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ILPAC Unit P1: the Gaseous State 1 UNIT ~ 1] The Gaseous State 11I~~llltrl]nl Pl-A N27913 c Inner London Education Authority 1963 First published 1963 by John Murray (Publishers) Ltd 50 Albemarle Street, London W1X 4BD All rights reserved. Unauthorised duplication contravenes applicable laws Printed and bound in Great Britain by Martin's of Berwick British Library Cataloguing in Publication Data ILPAC Unit P1: The gaseous state 1. Science 500 Q161.2 ISBN 0 7195 4039 9 ii CONTENTS PREFACE v Acknowledgements vi Key to ILPAC activity symbols and hazard symbols vii INTRODUCTION 1 Pre-knowledge 2 PRE-TEST 3 LEVEL ONE STATES OF MATTER 5 Translation, rotation and vibration 6 THE GAS LAWS 7 Boyle's law and Charles' law 7 The combined gas law 10 Gay-Lussac's law of combining volumes 10 AVOGADRO'S THEORY AND ITS APPLICATIONS 11 Avogadro's theory 11 Using Avogadro's theory to calculate reacting volumes 11 Determining the formula of a gaseous hydrocarbon 13 Molar volume of gases 15 Another method for determining the Avogadro constant 1B THE IDEAL GAS EQUATION 19 Deriving the ideal gas equation 19 The gas constant, R 20 Calculations using the ideal gas equation 21 Determination of molar mass of a gas 23 Experiment 1 - determining the molar mass of a gas 23 Determination of molar mass of a volatile liquid 26 Experiment 2 - determining the molar mass of a volatile liquid 27 LEVEL ONE CHECKLIST 31 LEVEL ONE TEST 33 LEVEL TWO TWO MORE GAS LAWS 37 Graham's law of effusion 37 Experiment 3 - determining the molar mass of a gas by effusion 3B Dalton's law of partial pressures 41 THE KINETIC THEORY OF GASES 44 A theoretical model of a gas 44 Deriving the gas laws from kinetic theory 46 DEVIATIONS FROM IDEAL BEHAVIOUR 49 Non-ideal behaviour 49 The van der Waals equation 51 iii THE VARIATION OF MOLECULAR SPEEDS 53 The Maxwell distribution 54 Use of the Maxwell distribution curve 55 Measuring molecular speeds - the Zartman experiment 58 The root-mean-square speed of gas molecules 59 LEVEL TWO CHECKLIST 60 END-OF-UNIT TEST 61 APPENDIX ONE THE LIQUEFACTION OF GASES 65 Andrews' isotherms and the critical point 65 Cooling of gases by expansion 66 APPENDIX TWO ADDITIONAL EXERCISES 69 ANSWERS TO EXERCISES 74 iv PREFACE This volume is one of twenty Units produced by ILPAC, the Independent Learning Project for Advanced Chemistry, written for students preparing for the Advanced Level examinations of the G.C.E. The Project has been sponsored by the Inner London Education Authority and the materials have been extensively tested in London schools and colleges. In its present revised form, however, it is intended for a wider audience; the syllabuses of all the major Examination Boards have been taken into account and questions set by these boards have been included. Although ILPAC was initially conceived as a way of overcoming some of the difficulties presented by uneconomically small sixth forms, it has frequently been adopted because its approach to learning has certain advantages over more traditional teaching methods. Students assume a greater responsibility for their own learning and can work, to some extent, at their own pace, while teachers can devote more time to guiding individual students and to managing resources. By providing personal guidance, and detailed solutions to the many exercises, supported by the optional use of video-cassettes, the Project allows students to study A-level chemistry with less teacher-contact time than a conventional course demands. The extent to which this is possible must be determined locally; potentially hazardous practical work must, of course, be supervised. Nevertheless, flexibility in time-tabling makes ILPAC an attractive propo- sition in situations where classes are small or suitably-qualified teachers are scarce. In addition, ILPAC can provide at least a partial solution to other problems. Students with only limited access to laboratories, for example, those studying at evening classes, can concentrate upon ILPAC practical work in the laboratory, in the confidence that related theory can be systematically studied elsewhere. Teachers of A-level chemistry who are inexperienced, or whose main discipline is another science, will find ILPAC very supportive. The materials can be used effectively where upper and lower sixth form classes are timetabled together. ILPAC can provide 'remedial' material for students in higher education. Schools operating sixth form consortia can benefit from the cohesion that ILPAC can provide in a fragmented situation. The project can be adapted for use in parts of the world where there is a severe shortage of qualified chemistry teachers. And so on. A more detailed introduction to ILPAC, with specific advice both to students and to teachers, is included in the first volume