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ANALYTICAL I Analytical I (unable to fetch text document from uri [status: 0 (UnableToConnect), message: "Error: TrustFailure (Ssl error:1000007d:SSL routines:OPENSSL_internal:CERTIFICATE_VERIFY_FAILED)"]) TABLE OF CONTENTS

1: INTRODUCTION TO ANALYTICAL

1.1: WHAT IS ? 1.2: THE ANALYTICAL PERSPECTIVE 1.3: COMMON ANALYTICAL PROBLEMS 1.4: INTRODUCTION TO ANALYTICAL CHEMISTRY (EXERCISES) 1.5: INTRODUCTION TO ANALYTICAL CHEMISTRY (SUMMARY) 2: BASIC TOOLS OF ANALYTICAL CHEMISTRY In the chapters that follow we will explore many aspects of analytical chemistry. In the process we will consider important questions such as “How do we treat experimental data?”, “How do we ensure that our results are accurate?”, “How do we obtain a representative sample?”, and “How do we select an appropriate analytical technique?” Before we look more closely at these and other questions, we will first review some basic tools of importance to analytical .

2.1: MEASUREMENTS IN ANALYTICAL CHEMISTRY 2.2: CONCENTRATION 2.3: STOICHIOMETRIC CALCULATIONS 2.4: BASIC EQUIPMENT 2.5: PREPARING 2.6: SPREADSHEETS AND COMPUTATIONAL SOFTWARE 2.7: THE LABORATORY NOTEBOOK 2.8: BASIC TOOLS OF ANALYTICAL CHEMISTRY (EXERCISES) 2.9: BASIC TOOLS OF ANALYTICAL CHEMISTRY (SUMMARY) 3: THE VOCABULARY OF ANALYTICAL CHEMISTRY If you leaf through an issue of the journal Analytical Chemistry, you will soon discover that the authors and readers share a common vocabulary of analytical terms. You are probably familiar with some of these terms, such as accuracy and precision, but other terms, such as analyte and matrix may be less familiar to you. In order to participate in the community of analytical chemists, you must first understand its vocabulary.

3.1: ANALYSIS, DETERMINATION, AND MEASUREMENT 3.2: TECHNIQUES, METHODS, PROCEDURES, AND PROTOCOLS 3.3: CLASSIFYING ANALYTICAL TECHNIQUES 3.4: SELECTING AN ANALYTICAL METHOD 3.5: DEVELOPING THE PROCEDURE 3.6: PROTOCOLS 3.7: THE IMPORTANCE OF ANALYTICAL METHODOLOGY 3.8: THE VOCABULARY OF ANALYTICAL CHEMISTRY (EXERCISES) 3.9: THE VOCABULARY OF ANALYTICAL CHEMISTRY (SUMMARY) 4: EVALUATING ANALYTICAL DATA When using an analytical method we make three separate evaluations of experimental error. First, before beginning an analysis we evaluate potential sources of errors to ensure that they will not adversely effect our results. Second, during the analysis we monitor our measurements to ensure that errors remain acceptable. Finally, at the end of the analysis we evaluate the quality of the measurements and results, comparing them to our original design criteria.

4.1: CHARACTERIZING MEASUREMENTS AND RESULTS 4.2: CHARACTERIZING EXPERIMENTAL ERRORS 4.3: PROPAGATION OF UNCERTAINTY 4.4: THE DISTRIBUTION OF MEASUREMENTS AND RESULTS 4.5: STATISTICAL ANALYSIS OF DATA 4.6: STATISTICAL METHODS FOR NORMAL DISTRIBUTIONS 4.7: DETECTION LIMITS 4.8: USING EXCEL AND R TO ANALYZE DATA 4.9: EVALUATING ANALYTICAL DATA (EXERCISES)

1 10/3/2021 4.10: EVALUATING ANALYTICAL DATA (SUMMARY) 5: STANDARDIZING ANALYTICAL METHODS Standardization is the process of determining the relationship between the signal and the amount of analyte in a sample. Previously, we defined this relationship as Stotal=kACA+Sreag where Stotal is the signal, nA is the moles of analyte, CA is the analyte’s concentration, kA is the method’s sensitivity for the analyte, and Sreag is the contribution to Stotal from sources other than the sample. To standardize a method we must determine values for kA and Sreag, which is the subject of this chapt

5.1: ANALYTICAL STANDARDS 5.2: CALIBRATING THE SIGNAL 5.3: DETERMINING THE SENSITIVITY 5.4: LINEAR REGRESSION AND CALIBRATION CURVES 5.5: BLANK CORRECTIONS 5.6: USING EXCEL AND R FOR A REGRESSION ANALYSIS 5.7: STANDARDIZING ANALYTICAL METHODS (EXERCISES) 5.8: STANDARDIZING ANALYTICAL METHODS (SUMMARY) 6: EQUILIBRIUM CHEMISTRY Regardless of the problem on which an analytical is working, its requires a knowledge of chemistry and the ability to apply that knowledge. For example, an analytical chemist studying the effect of pollution on spruce trees needs to know the chemical differences between p‑hydroxybenzoic and p‑hydroxyacetophenone, two phenols found in the needles of spruce trees. Your ability to “think as a chemist” is a product of your experience in the classroom and in the laboratory.

6.1: REVERSIBLE REACTIONS AND CHEMICAL EQUILIBRIA 6.2: THERMODYNAMICS AND EQUILIBRIUM CHEMISTRY 6.3: MANIPULATING EQUILIBRIUM CONSTANTS 6.4: EQUILIBRIUM CONSTANTS FOR CHEMICAL REACTIONS 6.5: LE CHÂTELIER’S PRINCIPLE 6.6: LADDER DIAGRAMS 6.7: SOLVING EQUILIBRIUM PROBLEMS 6.8: BUFFER SOLUTIONS 6.9: ACTIVITY EFFECTS 6.10: USING EXCEL AND R TO SOLVE EQUILIBRIUM PROBLEMS 6.11: SOME FINAL THOUGHTS ON EQUILIBRIUM CALCULATIONS 6.12: EQUILIBRIUM CHEMISTRY (EXERCISES) 6.13: EQUILIBRIUM CHEMISTRY (SUMMARY) 7: GRAVIMETRIC METHODS Gravimetry includes all analytical methods in which the analytical signal is a measurement of mass or a change in mass. When you step on a scale after exercising you are making, in a sense, a gravimetric determination of your mass. Mass is the most fundamental of all analytical measurements, and gravimetry is unquestionably our oldest quantitative analytical technique.

7.1: OVERVIEW OF GRAVIMETRIC METHODS 7.2: PRECIPITATION GRAVIMETRY 7.3: VOLATILIZATION GRAVIMETRY 7.4: PARTICULATE GRAVIMETRY 7.5: GRAVIMETRIC METHODS (EXERCISES) 7.6: GRAVIMETRIC METHODS (SUMMARY) 8: TITRIMETRIC METHODS Titrimetry, in which volume serves as the analytical signal, made its first appearance as an analytical method in the early eighteenth century. Titrimetric methods were not well received by the analytical chemists of that era because they could not duplicate the accuracy and precision of a gravimetric analysis. Not surprisingly, few standard texts from the 1700s and 1800s include titrimetric methods of analysis.

8.1: OVERVIEW OF TITRIMETRY 8.2: ACID– 8.3: COMPLEXATION TITRATIONS 8.4: TITRATIONS

2 10/3/2021 8.5: PRECIPITATION TITRATIONS 8.6: TITRIMETRIC METHODS (EXERCISES) 8.7: TITRIMETRIC METHODS (SUMMARY) BACK MATTER

INDEX GLOSSARY

3 10/3/2021 CHAPTER OVERVIEW

1: INTRODUCTION TO ANALYTICAL CHEMISTRY

Chemistry is the study of matter, including its composition and structure, its physical properties, and its reactivity. There are many ways to study chemistry, but, we traditionally divide it into five fields: , , , , and analytical chemistry. Although this division is historical and, perhaps, arbitrary—as witnessed by current interest in interdisciplinary areas such as bioanalytical chemistry and —these five fields remain the simplest division spanning the discipline of chemistry.

