Harris: Quantitative Chemical Analysis, Eight Edition CHAPTER 03: EXPERIMENTAL ERROR
|
|
- Adela Malone
- 5 years ago
- Views:
Transcription
1 Harris: Quantitative Chemical Analysis, Eight Edition CHAPTER 03: EXPERIMENTAL ERROR
2
3 Chapter 3. Experimental Error -There is error associated with every measurement. -There is no way to measure the true value of anything. - The best way we can do in a chemical analysis is to apply a technique that experience tells us is reliable. - Repetition of one method of measurement several times tells us the precision (reproducibility) of the measurement - If the results of measuring the same quantity by different methods agree with one another, then we become confident that the results are accurate, which means they are near the true value.
4 Chapter 3. Experimental Error 3-1. Significant Figures The number of significant ifi tfigures is the minimum i number of fdigits it needed dto write a given value in scientific notation without loss of accuarcy. Fig Scale of a spectrophotometer. p Absorbance is a logarithmic scale. Absorbance = 0.34 by interpolation. and 3 are completely certain and the number 4 is an estimate. This number has three significant figures.
5 Chapter 3. Experimental Error 3-. Significant Figures in Arithmetic ( rule of thumb ) 1) Addition & Substraction - In the addition or subtraction of numbers expressed in scientific notation, all numbers should first be expressed with the same exponent. - If the numbers being added do not have the same number of significant figures, we are limited by the least certain one. Rounding off - In the special case where the number is exactly halfway, round to the nearest even digit. ex) , , When rounding off, look at all the digits beyond the last place desired. ex)
6 Chapter 3. Experimental Error 3-. Significant Figures in Arithmetic ( rule of thumb ) ) Multiplication & Division We are normally limited to the number of digits contained in the number with the fewest significant figures. But use the rule of thumb with Caution!! A rule of thumb sometimes suggested for multiplication and division that the answer should be rounded so that it contains the same number of significant digits as the original number with the smallest number of significant digits. Unfortunately, this procedure can lead to incorrect rounding. For example, consider the two calculations = 1.08 and = B h l j d ibd h fi ldb dd 11 d By the rule just described, the first answer would be rounded to 1.1 and the second to 0.96.
7 Use the rule of thumb with Caution!! However, if the last digit of each number making up the first quotient is uncertain by 1, the relative uncertainties associated with each of these numbers are 1/4, 1/45, and 1/1000. Because the first relative uncertainty is much larger than the other two, the relative uncertainty in the result is also 1/4; the absolute uncertainty is then /4 = = 0.04 By the same argument, the absolute uncertainty of the second answer is given by /4 = = Therefore, the first result should be rounded to three significant figures, or 1.08, but the second should be rounded to only two; that is, 0.96 * Rounding should only be done on the final answer (not intermediate results), g y ( ) to avoid accumulating round-off errors
8 3-. Significant Figures in Arithmetic 3) Logarithms and Antilogarithms * Number of digits in mantissa of log x = number of significant figures in x : log ( ) = digits character mantissa * Number of digits in the mantissa of x = Number of significant figures in the antilogarithm, antilog x (=10 x ) antilog 6.14 = = mantissa, 3 digits 3 digits
9 3.3. Significant Figures and Graphs - When the graph is used to read data points, better is a fine grid superimposed on the graph - Rulings on graph should be compatible with the number of significant figures of the coordinates. a) Divisions are fine enough (0.53, 0.63), (1.08, 1.47)
10 3.3. Significant Figures and Graphs - When the graph is used to read data points, better is a fine grid superimposed on the graph -Rulings on graph should be compatible with the number of significant figures of the coordinates. b) Divisions are not fine enough (0.53, 0.63), (1.08, 1.47)
11 3.3. Significant Figures and Graphs When you are not expected to be able to read coordinates accurately on the graph, Qualitative behavior of data is OK (i.e., fine grid is not required)
12 3-4. Types of Errors in Experimental Data 1) Systematic errors (= Determinate Errors) - It is always in the same direction (unidirectional), and could be discovered and corrected. -It causes the mean of a set of data to differ from the accepted value ( Next slide, analyst 3 ) ) Random Error ( = Indeterminate error) 3) Gross Errors
13 Systematic error (Analyst 3 & 4) Fig 5-3, p.94
14 3-4. Types of Errors in Experimental Data 1) Systematic errors (= Determinate Errors) i) Instrument t Errors - imperfections in measuring devices. pipets, burets and volumetric flasks frequently deliver or contain volumes slightly different from those indicate by their graduations. The reasons are as following: Use of glassware at a temp. that differs significantly from the calibration temp. Distortions in container walls due to heating while drying. Errors in the original calibration. Contaminants on the inner surfaces of the container. Most systematic errors of this type are readily eliminated by calibration ( see next slide, textbook Fig. 3-3) - instruments powered by electricity. decreased voltage of battery-operated power supplies increased resistance in circuits because of dirty electrical contacts temp. effects on resistor
15 3.3. Significant Figures and Graphs Most systematic errors of this type are readily eliminated by calibration! Ex.) Buret reading: 9.43 ml, Correction: - 003mL 0.03 Actual volume = =9.40 ml Fig. 3-3 Calibration Curve for a 50 ml buret
16 3-4. Types of Errors in Experimental Data ii) Method Errors Nonideal chemical or physical behavior of the reagents and reactions upon which an analysis is based. incompleteness of the reaction (ex: decomposition of pyridine ring) slowness of the reaction possible occurrence of side reactions that interfere with the measurement process in volumetric titration, the small excess of reagent required to cause an indicator to undergo the color change that signals completion of the reaction Errors inherent in a method are frequently difficult to detect, and are thus the most serious of the three types of determinate error.