only. Details of the Project Team and Trial Schools appear inside the back cover. LONDON 1983 v ACKNOWLEDGEMENTS Thanks are due to the following examination boards for permission to reproduce questions from past A-level papers: Oxford Delegacy of Local Examinations End-of-Unit Test 10(1977), 11(1977) Southern Universities Joint Board Level One Test 9(1976) The Associated Examining Board Teacher-marked exercise, p6S(1977) Level One Test 6(1975) University of London Entrance and Schools Examinations Council Exercise 24(L1976) Teacher-marked Exercise, p53(L19S1) Level One Test 1(N1976), 2(L19S0), 3(N197S), 4(N1974), 5(L19S0), S(N197S) End-of-Unit Test 1(N19S0), 4,5&6(N1974), 9(L19S1), 12(L1977) Where answers to these questions are included, they are provided by ILPAC and not by the examination boards. Questions from papers of other examining boards appear in other Units. Photographs are included by permission as follows: Explo8ion, p 22 - Popperfoto Snooker table, p 53 - Colorsport Photographs of students - Tony Langham vi SYMBOLS USED IN ILPAC UNITS 0 W Reading Revealing exercises Exercise Discussion ~ ® ~\;lTest ~ Computer programme ~ Experiment 'A' Level question I[ 11 Video programme 'A' Level part question 00 [Q8 Film loop 'A' Level question Special paper Model-making Worked example Teacher-marKed exercise INTERNATIONAL HAZARD SYMBOLS Harmful Toxic Radioactive ~ ~ [iJ Flammable II Explosive ~ ,:v J!t Corrosive Oxidising -- ~ vii INTRO DUCTION In this Unit. we look first at the properties which distinguish gases from liquids and solids. Then we examine some of the experimental laws which describe the behaviour of gases. The most important of these laws is expressed by what is known as the ideal gas equation: pV == nRT Only hypothetical 'ideal' gases observe these laws precisely under all conditions, but we often apply them successfully to real gases. Level One ends with the application of the ideal gas equation to methods for deter- mining molar mass. In Level Two we first consider two more gas laws and then we develop the simple kinetic theory of gases to explain their behaviour. We show how the gas laws can be derived from the theory by making some assumptions about the nature of molecules in gases. We then explain how the approximate truth of these assumptions accounts for the observed deviations from the gas laws. Finally we consider the measurement and calculation of molecular speeds and the way molecular speeds vary in a sample of gas. In Appendix One we consider the liquefaction of gases, and in Appendix Two we give some additional numerical exercises. There are three experiments in this Unit; two are in Level One and one is in Level Two. There are two ILPAC video-programmes designed to accompany this Unit. They are not essential, but you should try to see them at the appropriate times if they are available. Volumes of reacting gases The distribution of molecular speeds 1 PRE-KNOWLEDGE Before you start work on this Unitl you should be able to: (1) obtain a value of temperature in K from one in °C; 3 (2) obtain a value of volume in dm from one in cm3; (3) obtain a value of pressure in atm from one in mmHg; (4) explain the abbreviation s.t.p; (5) calculate the relative molecular mass and the molar mass of a substance from its chemical formula; (6) calculate the amount of a substanc? from its mass and molar massl using the correct symbols and units; (7) calculate the density of a substance from its mass and volumel using the correct symbols and units; (8) define the Avogadro constant I L. PRE-TEST To find out whether you are ready to start Level Onel try the following testl which is based 011 the pre-knowledge items. You should not spend more than 30 minutes on this test. Hand your answers to your teacher for marking. 2 PRE-TEST 1. Express the following quantities in different units as indicated: (a) 23 DC (in K), (b) 59.0 cm3 (in dm3), (c) 758 mmHg (in atrn l. (3 ) 2. Explain the terms: (a) s.t.p., (b) the Avogadro constant. (4 ) 3. (a) Calculate the relative molecular mass of chloroethane, C2H5Cl. (1) (b) 25.0 cm3 of liquid chloroethane weighs 22.5 g. What amount of chloroethane is this? Use correct symbols and units. (2) (c) What is the density, p, of chloroethane? Use correct symbols and units. (C = 12.0, H = 1.0, Cl = 35.5) (2) (Total 12 marks) 3- LEVEL ONE STATES OF MATTER Gases have properties which enable us to distinguish them easily from solids and liquids, and these distinctive properties can be simply explained in terms of the spacing and movement of molecules. Objectives. When you have finished this section, you should be able to: (1) state the properties which distinguish gases from liquids and solids; (2) explain these distinctive properties in terms of the spacing and movement of molecules.
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