Thumbnail: Several graduated cylinders of various thickness and heights with white side markings in front of a large beaker. They are all filled about halfway with red or blue chemical compounds. The blue ink is showing signs of Brownian motion when dissolving into water. Image used with permission (CC BY-SA 3.0; Horia Varlan from Bucharest, Romania). CONTRIBUTORS

David Harvey (DePauw University)

1.1: WHAT IS ANALYTICAL CHEMISTRY? Analytical chemistry is too broad and too active a discipline for us to define completely. This description is misleading. In this chapter we will try to say a little about what analytical chemistry is, as well as a little about what analytical chemistry is not. Analytical chemistry is often described as the area of chemistry responsible for characterizing the composition of matter, both qualitatively (Is there any lead in this sample?) and quantitatively (How much lead is in this sample?).

1.2: THE ANALYTICAL PERSPECTIVE Many analytical chemists describe this perspective as an analytical approach to solving problems. Although there are probably as many descriptions of the analytical approach as there are analytical chemists, it is convenient for our purpose to define it as the five- step process.

1.3: COMMON ANALYTICAL PROBLEMS This is the scope of a qualitative analysis is to identify what is present in a sample. Perhaps the most common analytical problem is a quantitative analysis.

1.4: INTRODUCTION TO ANALYTICAL CHEMISTRY (EXERCISES) These are homework exercises to accompany "Chapter 1: Introduction to Analytical Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

1.5: INTRODUCTION TO ANALYTICAL CHEMISTRY (SUMMARY) This is a summary to accompany "Chapter 1: Introduction to Analytical Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

1 10/3/2021 1.1: What is Analytical Chemistry? 1.1: What is Analytical Chemistry?

David Harvey 1.1.1 9/12/2021 https://chem.libretexts.org/@go/page/167726 1.2: The Analytical Perspective 1.2: The Analytical Perspective

David Harvey 1.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167727 1.3: Common Analytical Problems 1.3: Common Analytical Problems

David Harvey 1.3.1 9/12/2021 https://chem.libretexts.org/@go/page/167728 1.4: Introduction to Analytical Chemistry (Exercises) 1.E: Introduction to Analytical Chemistry (Exercises)

David Harvey 1.4.1 9/12/2021 https://chem.libretexts.org/@go/page/167729 1.5: Introduction to Analytical Chemistry (Summary) 1.S: Introduction to Analytical Chemistry (Summary)

David Harvey 1.5.1 9/12/2021 https://chem.libretexts.org/@go/page/167730 CHAPTER OVERVIEW

2: BASIC TOOLS OF ANALYTICAL CHEMISTRY In the chapters that follow we will explore many aspects of analytical chemistry. In the process we will consider important questions such as “How do we treat experimental data?”, “How do we ensure that our results are accurate?”, “How do we obtain a representative sample?”, and “How do we select an appropriate analytical technique?” Before we look more closely at these and other questions, we will first review some basic tools of importance to analytical chemists.

2.1: MEASUREMENTS IN ANALYTICAL CHEMISTRY Analytical chemistry is a quantitative science. Whether determining the concentration of a species, evaluating an , measuring a reaction rate, or drawing a correlation between a compound’s structure and its reactivity, analytical chemists engage in “measuring important chemical things.” In this section we briefly review the use of units and significant figures in analytical chemistry.

2.2: CONCENTRATION Concentration is a general measurement unit stating the amount of solute present in a known amount of solution. Although we associate the terms “solute” and “solution” with liquid samples, we can extend their use to gas-phase and solid-phase samples as well. Table 2.4 lists the most common units of concentration.

2.3: STOICHIOMETRIC CALCULATIONS A balanced reaction, which gives the stoichiometric relationship between the moles of reactants and the moles of products, provides the basis for many analytical calculations.

2.4: BASIC EQUIPMENT The array of equipment for making analytical measurements is impressive, ranging from the simple and inexpensive, to the complex and expensive. With three exceptions—measuring mass, measuring volume, and drying materials—we will postpone the discussion of equipment to later chapters where its application to specific analytical methods is relevant.

2.5: PREPARING SOLUTIONS Preparing a solution of known concentration is perhaps the most common activity in any analytical lab. The method for measuring out the solute and depend on the desired concentration unit and how exact the solution’s concentration needs to be known. Pipets and volumetric flasks are used when a solution’s concentration must be exact; graduated cylinders, beakers and reagent bottles suffice when concentrations need only be approximate. Two methods for preparing solutions are described.

2.6: SPREADSHEETS AND COMPUTATIONAL SOFTWARE Analytical chemistry is an inherently quantitative discipline. Whether you are completing a statistical analysis, trying to optimize experimental conditions, or exploring how a change in pH affects a compound’s , the ability to work with complex mathematical equations is essential. Spreadsheets, such as Microsoft Excel can be an important tool for analyzing your data and for preparing graphs of your results. Scattered throughout the text you will find instructions for using spreadsheet

2.7: THE LABORATORY NOTEBOOK Your laboratory notebook is your most important tool when working in the lab. If kept properly, you should be able to look back at your laboratory notebook several years from now and reconstruct the experiments on which you worked. Maintaining a laboratory notebook may seem like a great deal of effort, but if you do it well you will have a permanent record of your work. Scientists working in academic, industrial and governmental research labs rely on their notebooks to provide a written record.

2.8: BASIC TOOLS OF ANALYTICAL CHEMISTRY (EXERCISES) These are homework exercises to accompany "Chapter 2: Basic Tools of Analytical Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

2.9: BASIC TOOLS OF ANALYTICAL CHEMISTRY (SUMMARY) This is a summary to accompany "Chapter 2: Basic Tools of Analytical Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

1 10/3/2021 2.1: Measurements in Analytical Chemistry 2.1: Measurements in Analytical Chemistry

David Harvey 2.1.1 9/12/2021 https://chem.libretexts.org/@go/page/167732 2.2: Concentration 2.2: Concentration

David Harvey 2.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167733 2.3: Stoichiometric Calculations 2.3: Stoichiometric Calculations

David Harvey 2.3.1 9/12/2021 https://chem.libretexts.org/@go/page/167734 2.4: Basic Equipment 2.4: Basic Equipment

David Harvey 2.4.1 9/12/2021 https://chem.libretexts.org/@go/page/167735 2.5: Preparing Solutions 2.5: Preparing Solutions

David Harvey 2.5.1 9/12/2021 https://chem.libretexts.org/@go/page/167736 2.6: Spreadsheets and Computational Software 2.6: Spreadsheets and Computational Software

David Harvey 2.6.1 9/12/2021 https://chem.libretexts.org/@go/page/167737 2.7: The Laboratory Notebook 2.7: The Laboratory Notebook

David Harvey 2.7.1 9/12/2021 https://chem.libretexts.org/@go/page/167738 2.8: Basic Tools of Analytical Chemistry (Exercises) 2.E: Basic Tools of Analytical Chemistry (Exercises)

David Harvey 2.8.1 10/3/2021 https://chem.libretexts.org/@go/page/167739 2.9: Basic Tools of Analytical Chemistry (Summary) 2.S: Basic Tools of Analytical Chemistry (Summary)

David Harvey 2.9.1 9/12/2021 https://chem.libretexts.org/@go/page/167740 CHAPTER OVERVIEW

3: THE VOCABULARY OF ANALYTICAL CHEMISTRY If you leaf through an issue of the journal Analytical Chemistry, you will soon discover that the authors and readers share a common vocabulary of analytical terms. You are probably familiar with some of these terms, such as accuracy and precision, but other terms, such as analyte and matrix may be less familiar to you. In order to participate in the community of analytical chemists, you must first understand its vocabulary.

3.1: ANALYSIS, DETERMINATION, AND MEASUREMENT The first important distinction we will make is among the terms analysis, determination, and measurement. An analysis provides chemical or physical information about a sample. The component of interest in the sample is called the analyte, and the remainder of the sample is the matrix. In an analysis we determine the identity, concentration, or properties of an analyte. To make this determination we measure one or more of the analyte’s chemical or physical properties.

3.2: TECHNIQUES, METHODS, PROCEDURES, AND PROTOCOLS Suppose you are asked to develop an analytical method to determine the concentration of lead in drinking water. How would you approach this problem? To provide a structure for answering this question let’s draw a distinction among four levels of analytical methodology: techniques, methods, procedures, and protocols.

3.3: CLASSIFYING ANALYTICAL TECHNIQUES Analyzing a sample generates a chemical or physical signal that is proportional to the amount of analyte in the sample. This signal may be anything we can measure, such as mass or absorbance. It is convenient to divide analytical techniques into two general classes depending on whether the signal is proportional to the mass or moles of analyte, or to the analyte’s concentration.