17 3-4. Types of Errors in Experimental Data iii) Personal Errors Many measurements require personal ljudgments. - Prejudice (bias) Most of us have a natural tendency to estimate scale readings in a direction that improves the precision in a set of results or causes the results to fall closer to a preconceived notion of the true value. level of a liquid in buret color at the end point in titration the position of a pointer between two scales
18 3-4. Types of Errors in Experimental Data iii) Personal Errors Many measurements require personal ljudgments. - Number bias prefer 0 or 5 even number over odd number. * Detection of determinate errors. 1. Analysis of standard reference materials. a second reliable analytical method 3. Blank determinations 4. Variation in sample size in case of a constant error
19 3-4. Types of Errors in Experimental Data * Determinate Error may be either constant or proportional Constant Errors : magnitude is independent of size of the quantity measured. Ex). 500 mg of precipitate 0.5 mg wash out 50 mg of precipitate 0.5 mg wash out 0.5 relative error = = % relative error = = -1.0% 50 Proportional Errors : increase or decrease in proportion to the size of the sample taken for analysis. Ex). the presence of interfering contaminants in the sample.
20 Absolute and Relative Uncertainty - Uncertainty is usually expressed as the standard deviation. Absolute Uncertainty : margin of uncertainty associated with a measurement. Ex). a buret reading : 1.35±0.0 ml Relative Uncertainty : comparing the size of the absolute uncertainty to the size of its associated measurement. R.U = absolute uncertainty magnitude of measurement 0.0 ml ex). RU R.U = = = ppt = 0 0. % 1.35 ml
21 3-4. Types of Errors in Experimental Data ) Random Error ( = Indeterminate error) - It arises from natural limitation on our ability to make physical measurements. - It causes data to be scattered more or less systematically around a mean value. The precision of the data reflects the indeterminate errors in an analysis. - Sometimes positive, sometimes negative. - It is the ultimate limitation on the determination of a quantity. See next slide Ex). Electrical noise : small fluctuation resulting from electrical instability of the meter itself (voltameter)
22 3-4. Types of Errors in Experimental Data 3) Gross Errors - personal and arise from carelessness or ineptitude on the part of the experimenter. - Gross errors usually affect only a single result in a set of replicate data, causing it to differ significantly from the remaining results for that set. (outliers) Ex). Arithmetic mistakes Reading scale backward Reversing a sign Spilling a solution - They can be eliminated through self-discipline
23 3-4-1 Methods For Expressing Precision and Accuracy Precision : A measure of reproducibility of a result defined as the agreement between the numerical values of two or more measurements that have been made in an identical method. Accuracy : How close a measured value is to the true one Accuracy : How close a measured value is to the true one - the nearness of a measurement to its accepted value - Accuracy is expressed in terms of error.
