THE CALCULATIONS OF GENERAL CHEMISTRY
CONTENTS 1 ESSENTIAL MATHEMATICS 1 1 SIGNI?CANT FIGURES 1 2 SIGNI?CANT FIGURES AND MATHEMATICAL OPERATIONS 1 3 SCIENTI?C NOTATION AND EXPONENTS 1 4 LOGARITHMS 1 5 ALGEBRAIC EQUATIONS 1 6 PROBLEMS 2 SYSTEMS OF MEASUREMENT 2 1 MEASUREMENTS IN CHEMISTRY 2 2 MEASUREMENT OF MASS, LENGTH, AND TIME 2 3 TEMPERATURE 2 4 DERIVED UNITS 2 5 DENSITY AND SPECI?C GRAVITY 2 6 DIMENSIONAL ANALYSIS AND CONVERSION FACTORS 2 7 PROBLEMS 3 ATOMIC STRUCTURE AND ISOTOPES 3 1 ATOMIC THEORY 3 2 THE STRUCTURE OF THE ATOM 3 3 ISOTOPES 3 4 RELATIVE ATOMIC MASS 3 5 PROBLEMS 4 FORMULA AND MOLECULAR MASS 4 1 FORMULA MASS 4 2 MOLECULAR MASS 4 3 MOLAR MASS 4 4 PROBLEMS 5 MEASURING CHEMICAL QUANTITIES: THE MOLE 5 1 THE MOLE AND AVOGADRO’S NUMBER 5 2 THE MOLE AND MOLAR MASS 5 3 CALCULATING THE NUMBER OF MOLES 5 4 PROBLEMS 6 FORMULAS OF COMPOUNDS AND PERCENT COMPOSITION 6 1 PERCENT COMPOSITION 6 2 EMPIRICAL FORMULA 6 3 MOLECULAR FORMULA 6 4 PROBLEMS 7 CHEMICAL FORMULAS AND NOMENCLATURE 7 1 GENERAL BACKGROUND 7 2 CHEMICAL FORMULA 7 3 OXIDATION NUMBERS 7 4 WRITING THE FORMULAS OF COMPOUNDS 7 5 NOMENCLATURE OF INORGANIC COMPOUNDS 7 6 PROBLEMS 8 CHEMICAL EQUATIONS 8 1 WRITING CHEMICAL EQUATIONS 8 2 BALANCING CHEMICAL EQUATIONS 8 3 TYPES OF CHEMICAL REACTIONS 8 4 PROBLEMS 9 STOICHIOMETRY 9 1 REACTION STOICHIOMETRY 9 2 INFORMATION FROM A BALANCED EQUATION 9 3 TYPES OF STOICHIOMETRIC PROBLEMS 9 4 LIMITING REAGENTS 9 5 REACTION YIELDS: THEORETICAL, ACTUAL, AND PERCENT YIELDS 9 6 PROBLEMS 10 STRUCTURE OF THE ATOM 10 1 ELECTRONIC STRUCTURE OF THE ATOM 10 2 ELECTROMAGNETIC RADIATION 10 3 THE NATURE OF MATTER AND QUANTUM THEORY 10 4 THE HYDROGEN ATOM 10 5 THE QUANTUM-MECHANICAL DESCRIPTION OF THE HYDROGEN ATOM 10 6 QUANTUM MECHANICS AND ATOMIC ORBITALS 10 7 ELECTRONIC CON?GURATION OF MULTIELECTRON ATOMS 10 8 PROBLEMS 11 GAS LAWS 11 1 STANDARD TEMPERATURE AND PRESSURE 11 2 BOYLE’S LAW: PRESSURE VS VOLUME 11 3 CHARLES’S LAW: TEMPERATURE VS VOLUME 11 4 THE COMBINED GAS LAW 11 5 GAY-LUSSAC’S LAW AND REACTIONS INVOLVING GASES 11 6 AVOGADRO’S LAW 11 7 THE IDEAL GAS LAW 11 8 DENSITY AND MOLECULAR MASS OF A GAS 11 9 MOLAR VOLUME OF AN IDEAL GAS 11 10 DALTON’S LAW OF PARTIAL PRESSURES 11 11 