3.4: SELECTING AN ANALYTICAL METHOD A method is the application of a technique to a specific analyte in a specific matrix. We can develop an analytical method for determining the concentration of lead in drinking water using any of the techniques mentioned in the previous section. The requirements of the analysis determine the best method and consideration is given the following criteria: accuracy, precision, sensitivity, selectivity, robustness, ruggedness, scale of operation, analysis time, availability of equipment, and cost.

3.5: DEVELOPING THE PROCEDURE After selecting a method the next step is to develop a procedure that will accomplish the goals of our analysis. In developing the procedure attention is given to compensating for interferences, to selecting and calibrating equipment, to acquiring a representative sample, and to validating the method.

3.6: PROTOCOLS A protocol is a set of stringent written guidelines specifying an exact procedure that must be followed before an agency will accept the results of an analysis. A protocol contains explicit instructions regarding internal and external quality assurance and quality control (QA/QC) procedures. The goal of internal QA/QC is to ensure that a laboratory’s work is both accurate and precise. External QA/QC is a process in which an external agency certifies a laboratory.

3.7: THE IMPORTANCE OF ANALYTICAL METHODOLOGY The importance of analytical methodology is evident if we examine environmental monitoring programs. The purpose of a monitoring program is to determine the present status of an environmental system, and to assess long term trends in the system’s health. These are broad and poorly defined goals. In many cases, an environmental monitoring program begins before the essential questions are known. This is not surprising since it is difficult to formulate questions in the absence of any results.

3.8: THE VOCABULARY OF ANALYTICAL CHEMISTRY (EXERCISES) These are homework exercises to accompany "Chapter 3: The Vocabulary of Analytical Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

3.9: THE VOCABULARY OF ANALYTICAL CHEMISTRY (SUMMARY) This is a summary to accompany "Chapter 3: The Vocabulary of Analytical Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

1 10/3/2021 3.1: Analysis, Determination, and Measurement 3.1: Analysis, Determination, and Measurement

David Harvey 3.1.1 9/12/2021 https://chem.libretexts.org/@go/page/167742 3.2: Techniques, Methods, Procedures, and Protocols 3.2: Techniques, Methods, Procedures, and Protocols

David Harvey 3.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167743 3.3: Classifying Analytical Techniques 3.3: Classifying Analytical Techniques

David Harvey 3.3.1 9/12/2021 https://chem.libretexts.org/@go/page/167744 3.4: Selecting an Analytical Method 3.4: Selecting an Analytical Method

David Harvey 3.4.1 10/3/2021 https://chem.libretexts.org/@go/page/167745 3.5: Developing the Procedure 3.5: Developing the Procedure

David Harvey 3.5.1 9/12/2021 https://chem.libretexts.org/@go/page/167746 3.6: Protocols 3.6: Protocols

David Harvey 3.6.1 9/12/2021 https://chem.libretexts.org/@go/page/167747 3.7: The Importance of Analytical Methodology 3.7: The Importance of Analytical Methodology

David Harvey 3.7.1 9/12/2021 https://chem.libretexts.org/@go/page/167748 3.8: The Vocabulary of Analytical Chemistry (Exercises) 3.E: The Vocabulary of Analytical Chemistry (Exercises)

David Harvey 3.8.1 9/12/2021 https://chem.libretexts.org/@go/page/167749 3.9: The Vocabulary of Analytical Chemistry (Summary) 3.S: The Vocabulary of Analytical Chemistry (Summary)

David Harvey 3.9.1 9/12/2021 https://chem.libretexts.org/@go/page/167750 CHAPTER OVERVIEW

4: EVALUATING ANALYTICAL DATA When using an analytical method we make three separate evaluations of experimental error. First, before beginning an analysis we evaluate potential sources of errors to ensure that they will not adversely effect our results. Second, during the analysis we monitor our measurements to ensure that errors remain acceptable. Finally, at the end of the analysis we evaluate the quality of the measurements and results, comparing them to our original design criteria.

4.1: CHARACTERIZING MEASUREMENTS AND RESULTS One way to characterize data from multiple measurements/runs is to assume that the measurements are randomly scattered around a central value that provides the best estimate of expected, or “true” value. There are two common ways to estimate central tendency: the mean and the median.

4.2: CHARACTERIZING EXPERIMENTAL ERRORS We call errors affecting the accuracy of an analysis determinate. Although there may be several different sources of determinate error, each source has a specific magnitude and sign. Some sources of determinate error are positive and others are negative, and some are larger in magnitude and others are smaller. The cumulative effect of these determinate errors is a net positive or negative error in accuracy.

4.3: PROPAGATION OF UNCERTAINTY A propagation of uncertainty allows us to estimate the uncertainty in a result from the uncertainties in the measurements used to calculate the result.

4.4: THE DISTRIBUTION OF MEASUREMENTS AND RESULTS A population is the set of all objects in the system we are investigating. For our experiment, the population is all United States pennies in circulation. This population is so large that we cannot analyze every member of the population. Instead, we select and analyze a limited subset, or sample of the population.

4.5: STATISTICAL ANALYSIS OF DATA A confidence interval is a useful way to report the result of an analysis because it sets limits on the expected result. In the absence of determinate error, a confidence interval indicates the range of values in which we expect to find the population’s expected mean. When we report a 95% confidence interval for the mass of a penny as 3.117 g ± 0.047 g, for example, we are claiming that there is only a 5% probability that the expected mass of penny is less than 3.070 g or more than 3.164 g.

4.6: STATISTICAL METHODS FOR NORMAL DISTRIBUTIONS The normal distribution is the most common distribution used for experimental results. Because the area between any two limits of a normal distribution is well defined, constructing and evaluating significance tests is straightforward.

4.7: DETECTION LIMITS A method’s as the smallest concentration or absolute amount of analyte that has a signal significantly larger than the signal from a suitable blank. Although our interest is in the amount of analyte, in this section we will define the detection limit in terms of the analyte’s signal.

4.8: USING EXCEL AND R TO ANALYZE DATA It can be tedious to work problems using nothing more than a calculator. Both Excel and R include functions for descriptive statistics, for finding probabilities for different distributions, and for carrying out significance tests. In addition, R provides useful functions for visualizing your data.

4.9: EVALUATING ANALYTICAL DATA (EXERCISES) These are homework exercises and select solutions to "Chapter 4: Evaluating Analytical Data" from Harvey's "Analytical Chemistry 2.0" Textmap.

4.10: EVALUATING ANALYTICAL DATA (SUMMARY) This is the summary to "Chapter 4: Evaluating Analytical Data" from Harvey's "Analytical Chemistry 2.0" Textmap.

1 10/3/2021 4.1: Characterizing Measurements and Results 4.1: Characterizing Measurements and Results

David Harvey 4.1.1 9/12/2021 https://chem.libretexts.org/@go/page/167752 4.2: Characterizing Experimental Errors 4.2: Characterizing Experimental Errors

David Harvey 4.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167753 4.3: Propagation of Uncertainty 4.3: Propagation of Uncertainty

David Harvey 4.3.1 9/12/2021 https://chem.libretexts.org/@go/page/167754 4.4: The Distribution of Measurements and Results 4.4: The Distribution of Measurements and Results

David Harvey 4.4.1 9/12/2021 https://chem.libretexts.org/@go/page/167755 4.5: Statistical Analysis of Data 4.5: Statistical Analysis of Data

David Harvey 4.5.1 9/12/2021 https://chem.libretexts.org/@go/page/167756 4.6: Statistical Methods for Normal Distributions 4.6: Statistical Methods for Normal Distributions

David Harvey 4.6.1 9/12/2021 https://chem.libretexts.org/@go/page/167757 4.7: Detection Limits 4.7: Detection Limits

David Harvey 4.7.1 9/12/2021 https://chem.libretexts.org/@go/page/167758 4.8: Using Excel and R to Analyze Data 4.8: Using Excel and R to Analyze Data

David Harvey 4.8.1 9/12/2021 https://chem.libretexts.org/@go/page/167759 4.9: Evaluating Analytical Data (Exercises) 4.E: Evaluating Analytical Data (Exercises)

David Harvey 4.9.1 9/12/2021 https://chem.libretexts.org/@go/page/167760 4.10: Evaluating Analytical Data (Summary) 4.S: Evaluating Analytical Data (Summary)

David Harvey 4.10.1 9/12/2021 https://chem.libretexts.org/@go/page/167761 CHAPTER OVERVIEW

5: STANDARDIZING ANALYTICAL METHODS Standardization is the process of determining the relationship between the signal and the amount of analyte in a sample. Previously, we defined this relationship as Stotal=kACA+Sreag where Stotal is the signal, nA is the moles of analyte, CA is the analyte’s concentration, kA is the method’s sensitivity for the analyte, and Sreag is the contribution to Stotal from sources other than the sample. To standardize a method we must determine values for kA and Sreag, which is the subject of this chapt

5.1: ANALYTICAL STANDARDS To standardize an analytical method we use standards containing known amounts of analyte. The accuracy of a standardization, therefore, depends on the quality of the reagents and glassware used to prepare these standards. We divide analytical standards into two categories: primary standards and secondary standards.

