tables in the text whenever necessary in solving problems. For this chapter, Appendix B.3 may be particularly useful. Answers to odd-numbered problems appear in the back of the book.
1. A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure P1.1a. The atoms reside at the corners of cubes of side L = 0.200 nm. One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, ...view middle of the document...
Find its radius.
7. Calculate the mass of an atom of (a) helium, (b) iron, and (c) lead. Give your answers in grams. The atomic masses of these atoms are 4.00 u, 55.9 u, and 207 u, respectively.
8. The paragraph preceding Example 1.1 in the text mentions that the atomic mass of aluminum is
27.0 u = 27.0 (1.66 ( 10(27 kg. Example 1.1 itself says that 27.0 g of aluminum contains 6.02 ( 1023 atoms. (a) Prove that each one of these two statements implies the other. (b) What If? What if it’s not aluminum? Let M represent the numerical value of the mass of one atom of any chemical element in atomic mass units. Prove that M grams of the substance contains a particular number of atoms, the same number for all elements. Calculate this number precisely from the value for u quoted in the text. The number of atoms in M grams of an element is called Avogadro’s number NA. The idea can be extended: Avogadro’s number of molecules of a chemical compound has a mass of M grams, where M atomic mass units is the mass of one molecule. Avogadro’s number of atoms or molecules is called one mole, symbolized as 1 mol. A periodic table of the elements, as in Appendix C, and the chemical formula for a compound contain enough information to find the molar mass of the compound. (c) Calculate the mass of one mole of water, H2O. (d) Find the molar mass of CO2.
9. On your wedding day your lover gives you a gold ring of mass 3.80 g. Fifty years later its mass is 3.35 g. On the average, how many atoms were abraded from the ring during each second of your marriage? The atomic mass of gold is 197 u.
10. A small cube of iron is observed under a microscope. The edge of the cube is 5.00 ( 10–6 cm long. Find (a) the mass of the cube and (b) the number of iron atoms in the cube. The atomic mass of iron is 55.9 u, and its density is 7.86 g/cm3.
11. A structural I beam is made of steel. A view of its cross-section and its dimensions are shown in Figure P1.11. The density of the steel is 7.56 ( 103 kg/m3. (a) What is the mass of a section 1.50 m long? (b) Assume that the atoms are predominantly iron, with atomic mass
55.9 u. How many atoms are in this section?
12. A child at the beach digs a hole in the sand and uses a pail to fill it with water having a mass of 1.20 kg. The mass of one molecule of water is 18.0 u. (a) Find the number of water molecules in this pail of water. (b) Suppose the quantity of water on Earth is constant at 1.32 ( 1021 kg. How many of the water molecules in this pail of water are likely to have been in an equal quantity of water that once filled one particular claw-print left by a Tyrannosaur, hunting on a similar beach?
Section 1.4 Dimensional Analysis
13. The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position s = kamtn, where k is a dimensionless constant. Show by dimensional analysis that this...