Laboratory Mathematics – US Army Subcourse

Table of contents :
ADMINISTRATION……Page 2
TABLE OF CONTENTS……Page 3
INTRODUCTION……Page 5
LESSON 1……Page 7
1-2. SOME FUNDAMENTAL PROPERTIES OF REAL NUMBERS……Page 8
1-3. DEFINITIONS OF SUBTRACTION AND DIVISION……Page 9
1-6. PROPERTIES OF FRACTIONS……Page 10
1-7. ORDER OF OPERATIONS……Page 11
1-8. EXERCISES, SECTION I……Page 12
1-9. DISCUSSION……Page 14
1-11. RULES OF EQUALITY……Page 15
1-13. PROBLEM—SOLVING TECHNIQUES……Page 16
1-14. EXERCISES, SECTION II……Page 18
1-17. EXERCISES, SECTION III……Page 20
1-20. RULES OF EXPONENTIATION……Page 23
1-21. EXPRESSING NUMBERS IN TERMS OF SCIENTIFIC NOTATION……Page 24
1-22. CHANGING THE SIGN OF THE EXPONENT……Page 26
1-23. MULTIPLICATION OF NUMBERS EXPRESSED IN SCIENTIFIC NOTATION……Page 27
1-24. DIVISION OF NUMBERS EXPRESSED IN SCIENTIFIC NOTATION……Page 29
1-25. EXERCISES, SECTION IV……Page 30
1-27. DETERMINING THE NUMBER OF SIGNIFICANT FIGURES IN A NUMBER……Page 32
1-29. LABORATORY APPLICATION……Page 33
1-30. EXERCISES, SECTION V……Page 34
1-31. DISCUSSION……Page 35
1-34. DETERMINATION OF THE CHARACTERISTIC……Page 36
1-35. DETERMINATION OF THE MANTISSA……Page 38
1-36. DETERMINATION OF THE LOGARITHM OF A NUMBER……Page 39
1-37. LOGARITHMS OF NUMBERS EXPRESSED AS EXPONENTIALS……Page 40
1-38. DETERMINATION OF ANTILOGARITHMS……Page 41
1-39. USE OF LOGARITHMS IN MULTIPLICATION……Page 43
1-41. USE OF LOGARITHMS TO FIND ROOTS OF NUMBERS……Page 44
1-43. EXERCISES, SECTION VI……Page 45
1-44. SOLUTIONS TO EXERCISES, SECTION I (PARAGRAPH 1-8)……Page 48
1-45. SOLUTIONS TO EXERCISES, SECTION II (PARAGRAPH 1-14)……Page 49
1-46. SOLUTIONS TO EXERCISES, SECTION III (PARAGRAPH 1-17)……Page 50
1-47. SOLUTIONS TO EXERCISES, SECTION IV (PARAGRAPH 1-25)……Page 51
1-48. SOLUTIONS TO EXERCISES, SECTION V (PARAGRAPH 1-30)……Page 52
1-49. SOLUTIONS TO EXERCISES, SECTION VI (PARAGRAPH 1-43)……Page 53
LESSON 2……Page 55
2-3. REAGENT GRADE OR ANALYTICAL REAGENT GRADE……Page 56
2-8. TECHNICAL OR COMMERCIAL GRADES……Page 57
2-13. MINIMUM SPECIFICATIONS FOR THE THREE TYPES OF WATER……Page 58
2-17. INTRODUCTION……Page 59
2-22. COLLOIDAL SOLUTION……Page 60
2-26. DISCUSSION……Page 61
2-27. WEIGHT/VOLUME PERCENT SOLUTIONS……Page 62
2-28. SOLVING WEIGHT/VOLUME PROBLEMS……Page 63
2-29. HYDRATES……Page 65
2-30. VOLUME/VOLUME PERCENT SOLUTION PROBLEMS……Page 69
2-31. WEIGHT/WEIGHT PERCENT SOLUTIONS……Page 70
2-32. PERCENT COMPOSITION PROBLEMS……Page 71
2-33. ADVANTAGES AND DISADVANTAGES OF PERCENT SOLUTIONS……Page 72
EXERCISES……Page 73
SOLUTIONS……Page 76
LESSON 3……Page 77