5.2: CALIBRATING THE SIGNAL The accuracy of our determination of kA and Sreag depends on how accurately we can measure the signal, Stotal. We measure signals using equipment, such as glassware and balances, and instrumentation, such as spectrophotometers and pH meters. To minimize determinate errors affecting the signal, we first calibrate our equipment and instrumentation.

5.3: DETERMINING THE SENSITIVITY To standardize an analytical method we also must determine the value of kA . In principle, it should be possible to derive the value of kA for any analytical method by considering the chemical and physical processes generating the signal. Unfortunately, such calculations are not feasible when we lack a sufficiently developed theoretical model of the physical processes, or are not useful because of nonideal chemical behavior.

5.4: LINEAR REGRESSION AND CALIBRATION CURVES In a single-point external standardization we determine the value of kA by measuring the signal for a single standard containing a known concentration of analyte. Using this value of kA and the signal for our sample, we then calculate the concentration of analyte in our sample. With only a single determination of kA, a quantitative analysis using a single-point external standardization is straightforward.

5.5: BLANK CORRECTIONS Thus far in our discussion of strategies for standardizing analytical methods, we have assumed the use of a suitable reagent blank to correct for signals arising from sources other than the analyte. We did not, however, ask an important question—“What constitutes an appropriate reagent blank?” Surprisingly, the answer is not immediately obvious.

5.6: USING EXCEL AND R FOR A REGRESSION ANALYSIS Although the calculations in this chapter are relatively straightforward—consisting, as they do, mostly of summations—it can be quite tedious to work through problems using nothing more than a calculator. Both Excel and R include functions for completing a linear regression analysis and for visually evaluating the resulting model.

5.7: STANDARDIZING ANALYTICAL METHODS (EXERCISES) This is a summary to accompany "Chapter 5: Standardizing Analytical Methods" from Harvey's "Analytical Chemistry 2.0" Textmap.

5.8: STANDARDIZING ANALYTICAL METHODS (SUMMARY) This is a summary to accompany "Chapter 5: Standardizing Analytical Methods" from Harvey's "Analytical Chemistry 2.0" Textmap.

1 10/3/2021 5.1: Analytical Standards 5.1: Analytical Standards

David Harvey 5.1.1 9/8/2021 https://chem.libretexts.org/@go/page/167763 5.2: Calibrating the Signal 5.2: Calibrating the Signal

David Harvey 5.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167764 5.3: Determining the Sensitivity 5.3: Determining the Sensitivity

David Harvey 5.3.1 9/12/2021 https://chem.libretexts.org/@go/page/167765 5.4: Linear Regression and Calibration Curves 5.4: Linear Regression and Calibration Curves

David Harvey 5.4.1 9/12/2021 https://chem.libretexts.org/@go/page/167766 5.5: Blank Corrections 5.5: Blank Corrections

David Harvey 5.5.1 9/26/2021 https://chem.libretexts.org/@go/page/167767 5.6: Using Excel and R for a Regression Analysis 5.6: Using Excel and R for a Regression Analysis

David Harvey 5.6.1 10/3/2021 https://chem.libretexts.org/@go/page/167768 5.7: Standardizing Analytical Methods (Exercises) 5.E: Standardizing Analytical Methods (Exercises)

David Harvey 5.7.1 9/12/2021 https://chem.libretexts.org/@go/page/167769 5.8: Standardizing Analytical Methods (Summary) 5.S: Standardizing Analytical Methods (Summary)

David Harvey 5.8.1 9/12/2021 https://chem.libretexts.org/@go/page/167770 CHAPTER OVERVIEW

6: EQUILIBRIUM CHEMISTRY Regardless of the problem on which an analytical chemist is working, its solution requires a knowledge of chemistry and the ability to apply that knowledge. For example, an analytical chemist studying the effect of pollution on spruce trees needs to know the chemical differences between p‑hydroxybenzoic acid and p‑hydroxyacetophenone, two phenols found in the needles of spruce trees. Your ability to “think as a chemist” is a product of your experience in the classroom and in the laboratory.

6.1: REVERSIBLE REACTIONS AND CHEMICAL EQUILIBRIA Although a system at equilibrium appears static on a macroscopic level, it is important to remember that the forward and reverse reactions continue to occur. A reaction at equilibrium exists in a steady-state, in which the rate at which a species forms equals the rate at which it is consumed. Hence, there is no further change in the amounts of these species.

6.2: THERMODYNAMICS AND EQUILIBRIUM CHEMISTRY Thermodynamics is the study of thermal, electrical, chemical, and mechanical forms of energy. The study of thermodynamics crosses many disciplines, including physics, engineering, and chemistry. Of the various branches of thermodynamics, the most important to chemistry is the study of the change in energy during a .

6.3: MANIPULATING EQUILIBRIUM CONSTANTS We will take advantage of two useful relationships when working with equilibrium constants. First, if we reverse a reaction’s direction, the equilibrium constant for the new reaction is simply the inverse of that for the original reaction. Second, if we add together two reactions to obtain a new reaction, the equilibrium constant for the new reaction is the product of the equilibrium constants for the original reactions.

6.4: EQUILIBRIUM CONSTANTS FOR CHEMICAL REACTIONS Several types of chemical reactions are important in analytical chemistry, either in preparing a sample for analysis or during the analysis. The most significant of these are: precipitation reactions, acid–base reactions, complexation reactions, and oxidation– reduction (redox) reactions. In this section we review these reactions and their equilibrium constant expressions.

6.5: LE CHÂTELIER’S PRINCIPLE The observation that a system at equilibrium responds to an external stress by reequilibrating in a manner that diminishes the stress, is formalized as Le Châtelier’s principle. One of the most common stresses to a system at equilibrium is to change the concentration of a reactant or product.

6.6: LADDER DIAGRAMS In this section we introduce the ladder diagram as a simple graphical tool for evaluating the equilibrium chemistry. Using ladder diagrams we will be able to determine what reactions occur when combining several reagents, estimate the approximate composition of a system at equilibrium, and evaluate how a change to solution conditions might affect an analytical method.

6.7: SOLVING EQUILIBRIUM PROBLEMS Ladder diagrams are a useful tool for evaluating chemical reactivity, usually providing a reasonable approximation of a chemical system’s composition at equilibrium. If we need a more exact quantitative description of the equilibrium condition, then a ladder diagram is insufficient. In this case we need to find an algebraic solution. In this section we will learn how to set-up and solve equilibrium problems. We will start with a simple problem and work toward more complex problems.

6.8: BUFFER SOLUTIONS As outlined below, the Henderson–Hasselbalch approximation provides a simple way to calculate the pH of a buffer, and to determine the change in pH upon adding a strong acid or strong base.

6.9: ACTIVITY EFFECTS The for a species corrects for any deviation between its physical and ideal concentration. For a gas, a pure solid, a pure liquid, or a non-ionic solute, the activity coefficient is approximately one under reasonable experimental conditions. For reactions involving only these species, the difference between activity and concentration is negligible. The activity coefficient for an , however, depends on the solution’s , the ion’s charge, and the ion’s size.

1 10/3/2021 6.10: USING EXCEL AND R TO SOLVE EQUILIBRIUM PROBLEMS In solving equilibrium problems we typically make one or more assumptions to simplify the algebra. These assumptions are important because they allow us to reduce the problem to an equation in x that we can solve by simply taking a square-root, a cube-root, or by using the quadratic equation. Without these assumptions, most equilibrium problems result in a cubic equation (or a higher-order equation) that is harder to solve. Both Excel and R are useful tools for solving such equations.

6.11: SOME FINAL THOUGHTS ON EQUILIBRIUM CALCULATIONS Several tools for evaluating the composition of a system at equilibrium were discussed; they differ in both accuracy and ease in answering questions involving equilibrium chemistry. If you need to know whether a reaction if favorable, or to estimate the pH of a solution, then a ladder diagram will meet your needs. On the other hand, if you require a more accurate estimate of a compound’s solubility, then a rigorous calculation that includes activity coefficients is necessary.