PARTIAL PRESSURE AND MOLE FRACTION 11 12 REAL GASES AND DEVIATION FROM THE GAS LAWS 11 13 GRAHAM’S LAW OF DIFFUSION 11 14 PROBLEMS 12 LIQUIDS AND SOLIDS 12 1 THE LIQUID STATE 12 2 POLAR COVALENT BONDS AND DIPOLE MOMENT 12 3 VAPOR PRESSURE AND THE CLAUSIUS-CLAPEYRON EQUATION 12 4 THE SOLID STATE 12 5 THE CRYSTAL SYSTEM 12 6 CALCULATIONS INVOLVING UNIT CELL DIMENSIONS 12 7 IONIC CRYSTAL STRUCTURE 12 8 RADIUS RATIO RULE FOR IONIC COMPOUNDS 12 9 DETERMINATION OF CRYSTAL STRUCTURE BY X-RAY DIFFRACTION 12 10 PROBLEMS 13 SOLUTION CHEMISTRY 13 1 SOLUTION AND SOLUBILITY 13 2 CONCENTRATION OF SOLUTIONS 13 3 SOLVING SOLUBILITY PROBLEMS 13 4 EFFECT OF TEMPERATURE ON SOLUBILITY 13 5 SOLUBILITY CURVES 13 6 EFFECT OF PRESSURE ON SOLUBILITY 13 7 PROBLEMS 14 VOLUMETRIC ANALYSIS 14 1 INTRODUCTION 14 2 APPLICATIONS OF TITRATION 14 3 ACID–BASE TITRATIONS 14 4 CALCULATIONS INVOLVING ACID–BASE TITRATION 14 5 BACK TITRATIONS 14 6 PROBLEMS 15 IDEAL SOLUTIONS AND COLLIGATIVE PROPERTIES 15 1 COLLIGATIVE PROPERTIES 15 2 VAPOR PRESSURE AND RAOULT’S LAW 15 3 ELEVATION OF BOILING POINT 15 4 DEPRESSION OF FREEZING POINT 15 5 OSMOSIS AND OSMOTIC PRESSURE 15 6 PROBLEMS 16 CHEMICAL KINETICS 16 1 RATES OF REACTION 16 2 MEASUREMENT OF REACTION RATES 16 3 REACTION RATES AND STOICHIOMETRY 16 4 COLLISION THEORY OF REACTION RATES 16 5 RATE LAWS AND THE ORDER OF REACTIONS 16 6 EXPERIMENTAL DETERMINATION OF RATE LAW USING INITIAL RATES 16 7 THE INTEGRATED RATE EQUATION 16 8 HALF-LIFE OF A REACTION 16 9 REACTION RATES AND TEMPERATURE: THE ARRHENIUS EQUATION 16 10 PROBLEMS 17 CHEMICAL EQUILIBRIUM 17 1 REVERSIBLE AND IRREVERSIBLE REACTIONS 17 2 THE EQUILIBRIUM CONSTANT 17 3 THE REACTION QUOTIENT 17 4 PREDICTING THE DIRECTION OF REACTION 17 5 POSITION OF EQUILIBRIUM 17 6 HOMOGENEOUS VS HETEROGENEOUS EQUILIBRIA 17 7 CALCULATING EQUILIBRIUM CONSTANTS 17 8 CALCULATING EQUILIBRIUM CONCENTRATIONS FROM K 17 9 QUALITATIVE TREATMENT OF EQUILIBRIUM: LE CHATELIER’S PRINCIPLE 17 10 PROBLEMS 18 IONIC EQUILIBRIA AND PH 18 1 THE IONIZATION OF WATER 18 2 DE?NITION OF ACIDITY AND BASICITY 18 3 THE PH OF A SOLUTION 18 4 THE POH OF A SOLUTION 18 5 THE ACID IONIZATION CONSTANT, KA 18 6 CALCULATING PH AND EQUILIBRIUM CONCENTRATIONS IN