24 Fig 5-3, p.94 Precision and Accuracy
25 Accuracy (= nearness to the truth ) Methods for expressing accuracy 1) Absolute Error = x i x t x i : observed value x t : accepted value (It may itself lfbe subject to considerable uncertainty) ) Relative Error = x x x i t t 100 %
26 Precision (= reproducibility) Methods for expressing precision x i i Mean or Average = x = N Geometric Mean = n i x i 1) Standard Deviation For a very large set of data σ = N i= 1 ( x μ ) i N σ: population S. D. μ: population p mean ( = true value) σ : variance
27 Methods for expressing precision For a small number of replicate measurements, S = N i= 1 ( x x) i N -1 S : sample standard deviation x : measured mean for the small set ) Relative Standard d Deviation (RSD) S RSD = x 1,000 (ppt) S CV (coefficient of variation) = 100 % x
28 Methods for expressing precision 3) Variance (S ) S = N i= 1 ( x x) i N -1 4) Spread or Range (w) = highest lowest
29
30 3-5. Propagation of Uncertainty from Random Error - We can easily estimate or measure the random error associated with a measurement. - Uncertainty is usually expressed as the standard deviation of calculated results or as a confidence interval. These parameters are based upon a series of replicate measurements. -In most experiments, it is necessary to perform successive arithmetic operations on several numbers, each of which has its associated random error. - The most likely uncertainty in the result is not the sum of individual errors, because some of these are likely positive and some negative. We expect some cancellation of errors. - The first uncertain figure should be the last significant figure : ex) (±0.000)
31 3-5. Propagation of Uncertainty from Random Error 1) Addition and Subtraction 176( 1.76 (±0.03) 03) e 1 Uncertainty in addition (±0.0) e and subtraction: (±0.0) e (± e 4 ) e 4 = e1 + e + e3 = Absolute uncertainty e 4 = ( 0.03) + (0.0) + (0.0) = Percent relative uncertainty = 100 = 1. 3% 3.06 Two expressions of final result : 3.06 (±0.04) (absolute uncertainty) 3.06 (±1%) (relative uncertainty)
32 3-5. Propagation of Uncertainty from Random Error ) Multiplication and Division Uncertainty in multiplication and division: For example, 1.76( ± 0.03) 1.89( ± 0.0) = 0.59( ± 0.0) 0) % e + e 5.64 ± e 4 = (% e1 ) + (% e ) (% 3 ) First, convert absolute uncertainties to percent relative uncertainties ( ± 1. 7 %) 1.89( ± ( ± 3. 4 %) 1 %) = 5.64 ± e 4 % e4 = (1. 7 ) + (1. 1) + (3. 4 ) = 4. 0% 4. = 0 % = Two expressions of final result : 56(±0)( 5.6 (±0.) (absolute uncertainty) 5.6 (±4%) (relative uncertainty)
33
34 tip) Propagation of Uncertainty in the Product x x Table 3-1 says that the uncertainty in the function y = x a is % e y = a (%e x ). If y = X, then %e y = (%e x ). A 3% uncertainty in x leads to a ()(3%) = 6% uncertainty in y. But what if we just apply the multiplication li formula 3-6 to the product x x? ( x ± e ) x( ± e ) = x ( ± ) ( 1 e3 % e + e 3 = (% e 1 ) (% ) = ( 3%) + (3%) = 4. % Which uncertainty is correct, 6 % or 4. %?
35 tip) Propagation of Uncertainty in the Product x x
36 3-6. Propagation of Uncertainty from Systematic Error Systematic error occurs in some common situations and is treated differently from random error in arithmetic operation 1) The Rectangular Distribution : uncertainty in atomic mass - atomic mass of oxygen in the periodic table : ± ( Next slide) - The uncertainty t isnot mainly from random error in measuring atomic mass, but it is predominantly from isotopic variation in samples of oxygen from different sources. Therefore, the atomic mass of oxygen in a particular lot of reagent has a systematic uncertainty - There is approximately equal probability of finding any atomic mass between and and negligible probability of finding an atomic mass outside of the range. - Mean: , range : The standard uncertainty (standard deviation) = ± a (range)/ 3
37 End Papers: Periodic Table
38 3-6. Propagation of Uncertainty from Systematic Error -Oxygen atomic mass from different sources approximates a rectangular distribution. - There is approximately equal probability bili of finding any atomic mass between and and negligible probability of finding any atomic mass outside of the range (a).
39 3-6. Propagation of Uncertainty from Systematic Error - Systematic error occurs in some common situations, and is treated differently from random error in arithmetic operations 1) The Rectangular Distribution : uncertainty in atomic mass - The periodic table gives the atomic mass of oxygen as ± g/mol. The uncertainty is not mainly from random error in measuring the atomic mass, but it is predominantly from isotopic variation in sampled oxygen from different sources. - The atomic mass of oxygen in a particular lot of reagent has a systematic uncertainty.
40 3-6. Propagation of Uncertainty from Systematic Error - Propagation of systematic uncertainty : uncertainty of n identical atoms = n x (standard uncertainty in atomic mass) - The sum of atomic masses of different elements : Use the rules for propagation of random uncertainty Example: what is the standard uncertainty in molecular mass of C H 4? From periodic table, Atomic mass of C = ± / 3 = ± Atomic mass of H = ± / = ±
41 3-6. Propagation of Uncertainty from Systematic Error -For the uncertainty in the sum of the masses of C +4H, we use equations for random error, because the uncertainties in the mass of C and H are independent of each other. One might be positive and one might be negative ± = ± = ±
42 3-6. Propagation of Uncertainty from Systematic Error ) The Triangular Distribution : multiple deliveries from one pipet - A 5 ml pipet is certified to deliver 5.00 ± 0.03 ml - The volume delivered by a pipet is reproducible, but can be in the range of 4.97 ~ 5.03 ml, depending on a pipet. p - However, the manufacturer works hard to make the volume close to 5.00mL. In such case, we approximate the volumes of a large number of pipets by the triangular distribution.