6.12: EQUILIBRIUM CHEMISTRY (EXERCISES) These are homework exercises to accompany "Chapter 6: Equilibrium Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

6.13: EQUILIBRIUM CHEMISTRY (SUMMARY) This is a summary to accompany "Chapter 6: Equilibrium Chemistry" from Harvey's "Analytical Chemistry 2.0" Textmap.

2 10/3/2021 6.1: Reversible Reactions and Chemical Equilibria 6.01: Reversible Reactions and Chemical Equilibria

David Harvey 6.1.1 9/12/2021 https://chem.libretexts.org/@go/page/167772 6.2: Thermodynamics and Equilibrium Chemistry 6.02: Thermodynamics and Equilibrium Chemistry

David Harvey 6.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167773 6.3: Manipulating Equilibrium Constants 6.03: Manipulating Equilibrium Constants

David Harvey 6.3.1 10/3/2021 https://chem.libretexts.org/@go/page/167774 6.4: Equilibrium Constants for Chemical Reactions 6.04: Equilibrium Constants for Chemical Reactions

David Harvey 6.4.1 9/12/2021 https://chem.libretexts.org/@go/page/167775 6.5: Le Châtelier’s Principle 6.05: Le Châtelier’s Principle

David Harvey 6.5.1 9/12/2021 https://chem.libretexts.org/@go/page/167776 6.6: Ladder Diagrams 6.06: Ladder Diagrams

David Harvey 6.6.1 9/12/2021 https://chem.libretexts.org/@go/page/167777 6.7: Solving Equilibrium Problems 6.07: Solving Equilibrium Problems

David Harvey 6.7.1 9/26/2021 https://chem.libretexts.org/@go/page/167778 6.8: Buffer Solutions 6.08: Buffer Solutions

David Harvey 6.8.1 9/12/2021 https://chem.libretexts.org/@go/page/167779 6.9: Activity Effects 6.09: Activity Effects

David Harvey 6.9.1 9/12/2021 https://chem.libretexts.org/@go/page/167780 6.10: Using Excel and R to Solve Equilibrium Problems 6.10: Using Excel and R to Solve Equilibrium Problems

David Harvey 6.10.1 9/12/2021 https://chem.libretexts.org/@go/page/167781 6.11: Some Final Thoughts on Equilibrium Calculations 6.11: Some Final Thoughts on Equilibrium Calculations

David Harvey 6.11.1 9/12/2021 https://chem.libretexts.org/@go/page/167782 6.12: Equilibrium Chemistry (Exercises) 6.E: Equilibrium Chemistry (Exercises)

David Harvey 6.12.1 9/12/2021 https://chem.libretexts.org/@go/page/167783 6.13: Equilibrium Chemistry (Summary) 6.S: Equilibrium Chemistry (Summary)

David Harvey 6.13.1 9/12/2021 https://chem.libretexts.org/@go/page/167784 CHAPTER OVERVIEW

7: GRAVIMETRIC METHODS Gravimetry includes all analytical methods in which the analytical signal is a measurement of mass or a change in mass. When you step on a scale after exercising you are making, in a sense, a gravimetric determination of your mass. Mass is the most fundamental of all analytical measurements, and gravimetry is unquestionably our oldest quantitative analytical technique.

7.1: OVERVIEW OF GRAVIMETRIC METHODS Before we consider specific gravimetric methods, let’s take a moment to develop a broad survey of gravimetry. Later, as you read through the descriptions of specific gravimetric methods, this survey will help you focus on their similarities instead of their differences. You will find that it is easier to understand a new analytical method when you can see its relationship to other similar methods.

7.2: PRECIPITATION GRAVIMETRY In precipitation gravimetry an insoluble compound forms when we add a precipitating reagent, or precipitant, to a solution containing our analyte. In most methods the precipitate is the product of a simple metathesis reaction between the analyte and the precipitant; however, any reaction generating a precipitate can potentially serve as a gravimetric method.

7.3: VOLATILIZATION GRAVIMETRY A second approach to gravimetry is to thermally or chemically decompose the sample and measure the resulting change in its mass. Alternatively, we can trap and weigh a volatile decomposition product. Because the release of a volatile species is an essential part of these methods, we classify them collectively as volatilization gravimetric methods of analysis.

7.4: PARTICULATE GRAVIMETRY Precipitation and volatilization gravimetric methods require that the analyte, or some other species in the sample, participate in a chemical reaction. In a direct precipitation gravimetric analysis, for example, we convert a soluble analyte into an insoluble form that precipitates from solution. In some situations, however, the analyte is already present as in a particulate form that is easy to separate from its liquid, gas, or solid matrix.

7.5: GRAVIMETRIC METHODS (EXERCISES) These are homework exercises to accompany "Chapter 8: Gravimetric Methods" from Harvey's "Analytical Chemistry 2.0" Textmap.

7.6: GRAVIMETRIC METHODS (SUMMARY) This is a summary to accompany "Chapter 8: Gravimetric Methods" from Harvey's "Analytical Chemistry 2.0" Textmap.

1 10/3/2021 7.1: Overview of Gravimetric Methods 8.1: Overview of Gravimetric Methods

David Harvey 7.1.1 9/12/2021 https://chem.libretexts.org/@go/page/167786 7.2: Precipitation Gravimetry 8.2: Precipitation Gravimetry

David Harvey 7.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167787 7.3: Volatilization Gravimetry 8.3: Volatilization Gravimetry

David Harvey 7.3.1 9/12/2021 https://chem.libretexts.org/@go/page/167788 7.4: Particulate Gravimetry 8.4: Particulate Gravimetry

David Harvey 7.4.1 10/3/2021 https://chem.libretexts.org/@go/page/167789 7.5: Gravimetric Methods (Exercises) 8.E: Gravimetric Methods (Exercises)

David Harvey 7.5.1 9/12/2021 https://chem.libretexts.org/@go/page/167790 7.6: Gravimetric Methods (Summary) 8.S: Gravimetric Methods (Summary)

David Harvey 7.6.1 9/12/2021 https://chem.libretexts.org/@go/page/167791 CHAPTER OVERVIEW

8: TITRIMETRIC METHODS Titrimetry, in which volume serves as the analytical signal, made its first appearance as an analytical method in the early eighteenth century. Titrimetric methods were not well received by the analytical chemists of that era because they could not duplicate the accuracy and precision of a gravimetric analysis. Not surprisingly, few standard texts from the 1700s and 1800s include titrimetric methods of analysis.

8.1: OVERVIEW OF TITRIMETRY In titrimetry we add a reagent, called the titrant, to a solution containing another reagent, called the titrand, and allow them to react. The type of reaction provides us with a simple way to divide titrimetry into the following four categories: (1) acid–base titrations, (2) complexometric titrations, (3) redox titrations, and (4) precipitation titrations.

8.2: ACID–BASE TITRATIONS Acid–base titrations, in which an acidic or basic titrant reacts with a titrand that is a base or an acid, is probably the most common used by students in laboratories. To understand the relationship between an acid–base titration’s end point and its equivalence point we must know how the pH changes during a titration. We will learn how to calculate a titration curve using the equilibrium calculations from Chapter 6.

8.3: COMPLEXATION TITRATIONS Complexometric titrations are based on metal– complexation. Practical analytical applications of complexation titrimetry were slow to develop because many metals and form a series of metal–ligand complexes.

8.4: REDOX TITRATIONS Redox titration are here the titrant is an oxidizing or reducing agent. In contrast to acid/base titrations, it is convenient for redox titrations to monitor the titration reaction’s potential instead of the concentration of one species.

8.5: PRECIPITATION TITRATIONS A reaction in which the analyte and titrant form an insoluble precipitate also can serve as the basis for a titration. We call this type of titration a precipitation titration.

8.6: TITRIMETRIC METHODS (EXERCISES) These are homework exercises to accompany "Chapter 9: Titrimetric Methods" from Harvey's "Analytical Chemistry 2.0" Textmap.

8.7: TITRIMETRIC METHODS (SUMMARY) This is a summary to accompany "Chapter 9: Titrimetric Methods" from Harvey's "Analytical Chemistry 2.0" Textmap.