SOLUTIONS OF WEAK ACIDS 18 7 PERCENT DISSOCIATION OF WEAK ACIDS 18 8 THE BASE DISSOCIATION CONSTANT, KB 18 9 RELATIONSHIP BETWEEN KA AND KB 18 10 SALT HYDROLYSIS: ACID–BASE PROPERTIES OF SALTS 18 11 THE COMMON-ION EFFECT 18 12 BUFFERS AND PH OF BUFFER SOLUTIONS 18 13 POLYPROTIC ACIDS AND BASES 18 14 MORE ACID–BASE TITRATION 18 15 PH TITRATION CURVES 18 16 PROBLEMS 19 SOLUBILITY AND COMPLEX-ION EQUILIBRIA 19 1 SOLUBILITY EQUILIBRIA 19 2 THE SOLUBILITY PRODUCT PRINCIPLE 19 3 DETERMINING KSP FROM MOLAR SOLUBILITY 19 4 CALCULATING MOLAR SOLUBILITY FROM KSP 19 5 KSP AND PRECIPITATION 19 6 COMPLEX-ION EQUILIBRIA AND FORMATION OF COMPLEX IONS 19 7 PROBLEMS 20 THERMOCHEMISTRY 20 1 INTRODUCTION 20 2 CALORIMETRY AND HEAT CAPACITY 20 3 ENTHALPY 20 4 HESS’S LAW OF HEAT SUMMATION 20 5 BOND ENERGIES AND ENTHALPY 20 6 PROBLEMS 21 CHEMICAL THERMODYNAMICS 21 1 DE?NITION OF TERMS 21 2 THE FIRST LAW OF THERMODYNAMICS 21 3 EXPANSION WORK 21 4 ENTROPY 21 5 THE SECOND LAW OF THERMODYNAMICS 21 6 CALCULATION OF ENTROPY CHANGES IN CHEMICAL REACTIONS 21 7 FREE ENERGY 21 8 THE STANDARD FREE ENERGY CHANGE 21 9 ENTHALPY AND ENTROPY CHANGES DURING A PHASE CHANGE 21 10 FREE ENERGY AND THE EQUILIBRIUM CONSTANT 21 11 VARIATION OF G AND EQUILIBRIUM CONSTANT WITH TEMPERATURE 21 12 PROBLEMS 22 OXIDATION AND REDUCTION REACTIONS 22 1 INTRODUCTION 22 2 OXIDATION AND REDUCTION IN TERMS OF ELECTRON TRANSFER 22 3 OXIDATION NUMBERS 22 4 OXIDATION AND REDUCTION IN TERMS OF OXIDATION NUMBER 22 5 DISPROPORTIONATION REACTIONS 22 6 OXIDIZING AND REDUCING AGENTS 22 7 HALF-CELL REACTIONS 22 8 BALANCING REDOX EQUATIONS 22 9 OXIDATION–REDUCTION TITRATION 22 10 PROBLEMS 23 FUNDAMENTALS OF ELECTROCHEMISTRY 23 1 GALVANIC CELLS 23 2 THE CELL POTENTIAL 23 3 STANDARD ELECTRODE POTENTIAL 23 4 THE ELECTROCHEMICAL SERIES 23 5 APPLICATIONS OF ELECTRODE POTENTIAL 23 6 CELL DIAGRAMS CELL FROM ELECTRODE POTENTIAL 23 8 THE STANDARD ELECTRODE POTENTIAL, THE GIBBS FREE ENERGY, AND THE EQUILIBRIUM CONSTANT 23 9 DEPENDENCE OF CELL POTENTIAL ON CONCENTRATION (THE NERNST EQUATION) 23 10 ELECTROLYSIS 23 11 FARADAY’S LAWS OF ELECTROLYSIS 23 12 PROBLEMS 24 RADIOACTIVITY AND NUCLEAR REACTIONS 24 1 DE?NITION OF TERMS 24 2 RADIOACTIVE DECAY AND NUCLEAR