43 3-6. Propagation of Uncertainty from Systematic Error - The probability falls off approximately in a linear manner as the volume deviates from 5.00 ml because the manufacturer works hard to make the volume close to 5.00mL. - There is negligible probability that a volume outside of 5.00 ± 0.03 ml will be delibered. - The standard uncertainty (standard deviation) = ± a (range)/ 6 3
44 3-6. Propagation of Uncertainty from Systematic Error Example: 1) What is the uncertainty in 100 ml if you use an uncalibrated 5 ml pipet four times to deliver of 100 ml? The uncertainty is a systematic error. So the standard uncertainty = ± 4x 0.03/ 003/ 6 = ± 4 x 0.01 = ± ml So uncalibrated pipet volume = ± ml - The difference between 5.00 ml and the actual volume delibered by a particular pipet is a systematic error. In other words, it is always the same, within a small random error - You could calibrate the pipet by weighing the water it delivers to eliminate a systematic error. In such case, the pipet always delivers, say, ± ml. The uncertainty (± ml) is random error.
45 3-6. Propagation of Uncertainty from Systematic Error Example: 1) What is the uncertainty in 100 ml if you use a calibrated pipet which delivers a mean volume of ml with a standard uncertainty of ± ml? You deliver four times, so the volume is 4 x ml = ml But the uncertainty = ± = ± 0.01 ml We use equations for random error, because the uncertainties in four delivered aliquots are independent of each other. One might be positive and one might be negative because they are random error. So calibrated pipet volume = ± 0.01 ml
Harris: Quantitative Chemical Analysis, Eight Edition CHAPTER 03: EXPERIMENTAL ERROR
Harris: Quantitative Chemical Analysis, Eight Edition CHAPTER 03: EXPERIMENTAL ERROR Chapter 3. Experimental Error -There is error associated with every measurement. -There is no way to measure the true
More information03.1 Experimental Error
03.1 Experimental Error Problems: 15, 18, 20 Dr. Fred Omega Garces Chemistry 251 Miramar College 1 Making a measurement In general, the uncertainty of a measurement is determined by the precision of the
More informationSource: Chapter 5: Errors in Chemical Analyses
Source: Chapter 5: Errors in Chemical Analyses Measurements invariably involve errors and uncertainties. it is impossible to perform a chemical analysis that is totally free of errors or uncertainties
More informationCh 3. EXPERIMENTAL ERROR
Ch 3. EXPERIMENTAL ERROR 3.1 Measurement data how accurate? TRUE VALUE? No way to obtain the only way is approaching toward the true value. (how reliable?) How ACCURATE How REPRODUCIBLE accuracy precision
More informationChapter 5. Errors in Chemical Analysis 熊同銘.
Chapter 5 Errors in Chemical Analysis 熊同銘 tmhsiung@gmail.com http://www.chem.ntou.edu.tw/ Slide 1 of 19 Contents in Chapter 5 5.1 Accuracy, Precision and Bias 5.2 Types of Errors in Experimental Data 5.3
More informationStatistics: Error (Chpt. 5)
Statistics: Error (Chpt. 5) Always some amount of error in every analysis (How much can you tolerate?) We examine error in our measurements to know reliably that a given amount of analyte is in the sample
More informationLecture 3. - all digits that are certain plus one which contains some uncertainty are said to be significant figures
Lecture 3 SIGNIFICANT FIGURES e.g. - all digits that are certain plus one which contains some uncertainty are said to be significant figures 10.07 ml 0.1007 L 4 significant figures 0.10070 L 5 significant
More informationChapter 3 Math Toolkit
Chapter 3 Math Toolkit Problems - any Subtitle: Error, where it comes from, how you represent it, and how it propagates into your calculations. Before we can start talking chemistry we must first make
More informationMeasurements, Sig Figs and Graphing
Measurements, Sig Figs and Graphing Chem 1A Laboratory #1 Chemists as Control Freaks Precision: How close together Accuracy: How close to the true value Accurate Measurements g Knowledge Knowledge g Power
More informationANALYTICAL CHEMISTRY 1 LECTURE NOTES
ANALYTICAL CHEMISTRY 1 LECTURE NOTES FUNDAMENTALS OF PRE ANALYSES TOPIC 1: Theory of Errors 1.0 Introduction Analytical chemistry is a specialised aspect of chemistry that deals with both qualitative analysis
More informationTopic 2 Measurement and Calculations in Chemistry
Topic Measurement and Calculations in Chemistry Nature of Measurement Quantitative observation consisting of two parts. number scale (unit) Examples 0 grams 6.63 10 34 joule seconds The Fundamental SI
More informationChapter 3 Experimental Error
Chapter 3 Experimental Error Homework Due Friday January 27 Problems: 3-2, 3-5, 3-9, 3-10, 3-11, 3-12, 3-14, 3-19 Chapter 3 Experimental Error Uncertainties They are everywhere!! We need to learn to understand
More informationExperiment 1 - Mass, Volume and Graphing
Experiment 1 - Mass, Volume and Graphing In chemistry, as in many other sciences, a major part of the laboratory experience involves taking measurements and then calculating quantities from the results
More informationWhy the fuss about measurements and precision?