3-2. CALCULATING GRAM MOLECULAR WEIGHT……Page 78
3-3. MOLES AND GRAM MOLECULAR WEIGHT……Page 79
3-5. SOLVING MOLARITY PROBLEMS……Page 81
3-7. DISCUSSION……Page 82
3-8. SOLVING MILLIMOLE PER LITER PROBLEMS……Page 84
3-9. PROBLEMS INVOLVING HYDRATES……Page 85
3-10. PROBLEMS INVOLVING ONLY PART OF THE MOLECULE……Page 86
3-11. ADVANTAGES AND DISADVANTAGES OF MOLAR SOLUTIONS……Page 87
EXERCISES……Page 88
SOLUTIONS……Page 90
LESSON 4……Page 91
4-2. DETERMINING THE GRAM EQUIVALENT WEIGHT……Page 92
4-4. EQUIVALENTS……Page 94
4-6. SOLVING NORMALITY PROBLEMS……Page 95
4-9. SOLVING MILLIEQUIVALENT PER LITER PROBLEMS……Page 98
4-10. PROBLEMS INVOLVING HYDRATES……Page 100
4-11. PROBLEMS THAT CONSIDER ONLY PART OF THE MOLECULE……Page 101
EXERCISES……Page 102
SOLUTIONS……Page 104
LESSON 5……Page 105
5-2. CONVERSION FROM mol/L TO g/dL AND FROM g/dL TO mol/L……Page 106
5-3. CONVERSION FROM Eq/L TO g/dL AND FROM g/dL TO Eq/L……Page 108
5-4. CONVERTING FROM mol/L TO Eq/L AND FROM Eq/L TO mol/L……Page 109
EXERCISES……Page 111
SOLUTIONS……Page 113
LESSON 6……Page 114
6-2. SIMPLE……Page 115
6-3. SERIAL DILUTIONS……Page 117
6-4. PREPARATION OF A WORKING SOLUTION FROM A STOCK SOLUTION……Page 118
6-5. PREPARATION OF STANDARDS BY MIXING……Page 121
EXERCISES……Page 124
SOLUTIONS……Page 126
LESSON 7……Page 127
7-1. DISCUSSION……Page 128
7-3. PERFORMING AN ACID-BASE TITRATION……Page 129
7-4. SOLVING TITRATION PROBLEMS……Page 130
7-5. CALCULATING THE REACTING STRENGTH OF A SOLUTION……Page 132
EXERCISES……Page 134
SOLUTIONS……Page 137
LESSON 8……Page 138
8-2. EXAMPLE……Page 139
8-3. SPECIFIC GRAVITY AND DENSITY……Page 140
8-5. PROBLEM SOLVING……Page 141
8-6. DETERMINING THE CONCENTRATION OF CONCENTRATED LIQUIDS……Page 143
EXERCISES……Page 147
SOLUTIONS……Page 149
LESSON 9……Page 150
9-2. ARRHENIUS CONCEPT……Page 151
9-3. BRONSTED-LOWRY THEORY……Page 152
9-5. DISCUSSION……Page 153
9-6. LAW OF MASS ACTION……Page 154
9-7. EXAMPLE……Page 155
9-8. DISCUSSION……Page 156
9-9. ION PRODUCT OF WATER……Page 157
9-11. APPLICATION OF CONCEPT OF pH……Page 158
9-14. pOH SCALE……Page 160
9-15. RELATIONSHIP BETWEEN pH AND pOH……Page 161
9-19. HYDROLYSIS OF THE SALT OF A WEAK ACID AND A WEAK BASE……Page 162
9-21. MECHANISM OF ACTION……Page 163
9-22. THE HENDERSON-HASSELBALCH EQUATION……Page 164
9-23 SOLVING BUFFER PROBLEMS……Page 165
EXERCISES……Page 171
SOLUTIONS……Page 174
APPENDIX A……Page 175
TABLE OF FOUR-PLACE LOGARITHMS……Page 177
TABLE OF COMMON ELEMENTS AND RADICALS……Page 180
APPROXIMATE CONCENTRATIONS OF COMMERCIAL ACIDS AND BASES……Page 181
METRIC PREFIXES……Page 182