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Army Medical Laboratory MathematicsLaboratory MathematicsDevelopmentTable of ContentsTable of Contents (cont)IntroductionCredit AwardedLesson AssignmentLesson 1. General Mathematics Review.Definitions of Subtraction and DivisionProperties of Zero (0)Order of OperationsExercisesExercises (cont)Section II. Properties of EqualityProperties of EqualitySolving First Degree EquationsProblem - Solving TechniquesExercisesExercises (cont)Section III. Rounding off numbersExercisesExercises (cont)Section IV. Scientific NotationExpressing Numbers in Terms of Scientific NotationDecimal Movement.Changing the Sign of the ExponentMultiplication of numbers expressed in scientific notationMultiplication of numbers expressed in scientific notation (cont)Division of numbers expressed in scientific notationExercisesExercises (cont)Section V. Significant FiguresImplied LimitsExercisesSection VI. LogarithmsParts of a LogarithmBy Rule.Determination of the MantissaDetermination of the logarithm of a numberLogarithms of Numbers Expressed as ExponentialsDetermination of antilogarithmDetermination of antilogarithm (cont)Use of Logarithms in MultiplicationUse of Logarithms in DivisionUse of Logarithms to Find the Product of Numbers with ExponentsExercisesExercises (cont)Solutions to ExercisesSolutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Lesson AssignmentLesson 2. Introduction to Solution Mathematics.Chemically pure gradeSection II. Grades of Laboratory WaterSection III. Parts of a SolutionSection IV. Types of SolutionsSection V. Percent ConcentrationWeight/Volume Percent SolutionsSolving Weight/Volume ProblemsSolving Weight/Volume Problems (cont)HydratesHydrates (cont)Hydrates (cont)Hydrates (cont)Volume/Volume Percent Solution ProblemsWeight/weight percent solutionsPercent Composition ProblemsAdvantages and Disadvantages of Percent SolutionsExercisesExercises (cont)Exercises (cont)Solutions to ExercisesLesson AssignmentLesson 3. Molar Solutions.Moles and gram molecular weightMoles and gram molecular weight (cont)Section II. Molarity and Molar SolutionsSection III. Millimoles per LiterDiscussionSolving Millimole Per Liter ProblemsSection IV. Variations of Molarity ProblemsProblems Involving Only Part of the MoleculeAdvantages and Disadvantages of Molar SolutionsExercisesExercises (cont)Solutions to ExercisesLesson AssignmentEquivalent Solutions.Determining the gram equivalent weightExceptions in calculating gram equivalent weightSection II. Normal SolutionsSolving Normality ProblemsSolving Normality Problems (cont)Section III. Milliequivalent per Liter (mEq/L) SolutionsSolving Milliequivalent per Liter ProblemsSection IV. Variations of Normality ProblemsProblems that consider only part of the moleculeExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 5. Conversion of Concentration Units.Conversion from mol/L to g/dL and from g/dL to mol/LConversion from Eq/L to g/dL and from g/dL to Eq/LConverting from mol/L to Eq/L and from Eq/L to mol/LConverting from mol/L to Eq/L and from Eq/L to mol/L (Cont)ExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 6. Dilutions.Simple DilutionsSerial dilutionPreparation of a Working Solution from a Stock SolutionBasic Rules for Solving C1V1 = C2V2 Problems.Basic Rules for Solving C1V1 = C2V2 Problems. (Cont)Preparation of standard by mixingPreparation of standard by mixing (Cont)Preparation of standard by mixing (Cont)ExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 7. Titration.Indicators and General Rules of UseSolving Titration Problems.Solving Titration Problems (cont)Calculate the reacting strength of a solutionCalculate the reacting strength of a solution (cont)ExercisesExercises (cont)Exercises (cont)Solutions to ExercisesLesson AssignmentLesson 8. Concentrated Acids and Bases.Specific gravity and densityPreparing Solutions from Concentrated LiquidsProblem SolvingDetermining the Concentration of Concentrated LiquidsConversion from g/mL to g/dLConversion From g/mL to Eq/LConversion From g/mL to Eq/L (cont)ExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 9. pH and Buffers.Bronsted-Lowry theorySection II. Dynamic EquilibriumLaw of mass actionExampleSection III. Dissociation of WaterIon Product of WaterSection IV. pH and pOHApplication of Concept of pHpH ScaleRelationship between pH and pOHSection V. Hydrolysis of SaltsSection VI. BuffersThe Henderson-Hasselbalch equationSolving Buffer ProblemsSolving Buffer Problems (cont)Solving Buffer Problems (cont)Solving Buffer Problems (cont)Solving Buffer Problems (cont)Solving Buffer Problems (cont)ExercisesExercises (cont)Exercises (cont)Solutions to ExercisesAppendix A. Review of Dimensional AnalysisAppendix A. Review of Dimensional Analysis (cont)Appendix B. Table of Four-Place LogarithmsAppendix B. Table of Four-Place Logarithms (cont)Appendix B. Table of Four-Place Logarithms (cont)Appendix C. Table of Common Elements and RadicalsApproximate Concentrations of Commercial Acids and BasesAppendix D. Metric Prefixes
Army Medical