Introduction In this tutorial you will learn the definitions, rules and techniques needed to record measurements in the laboratory to the proper precision (significant figures). You should also develop
More informationChem 222 #3 Ch3 Aug 31, 2004
Chem 222 #3 Ch3 Aug 31, 2004 Announcement Please work in the lab session you registered for. If you are found to work in any other lab without my permission, no points will be given for the lab. Please
More informationMeasurements Chapter 3
Measurements Chapter 3 Analytical Chemistry is the science of chemical measurement. Its object is the generation, treatment and evaluation of signals from which information is obtained on the composition
More informationJan 18, 2005 #3. Average (Ch. 4) Standard deviation Q-test Significant Figures (Ch 3) Error
Jan 18, 2005 #3 Average (Ch. 4) Standard deviation Q-test Significant Figures (Ch 3) Error Announcement When you send me an e- mail, please identify your full name and lab session. Jan 21 is the last day
More informationData Analysis I. CU- Boulder CHEM-4181 Instrumental Analysis Laboratory. Prof. Jose-Luis Jimenez Spring 2007
Data Analysis I CU- Boulder CHEM-4181 Instrumental Analysis Laboratory Prof. Jose-Luis Jimenez Spring 2007 Presentation will be posted on course web page based on lab manual, Skoog, web links 5 Objective
More informationChapters 0, 1, 3. Read Chapter 0, pages 1 8. Know definitions of terms in bold, glossary in back.
1 Chapters 0, 1, 3 Analytical chemistry is chemical measurement science. Qualitative analysis what is it? Quantitative analysis how much of it is there? This class covers the following: 1. Measurement
More informationChemistry Calibration of a Pipet and Acid Titration
Chemistry 3200 Today you are given a chance to brush up on some of the techniques that you will be using during the remainder of the semester. Lab grades will be based on obtaining the correct answer in
More informationAccuracy and Precision of Laboratory Glassware: Determining the Density of Water
Accuracy and Precision of Laboratory Glassware: Determining the Density of Water During the semester in the general chemistry lab, you will come into contact with various pieces of laboratory glassware.
More informationWhat is measurement uncertainty?
What is measurement uncertainty? What is measurement uncertainty? Introduction Whenever a measurement is made, the result obtained is only an estimate of the true value of the property being measured.
More informationADVANCED ANALYTICAL LAB TECH (Lecture) CHM
ADVANCED ANALYTICAL LAB TECH (Lecture) CHM 4130-0001 Spring 2013 Professor Andres D. Campiglia Textbook: Principles of Instrumental Analysis Skoog, Holler and Crouch, 5 th Edition, 6 th Edition or newest
More informationTopic 11: Measurement and Data Processing and Analysis. Topic Uncertainties and Errors in Measurement and Results
Topic 11: Measurement and Data Processing and Analysis Topic 11.1- Uncertainties and Errors in Measurement and Results Key Terms Random Error- above or below true value, usually due to limitations of equipment
More informationChem 321 Lecture 4 - Experimental Errors and Statistics 9/5/13
Chem 321 Lecture 4 - Experimental Errors and Statistics 9/5/13 Student Learning Objectives Experimental Errors and Statistics The tolerances noted for volumetric glassware represent the accuracy associated
More informationCHEM 334 Quantitative Analysis Laboratory
Calibration of Volumetric Glassware Introduction Volumetric glassware is a class of glass vessels that are calibrated to contain or deliver certain volumes of substances. Graduated cylinders, pipettes
More informationSource slideplayer.com/fundamentals of Analytical Chemistry, F.J. Holler, S.R.Crouch. Chapter 6: Random Errors in Chemical Analysis
Source lideplayer.com/fundamental of Analytical Chemitry, F.J. Holler, S.R.Crouch Chapter 6: Random Error in Chemical Analyi Random error are preent in every meaurement no matter how careful the experimenter.