1 10/3/2021 8.1: Overview of Titrimetry 9.1: Overview of Titrimetry

David Harvey 8.1.1 10/3/2021 https://chem.libretexts.org/@go/page/167793 8.2: Acid–Base Titrations 9.2: Acid–Base Titrations

David Harvey 8.2.1 9/12/2021 https://chem.libretexts.org/@go/page/167794 8.3: Complexation Titrations 9.3: Complexation Titrations

David Harvey 8.3.1 9/12/2021 https://chem.libretexts.org/@go/page/167795 8.4: Redox Titrations

David Harvey 8.4.1 9/11/2021 https://chem.libretexts.org/@go/page/167796 8.5: Precipitation Titrations 9.5: Precipitation Titrations

David Harvey 8.5.1 9/12/2021 https://chem.libretexts.org/@go/page/167797 8.6: Titrimetric Methods (Exercises) 9.E: Titrimetric Methods (Exercises)

David Harvey 8.6.1 9/12/2021 https://chem.libretexts.org/@go/page/167798 8.7: Titrimetric Methods (Summary) 9.S: Titrimetric Methods (Summary)

David Harvey 8.7.1 9/12/2021 https://chem.libretexts.org/@go/page/167799 Index

A analytical methods charge balance equation 3.4: Selecting an Analytical Method 6.7: Solving Equilibrium Problems abbreviation 3.7: The Importance of Analytical Methodology Chauvenet’s criterion 5.5: Blank Corrections 2.1: Measurements in Analytical Chemistry 4.6: Statistical Methods for Normal Distributions absorbance analytical signal chemical analysis 7.1: Overview of Gravimetric Methods 3.3: Classifying Analytical Techniques 1.1: What is Analytical Chemistry? accuracy Analytical titrations chemical reaction 8.4: Redox Titrations 3.4: Selecting an Analytical Method 6.2: Thermodynamics and Equilibrium Chemistry 4.2: Characterizing Experimental Errors Analyze Data Chesapeake Bay Monitoring Program acetic acid 4.8: Using Excel and R to Analyze Data 3.7: The Importance of Analytical Methodology 6.6: Ladder Diagrams argentometric titration Claude Berthollet acid 8.5: Precipitation Titrations 6.1: Reversible Reactions and Chemical Equilibria 6.4: Equilibrium Constants for Chemical Reactions asymmetric equivalence point Coagulation 6.7: Solving Equilibrium Problems 8.4: Redox Titrations 7.2: Precipitation Gravimetry 6.8: Buffer Solutions auxiliary complexing agent acid–base buffer common ion effect 8.3: Complexation Titrations 6.7: Solving Equilibrium Problems 6.8: Buffer Solutions auxiliary oxidizing agents acid–base titrations Complexation 8.4: Redox Titrations 6.4: Equilibrium Constants for Chemical Reactions 8.2: Acid–Base Titrations auxiliary reducing agent acid–base titrimetry 6.6: Ladder Diagrams 8.4: Redox Titrations 8.2: Acid–Base Titrations Complexation Reactions 8.4: Redox Titrations average 6.4: Equilibrium Constants for Chemical Reactions Acidity 4.6: Statistical Methods for Normal Distributions complexation titrations 8.2: Acid–Base Titrations 8.3: Complexation Titrations activity B Complexation Titrimetry 6.9: Activity Effects balanced reaction 8.3: Complexation Titrations Activity Coefficients 2.3: Stoichiometric Calculations concentration 6.9: Activity Effects base 2.2: Concentration Activity Effects 6.4: Equilibrium Constants for Chemical Reactions 2.4: Basic Equipment Berthollet 4.7: Detection Limits 6.9: Activity Effects 5.4: Linear Regression and Calibration Curves Alkalinity 6.1: Reversible Reactions and Chemical Equilibria 6.7: Solving Equilibrium Problems 8.2: Acid–Base Titrations binomial distribution 6.9: Activity Effects alternative hypotheses 4.4: The Distribution of Measurements and Results 6.10: Using Excel and R to Solve Equilibrium Problems 4.5: Statistical Analysis of Data blank 7.2: Precipitation Gravimetry alternative hypothesis 5.5: Blank Corrections 8.2: Acid–Base Titrations 4.5: Statistical Analysis of Data box plot concentration techniques amphiprotic 4.8: Using Excel and R to Analyze Data 3.3: Classifying Analytical Techniques 6.4: Equilibrium Constants for Chemical Reactions buffer concentrations Amphiprotic Species 6.8: Buffer Solutions 8.2: Acid–Base Titrations 6.4: Equilibrium Constants for Chemical Reactions buffer capacity 8.4: Redox Titrations analysis 6.8: Buffer Solutions conditional formation constant 3.1: Analysis, Determination, and Measurement Buffer Solutions 8.3: Complexation Titrations analyte 6.8: Buffer Solutions Confidence Interval 3.1: Analysis, Determination, and Measurement Buret 4.5: Statistical Analysis of Data 7.2: Precipitation Gravimetry 8.1: Overview of Titrimetry Confidence Intervals 7.4: Particulate Gravimetry 4.4: The Distribution of Measurements and Results 8.1: Overview of Titrimetry C Analytical Approach calculations 7.1: Overview of Gravimetric Methods 1.2: The Analytical Perspective constant determinate error analytical balance 2.3: Stoichiometric Calculations Calibration 4.2: Characterizing Experimental Errors 2.4: Basic Equipment continuing calibration blank analytical calculations 3.5: Developing the Procedure Calibration Curves 3.6: Protocols 2.3: Stoichiometric Calculations continuing calibration verification analytical chemistry 5.4: Linear Regression and Calibration Curves 3.6: Protocols 1.1: What is Analytical Chemistry? CCB 2.1: Measurements in Analytical Chemistry 3.6: Protocols Contract Laboratory Program analytical chemists CCV 3.6: Protocols 1.2: The Analytical Perspective 3.6: Protocols coprecipitates analytical method Central Limit Theorem 7.2: Precipitation Gravimetry 1.1: What is Analytical Chemistry? 4.4: The Distribution of Measurements and Results corresponding 3.4: Selecting an Analytical Method Central Tendency 6.8: Buffer Solutions 4.5: Statistical Analysis of Data 4.1: Characterizing Measurements and Results Cost 5.1: Analytical Standards 3.4: Selecting an Analytical Method 5.3: Determining the Sensitivity Characterization 6.6: Ladder Diagrams 8.2: Acid–Base Titrations Curvilinear regression analytical methodology characterization analysis 5.4: Linear Regression and Calibration Curves 3.7: The Importance of Analytical Methodology 1.3: Common Analytical Problems charge balance 6.7: Solving Equilibrium Problems D Equilibria gravimetric method Data 6.6: Ladder Diagrams 3.4: Selecting an Analytical Method 4.5: Statistical Analysis of Data equilibrium Gravimetry 4.8: Using Excel and R to Analyze Data 6.1: Reversible Reactions and Chemical Equilibria 3.3: Classifying Analytical Techniques Data Analysis 6.3: Manipulating Equilibrium Constants 7: Gravimetric Methods 6.5: Le Châtelier’s Principle 7.1: Overview of Gravimetric Methods 4.8: Using Excel and R to Analyze Data 6.6: Ladder Diagrams 7.2: Precipitation Gravimetry 5.6: Using Excel and R for a Regression Analysis 6.7: Solving Equilibrium Problems 7.3: Volatilization Gravimetry definitive techniques 6.9: Activity Effects 7.4: Particulate Gravimetry 7.1: Overview of Gravimetric Methods 6.10: Using Excel and R to Solve Equilibrium Grubb’s test Problems degrees of freedom 4.6: Statistical Methods for Normal Distributions 4.4: The Distribution of Measurements and Results equilibrium chemistry Descriptive Statistics 6.6: Ladder Diagrams H equilibrium concentration 4.8: Using Excel and R to Analyze Data Henderson–Hasselbalch approximation desiccant 6.7: Solving Equilibrium Problems 6.10: Using Excel and R to Solve Equilibrium 6.8: Buffer Solutions 2.4: Basic Equipment Problems histogram desiccator equilibrium constan 4.4: The Distribution of Measurements and Results 2.4: Basic Equipment 6.3: Manipulating Equilibrium Constants homogeneous precipitation detection limit equilibrium constant 7.2: Precipitation Gravimetry 3.4: Selecting an Analytical Method 6.2: Thermodynamics and Equilibrium Chemistry 4.7: Detection Limits 6.3: Manipulating Equilibrium Constants I determinate error Equilibrium Constants ICB 4.2: Characterizing Experimental Errors 6.3: Manipulating Equilibrium Constants 3.6: Protocols Determination 8.2: Acid–Base