Chemical Calculations At A Glance (P. Yates)

Chemical Calculations at a Glance
PAUL YATES

Chemical Calculations at a Glance

Chemical Calculations at a Glance
Paul Yates

C

2005 Blackwell Publishing Ltd

Editorial offices: Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK Tel: +44 (0)1865 776868 Blackwell Publishing Inc., 350 Main Street, Malden, MA 02148-5020, USA Tel: +1 781 388 8250 Blackwell PublishingAsia Pty Ltd, 550 Swanston Street, Carlton, Victoria 3053, Australia Tel: +61 (0)3 8359 1011 The right of the Author to be identified as the Author of this Work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic,mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. First published 2005 by Blackwell Publishing Ltd Library of Congress Cataloging-in-Publication Data Yates, Paul. Chemical calculations at a glance / Paul Yates. – 1st ed. p. cm. Includes index. ISBN 1-4051-1871-7 (pbk. : alk. paper) 1.Chemistry – Mathematics. I. Title. QD39.3.M3Y382 2005 540 .1 51 – dc22 ISBN 1-4051-1871-7 A catalogue record for this title is available from the British Library Set in 10/11 pt Times by TechBooks, New Delhi, India Printed and bound in India by Replika Press Pvt. Ltd, Kundli The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has beenmanufactured from pulp processed using acid-free and elementary chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. For further information on Blackwell Publishing, visit our website: www.blackwellpublishing.com 2004019623

Contents
Preface Acknowledgements A 1 2 3 4 B 5 6 7 8 9 10 C 1112 13 14 15 16 D 17 18 19 20 21 22 23 24 25 E 26 27 28 29 30 31 F 32 33 34 35 36 37 38 39 Introductory Skills Rules of Indices Scientific Notation Units Significant Figures and Decimal Places Handling Data Calculated Quantities Uncertainties Maximum Possible Error Maximum Probable Error Simple Statistics The t-Statistic Algebra Precedence Fractions Inequalities Rearranging Equations Ratios andProportionality Factorials Functions Functions of a Single Variable Functions of Many Variables Natural Logarithms Logarithms to Base 10 The Exponential Function Inverse Functions The Equation of a Straight Line Quadratic Equations Sequences and Series Spatial Mathematics Trigonometry Inverse Trigonometric Functions Coordinate Geometry Vectors Vector Multiplication Complex Numbers Calculus TheDerivative Differentiation Differentiation of Functions Differentiating Combinations of Functions Higher-Order Differentiation Stationary Points Partial Differentiation Integration vii viii 1 2 4 6 10 13 14 18 20 22 26 30 33 34 38 42 46 48 50 53 54 58 62 66 68 72 74 80 84 87 88 92 96 102 106 110 113 114 118 122 126 130 134 138 144

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Contents

40 Integration of Functions 41 Integration TechniquesG 1 2 3 4 5 Appendices SI Prefixes SI Unit Conversions Non-SI Units Values of Physical Constants Table of t-Values

148 152 159 160 160 160 161 161 163 191

H Solutions to Problems Index

vi

Preface
Why this book? I realise that I probably only have a few seconds to answer this question before you decide whether to read any further, so here are two points which summarise the philosophybehind it. The first is that wherever possible the mathematics is presented through the use of actual chemical examples. I firmly believe that this is much more valuable than using abstract problems. The end of chapter questions all contain traditional problems using x and y, but then go on to explore chemistry using the wealth of symbols to be found in physical chemistry textbooks. Second, at the...