More informationError Analysis. Table 1. Tolerances of Class A Pipets and Volumetric Flasks
Error Analysis Significant Figures in Calculations Most lab report must have an error analysis. For many experiments, significant figure rules are sufficient. Remember to carry at least one extra significant
More informationIdentification Of The Common Laboratory Glassware, Pipettes And Equipment. BCH 312 [Practical]
Identification Of The Common Laboratory Glassware, Pipettes And Equipment BCH 312 [Practical] (1) Identification of the common laboratory glassware : Conical flasks and beakers: Graduated cylinders Volumetric
More informationUncertainties in Measurement
Uncertainties in Measurement Laboratory investigations involve taking measurements of physical quantities. All measurements will involve some degree of experimental uncertainty. QUESTIONS 1. How does one
More informationMeasurements and Errors
1 Measurements and Errors If you are asked to measure the same object two different times, there is always a possibility that the two measurements may not be exactly the same. Then the difference between
More informationNaOH (aq) + HCl (aq) NaCl (aq) + H 2 O (l)
EXPERIMENT 21 Molarity of a Hydrochloric Acid Solution by Titration INTRODUCTION Volumetric analysis is a general term meaning any method in which a volume measurement is the critical operation; however,
More informationprecision accuracy both neither
I. Measurement and Observation There are two basic types of data collected in the lab: Quantitative : numerical information (e.g., the mass of the salt was.45 g) Qualitative : non-numerical, descriptive
More informationPractice Lab. Balances and calibration of volumetric tools
Practice Lab. Balances and calibration of volumetric tools Balances are a very basic and very valuable tool in any chemistry lab and any chemist must understand their use, their proper treatment, their
More informationAssessment of Accuracy and Precision
2 chapter Assessment of Accuracy and Precision S.S. Nielsen, Food Analysis Laboratory Manual, Food Science Texts Series, DOI 10.1007/978-1-4419-1463-7_2, Springer Science+Business Media, LLC 2010 9 Chapter
More informationFundamentals of data, graphical, and error analysis
Fundamentals of data, graphical, and error analysis. Data measurement and Significant Figures UTC - Physics 030L/040L Whenever we take a measurement, there are limitations to the data and how well we can
More informationChemistry Lab: Introduction to Measurement
Name Hour Chemistry Lab: Introduction to Measurement (adapted from Flinn ChemTopic Labs) Introduction Much of what we know about the physical world has been obtained from measurements made in the laboratory.
More informationIntroduction to Measurements & Error Analysis
Introduction to Measurements & Error Analysis The Uncertainty of Measurements Some numerical statements are exact: Mary has 3 brothers, and 2 + 2 = 4. However, all measurements have some degree of uncertainty
More informationUniversity of Massachusetts Boston - Chemistry Department Physical Chemistry Laboratory Introduction to Maximum Probable Error
University of Massachusetts Boston - Chemistry Department Physical Chemistry Laboratory Introduction to Maximum Probable Error Statistical methods describe random or indeterminate errors in experimental
More informationPart 01 - Notes: Identifying Significant Figures
Part 01 - Notes: Identifying Significant Figures Objectives: Identify the number of significant figures in a measurement. Compare relative uncertainties of different measurements. Relate measurement precision
More informationTOPIC 3: READING AND REPORTING NUMERICAL DATA
Page 1 TOPIC 3: READING AND REPORTING NUMERICAL DATA NUMERICAL DATA 3.1: Significant Digits; Honest Reporting of Measured Values Why report uncertainty? That is how you tell the reader how confident to
More informationMeasurement Uncertainties
Measurement Uncertainties Introduction We all intuitively know that no experimental measurement can be "perfect''. It is possible to make this idea quantitative. It can be stated this way: the result of
More informationUncertainty Analysis of Experimental Data and Dimensional Measurements
Uncertainty Analysis of Experimental Data and Dimensional Measurements Introduction The primary objective of this experiment is to introduce analysis of measurement uncertainty and experimental error.
More informationDensity of Aqueous Sodium Chloride Solutions
Experiment 3 Density of Aqueous Sodium Chloride Solutions Prepared by Ross S. Nord and Stephen E. Schullery, Eastern Michigan University PURPOSE Determine the concentration of an unknown sodium chloride
More informationECE 102 Engineering Computation
ECE 102 Engineering Computation Phillip Wong Error Analysis Accuracy vs. Precision Significant Figures Systematic and Random Errors Basic Error Analysis Physical measurements are never exact. Uncertainty
More informationInstrumentation & Measurement AAiT. Chapter 2. Measurement Error Analysis
Chapter 2 Measurement Error Analysis 2.1 The Uncertainty of Measurements Some numerical statements are exact: Mary has 3 brothers, and 2 + 2 = 4. However, all measurements have some degree of uncertainty
More informationExperimental Uncertainty (Error) and Data Analysis
Experimental Uncertainty (Error) and Data Analysis Advance Study Assignment Please contact Dr. Reuven at yreuven@mhrd.org if you have any questions Read the Theory part of the experiment (pages 2-14) and
More informationUncertainty, Error, and Precision in Quantitative Measurements an Introduction 4.4 cm Experimental error
Uncertainty, Error, and Precision in Quantitative Measurements an Introduction Much of the work in any chemistry laboratory involves the measurement of numerical quantities. A quantitative measurement
More informationSIGNIFICANT FIGURES. x 100%
Page 1 SIGNIFICANT FIGURES ASSIGNED READING: Zumdahal, et.al, Chemistry (10 th ed.), Chapter 1, Sec. 4 and 5. I. Accuracy and Precision It is important to remember, here at the outset of this course, that
More informationents & Uncertainties Significant Figures 1.005, Round best to the experimental want to meters and use 300 m 2. significant figures because of
Introduction to Measureme ents & Uncertainties Significant Figures A measurement and its experimental uncertainty should have significance. All numerical results and/or measurements are expressed with
More informationMeasurements and Data Analysis
Measurements and Data Analysis 1 Introduction The central point in experimental physical science is the measurement of physical quantities. Experience has shown that all measurements, no matter how carefully
More information1 Measurement Uncertainties
1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.