Titrations ICV 3.1: Analysis, Determination, and Measurement Equipment 3.6: Protocols 4.4: The Distribution of Measurements and Results 3.4: Selecting an Analytical Method digestion equivalence ICV and 3.6: Protocols 7.2: Precipitation Gravimetry 8.1: Overview of Titrimetry dilution 8.2: Acid–Base Titrations ignition 2.5: Preparing Solutions equivalence point 7.2: Precipitation Gravimetry direct analysis 8.1: Overview of Titrimetry inclusion 7.1: Overview of Gravimetric Methods 8.2: Acid–Base Titrations 7.2: Precipitation Gravimetry direct titration 8.4: Redox Titrations indeterminate errors Equivalence Points 8.1: Overview of Titrimetry 4.2: Characterizing Experimental Errors displacement titration 8.1: Overview of Titrimetry Indicator Equivalent Weights 8.1: Overview of Titrimetry 8.1: Overview of Titrimetry dissociation 8.2: Acid–Base Titrations 8.2: Acid–Base Titrations error 8.5: Precipitation Titrations 6.4: Equilibrium Constants for Chemical Reactions indirect analysis 6.8: Buffer Solutions 4.2: Characterizing Experimental Errors Ethylenediaminetetraacetic 7.1: Overview of Gravimetric Methods initial calibration blank 6.4: Equilibrium Constants for Chemical Reactions 8.3: Complexation Titrations 6.8: Buffer Solutions ethylenediaminetetraacetic acid 3.6: Protocols Distribution of Measurements 8.3: Complexation Titrations initial calibration verification 4.4: The Distribution of Measurements and Results Excel 3.6: Protocols Dixon’s Q‑test 2.6: Spreadsheets and Computational Software Inorganic Analysis 4.6: Statistical Methods for Normal Distributions 4.8: Using Excel and R to Analyze Data 7.3: Volatilization Gravimetry dot chart 5.6: Using Excel and R for a Regression Analysis Interferences Experimental Errors 4.8: Using Excel and R to Analyze Data 3.5: Developing the Procedure Drying 4.2: Characterizing Experimental Errors interferent External Standards 2.4: Basic Equipment 3.4: Selecting an Analytical Method 5.3: Determining the Sensitivity internal standard E 5.3: Determining the Sensitivity F EDTA ionic strength Fajans method 6.9: Activity Effects 8.3: Complexation Titrations 8.5: Precipitation Titrations IUPAC formality 4.7: Detection Limits 3.3: Classifying Analytical Techniques Electrogravimetry 2.2: Concentration formation constant 7.1: Overview of Gravimetric Methods J End point 6.4: Equilibrium Constants for Chemical Reactions Jones reductor Formation constants 8.2: Acid–Base Titrations 8.4: Redox Titrations 8.3: Complexation Titrations 8.3: Complexation Titrations 8.5: Precipitation Titrations fundamental analysis K End points 1.3: Common Analytical Problems Ka 8.1: Overview of Titrimetry 3.4: Selecting an Analytical Method G 5.4: Linear Regression and Calibration Curves 6.2: Thermodynamics and Equilibrium Chemistry Gibb’s free energy 6.4: Equilibrium Constants for Chemical Reactions 6.2: Thermodynamics and Equilibrium Chemistry Kb 6.2: Thermodynamics and Equilibrium Chemistry gravimetric analysis 6.4: Equilibrium Constants for Chemical Reactions environmental monitoring programs 7: Gravimetric Methods kernel density plot 3.7: The Importance of Analytical Methodology 4.8: Using Excel and R to Analyze Data Kjeldahl analysis method of standard additions pH 8.2: Acid–Base Titrations 5.3: Determining the Sensitivity 6.4: Equilibrium Constants for Chemical Reactions Microsoft Excel 6.10: Using Excel and R to Solve Equilibrium Problems 2.6: Spreadsheets and Computational Software L 8.2: Acid–Base Titrations laboratory Mohr method pH scale 8.5: Precipitation Titrations 2.7: The Laboratory Notebook 6.4: Equilibrium Constants for Chemical Reactions laboratory notebook molarity pipet 2.2: Concentration 2.7: The Laboratory Notebook 2.4: Basic Equipment Ladder diagram Moles PLOT 2.3: Stoichiometric Calculations 6.6: Ladder Diagrams 5.6: Using Excel and R for a Regression Analysis Ladder diagrams Monitoring Absorbance pnorm 8.3: Complexation Titrations 6.8: Buffer Solutions 4.8: Using Excel and R to Analyze Data Le Châtelier’s principle monitoring program point 3.7: The Importance of Analytical Methodology 6.5: Le Châtelier’s Principle 8.2: Acid–Base Titrations 6.6: Ladder Diagrams Monoprotic Polyprotic Le Chatelier's Principle 6.4: Equilibrium Constants for Chemical Reactions 6.4: Equilibrium Constants for Chemical Reactions 6.7: Solving Equilibrium Problems 6.5: Le Châtelier’s Principle 6.7: Solving Equilibrium Problems leveling Multivariate Regression population 5.4: Linear Regression and Calibration Curves 8.2: Acid–Base Titrations 4.4: The Distribution of Measurements and Results ligand Populations 6.4: Equilibrium Constants for Chemical Reactions N 4.4: The Distribution of Measurements and Results limit of identification potentiometric titration curve 4.7: Detection Limits 6.4: Equilibrium Constants for Chemical Reactions 8.2: Acid–Base Titrations Linear Regression normal calibration curve ppb 5.4: Linear Regression and Calibration Curves 5.3: Determining the Sensitivity 2.2: Concentration Normal Distribution ppm M 4.4: The Distribution of Measurements and Results 2.2: Concentration mass 4.5: Statistical Analysis of Data 4.6: Statistical Methods for Normal Distributions precipitant 2.4: Basic Equipment Normal Distributions 7.2: Precipitation Gravimetry 3.3: Classifying Analytical Techniques precipitate 4.1: Characterizing Measurements and Results 4.6: Statistical Methods for Normal Distributions 7.1: Overview of Gravimetric Methods normality 6.4: Equilibrium Constants for Chemical Reactions matrix 7.2: Precipitation Gravimetry 2.2: Concentration Precipitation 3.1: Analysis, Determination, and Measurement notebook 7.2: Precipitation Gravimetry matrix matching 2.7: The Laboratory Notebook 7.4: Particulate Gravimetry 5.3: Determining the Sensitivity 8.1: Overview of Titrimetry mean O 8.5: Precipitation Titrations 4.1: Characterizing Measurements and Results Occlusions precipitation gravimetry 4.6: Statistical Methods for Normal Distributions 7.1: Overview of Gravimetric Methods 7.2: Precipitation Gravimetry 7.2: Precipitation Gravimetry measurement Organic Analysis 3.1: Analysis, Determination, and Measurement Precipitation Reactions 7.3: Volatilization Gravimetry 4.1: Characterizing Measurements and Results 6.4: Equilibrium Constants for Chemical Reactions 4.2: Characterizing Experimental Errors Outliers Precipitation Titration 4.6: Statistical Methods for Normal Distributions Measurement Errors 8.5: Precipitation Titrations 4.2: Characterizing Experimental Errors oxidation Precipitation Titrimetry 6.4: Equilibrium Constants for Chemical Reactions measurements 8.5: Precipitation Titrations 6.6: Ladder Diagrams 2.1: Measurements in Analytical Chemistry precision 4.4: The Distribution of Measurements and Results oxidizing agent 3.4: Selecting an Analytical Method 6.4: Equilibrium Constants for Chemical Reactions Measuring Volume 4.2: Characterizing Experimental Errors 2.4: Basic Equipment 7.2: Precipitation Gravimetry median P 8.2: Acid–Base Titrations 4.1: Characterizing Measurements and Results paired data medication 4.6: Statistical Methods for Normal Distributions 6.2: Thermodynamics and Equilibrium Chemistry 4.5: Statistical Analysis of Data Particulate gravimetry primary standard meniscus 7.1: Overview of Gravimetric Methods 5.1: Analytical Standards 2.4: Basic Equipment 7.4: Particulate Gravimetry Probability Distributions metallochromic indicators particulates 4.4: The Distribution of Measurements and Results 4.8: Using Excel and R to Analyze Data 8.3: Complexation Titrations 7.4: Particulate Gravimetry method parts per billion procedure 3.2: Techniques, Methods, Procedures, and 3.2: Techniques, Methods, Procedures, and 2.2: Concentration Protocols