Laboratory MathematicsLaboratory MathematicsDevelopmentTable of ContentsTable of Contents (cont)IntroductionCredit AwardedLesson AssignmentLesson 1. General Mathematics Review.Definitions of Subtraction and DivisionProperties of Zero (0)Order of OperationsExercisesExercises (cont)Section II. Properties of EqualityProperties of EqualitySolving First Degree EquationsProblem - Solving TechniquesExercisesExercises (cont)Section III. Rounding off numbersExercisesExercises (cont)Section IV. Scientific NotationExpressing Numbers in Terms of Scientific NotationDecimal Movement.Changing the Sign of the ExponentMultiplication of numbers expressed in scientific notationMultiplication of numbers expressed in scientific notation (cont)Division of numbers expressed in scientific notationExercisesExercises (cont)Section V. Significant FiguresImplied LimitsExercisesSection VI. LogarithmsParts of a LogarithmBy Rule.Determination of the MantissaDetermination of the logarithm of a numberLogarithms of Numbers Expressed as ExponentialsDetermination of antilogarithmDetermination of antilogarithm (cont)Use of Logarithms in MultiplicationUse of Logarithms in DivisionUse of Logarithms to Find the Product of Numbers with ExponentsExercisesExercises (cont)Solutions to ExercisesSolutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Solutions to Exercises (cont)Lesson AssignmentLesson 2. Introduction to Solution Mathematics.Chemically pure gradeSection II. Grades of Laboratory WaterSection III. Parts of a SolutionSection IV. Types of SolutionsSection V. Percent ConcentrationWeight/Volume Percent SolutionsSolving Weight/Volume ProblemsSolving Weight/Volume Problems (cont)HydratesHydrates (cont)Hydrates (cont)Hydrates (cont)Volume/Volume Percent Solution ProblemsWeight/weight percent solutionsPercent Composition ProblemsAdvantages and Disadvantages of Percent SolutionsExercisesExercises (cont)Exercises (cont)Solutions to ExercisesLesson AssignmentLesson 3. Molar Solutions.Moles and gram molecular weightMoles and gram molecular weight (cont)Section II. Molarity and Molar SolutionsSection III. Millimoles per LiterDiscussionSolving Millimole Per Liter ProblemsSection IV. Variations of Molarity ProblemsProblems Involving Only Part of the MoleculeAdvantages and Disadvantages of Molar SolutionsExercisesExercises (cont)Solutions to ExercisesLesson AssignmentEquivalent Solutions.Determining the gram equivalent weightExceptions in calculating gram equivalent weightSection II. Normal SolutionsSolving Normality ProblemsSolving Normality Problems (cont)Section III. Milliequivalent per Liter (mEq/L) SolutionsSolving Milliequivalent per Liter ProblemsSection IV. Variations of Normality ProblemsProblems that consider only part of the moleculeExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 5. Conversion of Concentration Units.Conversion from mol/L to g/dL and from g/dL to mol/LConversion from Eq/L to g/dL and from g/dL to Eq/LConverting from mol/L to Eq/L and from Eq/L to mol/LConverting from mol/L to Eq/L and from Eq/L to mol/L (Cont)ExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 6. Dilutions.Simple DilutionsSerial dilutionPreparation of a Working Solution from a Stock SolutionBasic Rules for Solving C1V1 = C2V2 Problems.Basic Rules for Solving C1V1 = C2V2 Problems. (Cont)Preparation of standard by mixingPreparation of standard by mixing (Cont)Preparation of standard by mixing (Cont)ExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 7. Titration.Indicators and General Rules of UseSolving Titration Problems.Solving Titration Problems (cont)Calculate the reacting strength of a solutionCalculate the reacting strength of a solution (cont)ExercisesExercises (cont)Exercises (cont)Solutions to ExercisesLesson AssignmentLesson 8. Concentrated Acids and Bases.Specific gravity and densityPreparing Solutions from Concentrated LiquidsProblem SolvingDetermining the Concentration of Concentrated LiquidsConversion from g/mL to g/dLConversion From g/mL to Eq/LConversion From g/mL to Eq/L (cont)ExercisesExercises (cont)Solutions to ExercisesLesson AssignmentLesson 9. pH and Buffers.Bronsted-Lowry theorySection II. Dynamic EquilibriumLaw of mass actionExampleSection III. Dissociation of WaterIon Product of WaterSection IV. pH and pOHApplication of Concept of pHpH ScaleRelationship between pH and pOHSection V. Hydrolysis of SaltsSection VI. BuffersThe Henderson-Hasselbalch equationSolving Buffer ProblemsSolving Buffer Problems (cont)Solving Buffer Problems (cont)Solving Buffer Problems (cont)Solving Buffer Problems (cont)Solving Buffer Problems (cont)ExercisesExercises (cont)Exercises (cont)Solutions to ExercisesAppendix A. Review of Dimensional AnalysisAppendix A. Review of Dimensional Analysis (cont)Appendix B. Table of Four-Place LogarithmsAppendix B. Table of Four-Place Logarithms (cont)Appendix B. Table of Four-Place Logarithms (cont)Appendix C. Table of Common Elements and RadicalsApproximate Concentrations of Commercial Acids and BasesAppendix D. Metric Prefixes
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