More informationEXPERIMENT 5 THE ASSAY OF ASPIRIN
EXPERIMENT 5 THE ASSAY OF ASPIRIN Aspirin is made by combining two acids, salicylic acid and acetic acid. Therefore aspirin has two acid portions, each of which can be neutralized by base. One mole of
More informationEXPERIMENT 30A1: MEASUREMENTS. Learning Outcomes. Introduction. Experimental Value - True Value. 100 True Value
1 Learning Outcomes EXPERIMENT 30A1: MEASUREMENTS Upon completion of this lab, the student will be able to: 1) Use various common laboratory measurement tools such as graduated cylinders, volumetric flask,
More informationChapter 2. Theory of Errors and Basic Adjustment Principles
Chapter 2 Theory of Errors and Basic Adjustment Principles 2.1. Introduction Measurement is an observation carried out to determine the values of quantities (distances, angles, directions, temperature
More informationPropagation of Uncertainty
76 nalytical Chemistry 2.1 lthough we will not derive or further justify the rules presented in this section, you may consult this chapter s additional resources for references that discuss the propagation
More information11.1 Uncertainty and error in measurement (1 Hour) 11.2 Uncertainties in calculated results (0.5 Hour) 11.3 Graphical techniques (0.
Chapter 11 Measurement and Data Processing Page 1 Students are to read and complete any part that requires answers and will submit this assignment on the first day of class. You may use internet sources
More informationThe AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class
The AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class Part 1. Review the mole concept and how it s used. This includes mass (grams) to moles, moles-to-mass calculations,
More informationthat relative errors are dimensionless. When reporting relative errors it is usual to multiply the fractional error by 100 and report it as a percenta
Error Analysis and Significant Figures Errors using inadequate data are much less than those using no data at all. C. Babbage No measurement of a physical quantity can be entirely accurate. It is important
More informationDensity of Aqueous Sodium Chloride Solutions
Experiment 3 Density of Aqueous Sodium Chloride Solutions Prepared by Ross S. Nord and Stephen E. Schullery, Eastern Michigan University PURPOSE Determine the concentration of an unknown sodium chloride
More information1 Measurement Uncertainties
1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.
More informationCHM Accuracy, Precision, and Significant Figures (r14) C. Taylor 1/10
CHM 110 - Accuracy, Precision, and Significant Figures (r14) - 2014 C. Taylor 1/10 Introduction Observations are vitally important to all of science. Some observations are qualitative in nature - such
More informationSPH3U1 Lesson 03 Introduction. 6.1 Expressing Error in Measurement
SIGNIFICANT DIGITS AND SCIENTIFIC NOTATION LEARNING GOALS Students will: 6 ERROR Describe the difference between precision and accuracy Be able to compare values quantitatively Understand and describe
More informationA.0 SF s-uncertainty-accuracy-precision
A.0 SF s-uncertainty-accuracy-precision Objectives: Determine the #SF s in a measurement Round a calculated answer to the correct #SF s Round a calculated answer to the correct decimal place Calculate
More informationMeasurement: The Basics
I. Introduction Measurement: The Basics Physics is first and foremost an experimental science, meaning that its accumulated body of knowledge is due to the meticulous experiments performed by teams of
More informationPURPOSE: To determine the Rate Law for the following chemical reaction:
PURPOSE: To determine the Rate Law for the following chemical reaction: H 2 O 2 (aq) + 2 I - (aq) + 2 H 3 O + (aq) 4 H 2 O(l) + I 2 (aq) Hydrogen Iodide Hydronium Water Iodine Peroxide Ion Ion PRINCIPLES:
More informationREVIEW OF LAB TECHNIQUES
Experiment 1 REVIEW OF LAB TECHNIQUES Prepared by Masanobu M. Yamauchi and Ross S. Nord, Eastern Michigan University PURPOSE To review density calculations, Beer s Law and the use of electronic balances,
More informationREVIEW OF LAB TECHNIQUES
Experiment 1 REVIEW OF LAB TECHNIQUES Prepared by Masanobu M. Yamauchi and Ross S. Nord, Eastern Michigan University PURPOSE To review density calculations, Beer s Law and the use of electronic balances,
More informationDecimal Scientific Decimal Scientific
Experiment 00 - Numerical Review Name: 1. Scientific Notation Describing the universe requires some very big (and some very small) numbers. Such numbers are tough to write in long decimal notation, so
More informationAppendix B: Skills Handbook
Appendix B: Skills Handbook Effective communication is an important part of science. To avoid confusion when measuring and doing mathematical calculations, there are accepted conventions and practices
More informationTitration of an Unknown Acid
Experiment 6 Titration of an Unknown Acid Prepared by Stephen E. Schullery and Ross Nord, Eastern Michigan University PURPSE To determine the apparent molar mass of an unknown monoprotic acid by titrating
More informationMetric Prefixes UNITS & MEASUREMENT 10/6/2015 WHY DO UNITS AND MEASUREMENT MATTER?