Protocols Parts per million 3.4: Selecting an Analytical Method 2.2: Concentration product 5.3: Determining the Sensitivity peptization 6.5: Le Châtelier’s Principle method blank 7.2: Precipitation Gravimetry Products 3.5: Developing the Procedure personal error 2.3: Stoichiometric Calculations method error 6.5: Le Châtelier’s Principle 4.2: Characterizing Experimental Errors 4.2: Characterizing Experimental Errors propagation of uncertainty Method Errors 4.3: Propagation of Uncertainty 4.2: Characterizing Experimental Errors proportional determinate error 4.2: Characterizing Experimental Errors protocol S standard potential 3.2: Techniques, Methods, Procedures, and sample 6.4: Equilibrium Constants for Chemical Reactions Protocols 4.4: The Distribution of Measurements and Results Standard Reference Materials 4.2: Characterizing Experimental Errors Q Sample Distributions 4.4: The Distribution of Measurements and Results Qualitative Analysis Sample Means 6.2: Thermodynamics and Equilibrium Chemistry 1.3: Common Analytical Problems 4.6: Statistical Methods for Normal Distributions standardization Qualitative Applications Samples 5.3: Determining the Sensitivity 7.2: Precipitation Gravimetry 4.4: The Distribution of Measurements and Results Standardizing quality assurance Sampling 8.2: Acid–Base Titrations 3.6: Protocols 8.4: Redox Titrations 3.5: Developing the Procedure statistical analysis quality control Scale of Operation 3.6: Protocols 4.5: Statistical Analysis of Data 3.4: Selecting an Analytical Method statistical methods Quantitative Analysis scientific notation 1.3: Common Analytical Problems 4.6: Statistical Methods for Normal Distributions 2.1: Measurements in Analytical Chemistry stock solution quantitative science secondary standards 2.1: Measurements in Analytical Chemistry 2.5: Preparing Solutions 5.1: Analytical Standards stoichiometric quantitative transfer Selectivity 2.5: Preparing Solutions 2.3: Stoichiometric Calculations 3.4: Selecting an Analytical Method quartz crystal microbalance 8.2: Acid–Base Titrations stoichiometric relationship 7.4: Particulate Gravimetry selectivity coefficient 2.3: Stoichiometric Calculations 3.4: Selecting an Analytical Method R Sensitivity 3.4: Selecting an Analytical Method R 3.4: Selecting an Analytical Method strong acid 4.8: Using Excel and R to Analyze Data 5.3: Determining the Sensitivity 6.4: Equilibrium Constants for Chemical Reactions range 7.2: Precipitation Gravimetry 6.8: Buffer Solutions 8.2: Acid–Base Titrations strong 4.1: Characterizing Measurements and Results SI units reactant 8.2: Acid–Base Titrations 2.1: Measurements in Analytical Chemistry strong base 6.5: Le Châtelier’s Principle signal 6.4: Equilibrium Constants for Chemical Reactions Reactants 3.3: Classifying Analytical Techniques 6.8: Buffer Solutions 6.5: Le Châtelier’s Principle 5.2: Calibrating the Signal strong bases 8.1: Overview of Titrimetry reagent grade 8.2: Acid–Base Titrations 5.1: Analytical Standards significance test supernatant 4.5: Statistical Analysis of Data redox 7.2: Precipitation Gravimetry 8.4: Redox Titrations Significance Testing surface adsorbates 4.5: Statistical Analysis of Data redox indicator 7.2: Precipitation Gravimetry 8.4: Redox Titrations Significance Tests symbolic notation 4.8: Using Excel and R to Analyze Data Redox titration 2.2: Concentration 8.4: Redox Titrations Significant figures symmetric equivalence point 2.1: Measurements in Analytical Chemistry Redox Titration Curves 8.4: Redox Titrations 8.4: Redox Titrations slope Redox Titrimetry 5.4: Linear Regression and Calibration Curves T solubility 8.4: Redox Titrations technique reducing agent 6.7: Solving Equilibrium Problems 3.2: Techniques, Methods, Procedures, and 6.4: Equilibrium Constants for Chemical Reactions 6.10: Using Excel and R to Solve Equilibrium Problems Protocols reduction 7.2: Precipitation Gravimetry temperature 6.4: Equilibrium Constants for Chemical Reactions solubility product 6.2: Thermodynamics and Equilibrium Chemistry Regression 6.4: Equilibrium Constants for Chemical Reactions Tempmperature 5.6: Using Excel and R for a Regression Analysis solutions 8.2: Acid–Base Titrations Regression Analysis 2.5: Preparing Solutions theory 5.6: Using Excel and R for a Regression Analysis Specificity 7.2: Precipitation Gravimetry Regression Equation 3.4: Selecting an Analytical Method thermodynamically 5.4: Linear Regression and Calibration Curves spectrophotometric titration curve 6.2: Thermodynamics and Equilibrium Chemistry relative supersaturation 8.3: Complexation Titrations thermodynamics 7.2: Precipitation Gravimetry 6.2: Thermodynamics and Equilibrium Chemistry Repeatability 3.3: Classifying Analytical Techniques thermogram 4.2: Characterizing Experimental Errors Spreadsheets 7.3: Volatilization Gravimetry Reproducibility 2.6: Spreadsheets and Computational Software thermogravimetry 4.2: Characterizing Experimental Errors standard 7.3: Volatilization Gravimetry robust 5.5: Blank Corrections thermometric titration curve 3.4: Selecting an Analytical Method Standard Additions 8.1: Overview of Titrimetry room temperature 5.3: Determining the Sensitivity time 6.4: Equilibrium Constants for Chemical Reactions standard deviation 3.4: Selecting an Analytical Method rugged 4.1: Characterizing Measurements and Results titrand 3.4: Selecting an Analytical Method standard deviation about the regression 8.1: Overview of Titrimetry 5.4: Linear Regression and Calibration Curves 8.4: Redox Titrations Standard Error of the Mean 8.5: Precipitation Titrations 4.4: The Distribution of Measurements and Results titrant type 2 error Volatilization 8.1: Overview of Titrimetry 4.5: Statistical Analysis of Data 7.3: Volatilization Gravimetry 8.5: Precipitation Titrations volatilization gravimetric titration U 7.4: Particulate Gravimetry 8.2: Acid–Base Titrations ultramicro Volatilization Gravimetry titration curve 3.4: Selecting an Analytical Method 7.1: Overview of Gravimetric Methods 8.3: Complexation Titrations uncertainty 7.3: Volatilization Gravimetry 8.5: Precipitation Titrations 2.1: Measurements in Analytical Chemistry Volhard method Titration Curves 4.2: Characterizing Experimental Errors 8.5: Precipitation Titrations 8.1: Overview of Titrimetry 4.3: Propagation of Uncertainty volume 8.4: Redox Titrations 5.4: Linear Regression and Calibration Curves 2.4: Basic Equipment 8.5: Precipitation Titrations unit 3.3: Classifying Analytical Techniques titration error 2.2: Concentration volume percent 8.1: Overview of Titrimetry unit conversion 2.2: Concentration titrations 2.2: Concentration volumetric buret 8.5: Precipitation Titrations units 8.1: Overview of Titrimetry Titrimetry 2.2: Concentration volumetric flask 3.3: Classifying Analytical Techniques unpaired data 2.4: Basic Equipment 8.1: Overview of Titrimetry 8.2: Acid–Base Titrations 4.6: Statistical Methods for Normal Distributions volumetric pipet 8.3: Complexation Titrations unweighted linear regression 2.4: Basic Equipment 8.4: Redox Titrations 5.4: Linear Regression and Calibration Curves 8.5: Precipitation Titrations W tolerance V 4.2: Characterizing Experimental Errors weak acid total analysis technique validation 6.7: Solving Equilibrium Problems 3.5: Developing the Procedure 8.3: Complexation Titrations 3.3: Classifying Analytical Techniques Weak Acids total Youden blank Variance 4.1: Characterizing Measurements and Results 6.4: Equilibrium Constants for Chemical Reactions 5.5: Blank Corrections type 1 error Visualizing Data 4.8: Using Excel and R to Analyze Data 6.8: Buffer Solutions 4.5: Statistical Analysis of Data Weight percent 2.2: Concentration Glossary Sample Word 1 | Sample Definition 1