EQUATIONS 24 3 NUCLEAR TRANSMUTATION 24 4 RATES OF RADIOACTIVE DECAY AND HALF-LIFE 24 5 ENERGY OF NUCLEAR REACTIONS 24 6 PROBLEMS CHEMISTRY IN QUANTITATIVE LANGUAGE THIS PAGE INTENTIONALLY LEFT BLANK ESSENTIAL MATHEMATICS 1 1 SIGNI?CANT FIGURES SIGNI?CANT ?GURES ARE THE NUMBER OF DIGITS IN A MEASURED OR CALCULATED VALUE THAT ARE STATISTICALLY SIGNI?CANT OR OFFER REASONABLE AND RELIABLE INFORMATION SIGNI?CANT ?GURES IN ANY MEASUREMENT USUALLY CONTAIN DIGITS THAT ARE KNOWN WITH CERTAINTY AND ONE DIGIT THAT IS UNCERTAIN TO DETERMINE THE NUMBER OF SIGNI?CANT ?GURES, FOLLOW THESE RULES 1 ALL NONZERO DIGITS (1–9) ARE SIGNI?CANT FOR EXAMPLE, 125 HAS 3 SIGNI?CANT ?GURES AND 14 44 HAS 4 SIGNI?CANT ?GURES 2 LEADING ZEROS TO THE LEFT OF THE ?RST NONZERO DIGIT IN THE NUMBER ARE NOT SIGNI?CANT THEY ARE ONLY USED TO ?X THE POSITION OF THE DECIMAL FOR EXAMPLE: 0 007 HAS ONE SIGNI?CANT ?GURE 0 000105 HAS 3 SIGNI?CANT ?GURES 0 000000000015 HAS 2 SIGNI?CANT ?GURES 3 ZEROS BETWEEN NONZERO DIGITS ARE SIGNI?CANT FOR EXAMPLE: 5 005 HAS 4 SIGNI?CANT ?GURES 50 05 HAS 4 SIGNI?CANT ?GURES 500 0000075 HAS 10 SIGNI?CANT ?GURES 4 ALL ZEROS TO THE RIGHT OF THE DECIMAL POINT IN A NUMBER GREATER THAN 1 ARE SIGNI?CANT FOR EXAMPLE: 25 00 HAS 4 SIGNI?CANT ?GURES 0 1250 HAS 4 SIGNI?CANT ?GURES 0 2000 HAS 4 SIGNI?CANT ?GURES 5 ZEROS AT THE END OF A NUMBER MAY OR MAY NOT BE SIGNI?CANT THEY ARE SIGNI?CANT ONLY IF THERE IS A DECIMAL POINT IN THE NUMBER FOR EXAMPLE: 1500 HAS 2 SIGNI?CANT ?GURES 1500 HAS 4 SIGNI?CANT ?GURES CHEMISTRY IN QUANTITATIVE LANGUAGE 602,000,000,000,000,000,000,000 HAS 3 SIGNI?CANT ?GURES 404,570,000 HAS 5 SIGNI?CANT ?GURES 404,590,000 HAS 9 SIGNI?CANT ?GURES ROUNDING OFF ROUNDING OFF IS A PROCESS OF ELIMINATING NONSIGNI?CANT DIGITS FROM A CALCULATED NUMBER THE RULES GOVERNING ROUNDING OFF ARE SUMMARIZED BELOW: 1 IF THE NONSIGNI?CANT DIGIT IS LESS THAN 5, ROUND IT AND ALL DIGITS TO ITS RIGHT OFF FOR EXAMPLE, 100 5129 IS EQUAL TO 100 5 IF ROUNDED OFF TO 4 SIGNI?CANT ?GURES 2 IF THE NONSIGNI?CANT DIGIT TO THE RIGHT OF THE LAST DIGIT TO BE RETAINED IS A MULTIPLY 20 25 BY 125 125 AND GIVE THE ANSWER WITH THE PROPER SIGNI?CANT DIGITS THE CALCULATIONS OF GENERAL CHEMISTRY ESSENTIAL MATHEMATICS