Solutions Manual for Mathematics for Physical Chemistry

Solutions Manual for Mathematics for Physical ChemistryRobert G. Mortimer AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD • PARIS SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Academic Press is an Imprint of Elsevier Solutions Manual for Mathematics for Physical Chemistry Fourth Edition Professor Emeritus Rhodes College Memphis, Tennesseev Preface vii 1 Problem Solving and Numerical Mathematics e1 2 Mathematical Functions e7 3 Problem Solving and Symbolic Mathematics: Algebra e13 4 Vectors and Vector Algebra e19 5 Problem Solving and the Solution of Algebraic Equations e23 6 Differential Calculus e35 7 Integral Calculus e51 8 Differential Calculus with Several Independent Variables e59 9 Integral Calculus with Several Independent Variables e69 10 Mathematical Series e79 11 Functional Series and Integral Transforms e89 12 Differential Equations e97 13 Operators, Matrices, and Group Theory e113 14 The Solution of Simultaneous Algebraic Equations with More Than Two Unknowns e125 15 Probability, Statistics, and Experimental Errors e135 16 Data Reduction and the Propagation of Errors e145 Contentsvii This book provides solutions to nearly of the exercises and problems in Mathematics for Physical Chemistry, fourth edition, by Robert G. Mortimer. This edition is a revision of a third edition published by Elsevier/Academic Press in 2005. Some of exercises and problems are carried over from earlier editions, but some have been modified, and some new ones have been added. I am pleased to acknowledge the cooperation and help of Linda Versteeg-Buschman, Beth Campbell, Jill Cetel, and their collaborators at Elsevier. It is also a pleasure to acknowledge the assistance of all those who helped with all editions of the book for which this is the solutions manual, and especially to thank my wife, Ann, for her patience, love, and forbearance. There are certain errors in the solutions in this manual, and I would appreciate learning of them through the publisher. Robert G. Mortimer Preface Chapter 1 Problem Solving and Numerical Mathematics EXERCISES Exercise 1.1. Take a few fractions, such as 23,49 or 3 7 and represent them as decimal numbers, finding either all of the nonzero digits or the repeating pattern of digits. 2 3 = 0. · · · 4 9 = 0.4444444 · · · 3 7 = 0. · · · Exercise 1.2. Express the following in terms of SI base units. The electron volt (eV), a unit of energy, equals 1.6022 × 10−18 J. a. (13.6 eV)1.6022 × 10−19 J 1 eV  = 2.17896 × 10−19 J ≈ 2.18 × 10−18 J b. (24.17 mi)5280 ft 1 mi  12 in 1 ft  0.0254m 1 in  = 3.890 × 104 m c. (55 mi h−1) 5280 ft 1 mi  12 in 1 ft  0.0254 m 1 in   1 h 3600 s = 24.59 m s−1 ≈ 25 m s−1 d. (7.53 nm ps−1)  1 m 109 nm 1012 ps 1 s  = 7.53 × 103 m s−1 Exercise 1.3. Convert the following numbers to scientific notation: a. 0. = 2,34 × 10−6 b. 32.150 = 3.2150 × 101 Exercise 1.4. Round the following numbers to three significant digits a. ≈ 123,000,000,000 b. 46.45 ≈ 46.4 Exercise 1.5. Find the pressure P of a gas obeying the ideal gas equation PV = nRT if the volume V is 0.200 m3, the temperature T is 298.15 K and the amount of gas n is 1.000 mol. Take the smallest and largest value of each variable and verify your number of significant digits. Note that since you are dividing by V the smallest value of the quotient will correspond to the largest value of V. P = nRT V = (1.000 mol)(8.3145 J K−1 mol−1)(298.15 K) 0.200 m3 = 12395 J m−3 = 12395 N m−2 ≈ 1.24 × 104 Pa Pmax = nRT V = (1.0005 mol)(8.3145 J K−1 mol−1)(298.155 K) 0.1995 m3 = 1.243 × 104 Pa Pmin = nRT V = (0.9995 mol)(8.3145 J K−1 mol−1)(298.145 K) 0.2005 m3 = 1.236 × 104 Pa Mathematics for Physical Chemistry. © 2013 Elsevier Inc. All rights reserved. e