Laboratory Mathematics - US Army Subcourse

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