UNITS & MEASUREMENT WHY DO UNITS AND MEASUREMENT MATTER? Chemistry In Action On 9/3/99, $15,000,000 Mars Climate Orbiter entered Mar s atmosphere 100 km (6 miles) lower than planned and was destroyed by
More informationLiquid-in-glass thermometer
Liquid-in-glass thermometer Objectives The objective of this experiment is to introduce some basic concepts in measurement, and to develop good measurement habits. In the first section, we will develop
More informationDetermination of the K a Value and Molar Mass of an Unknown Weak Acid
10 Determination of the K a Value and Molar Mass of an Unknown Weak Acid Introduction In this experiment you will titrate a monoprotic weak acid with a strong base, and measure the titration curve with
More informationNotes Errors and Noise PHYS 3600, Northeastern University, Don Heiman, 6/9/ Accuracy versus Precision. 2. Errors
Notes Errors and Noise PHYS 3600, Northeastern University, Don Heiman, 6/9/2011 1. Accuracy versus Precision 1.1 Precision how exact is a measurement, or how fine is the scale (# of significant figures).
More informationDr. Kevin Moore CHM 111
Dr. Kevin Moore CHM 111 www.dictionary.com the science that deals with the composition and properties of substances and various elementary forms of matter Burdge Study of matter and the changes it undergoes
More informationUncertainty in numbers
1.03 Accuracy, Precision and Significant Figures Uncertainty in numbers Story: Taxi driver (13 years experience) points to a pyramid "...this here pyramid is exactly 4511 years old". After a quick calculation,
More informationSpectrophotometric Determination of Ferrocyanide in Effluents
Spectrophotometric Determination of Ferrocyanide in Effluents ECN-0025-1 INTRODUCTION This method is used to determine the concentration of ferrocyanide ion in photoprocessing solution effluents. The ion
More informationMEASUREMENTS AND ERRORS
Measurements 1 MESUREMENTS ND ERRORS ccuracy Error Precision Uncertainty Reliability measure of the closeness of agreement between an individual result and the accepted value. n accurate result is in close
More informationThe periodic table currently lists 116 different atoms. New atoms are being discovered.
CHEM100 Week 1 Notes Page 1 of 11 Chemistry is the study of matter. Matter is made up of atoms. The periodic table currently lists 116 different atoms. New atoms are being discovered. Atoms consist of
More informationGlossary of Common Laboratory Terms
Accuracy A measure of how close a measured value is to the true value. Assessed by means of percent recovery of spikes and standards. Aerobic Atmospheric or dissolved oxygen is available. Aliquot A measured
More informationCEM 333 Instrumental Analysis
CEM 333 Instrumental Analysis Simon J. Garrett Room: CEM 234 Phone: 355 9715 ext 208 E-mail: garrett@cem.msu.edu Lectures: Tuesday, Thursday 9:00-9:50 am Room 136 Office Hours: Tuesdays 10:00-11:00 am
More informationCHEM 334 Quantitative Analysis Laboratory
The Methods of Calibration Curve and Standard Addition Introduction One of the principle activities in the Quantitative Analysis Laboratory is the measurement of the concentration or total quantity of
More informationSince the publication of the ISO Guide to the Expression
DE SILVA: JOURNAL OF AOAC INTERNATIONAL VOL. 86, NO. 5, 003 1077 SPECIAL GUEST EDITOR SECTION Uncertainty of Analytical Determinations GALAPPATTI M.S. DE SILVA 4, PB Alwis Perera Mawatha, Katubedda, Sri
More information5. Statistical Evaluation of Acid-Base Indicators 1
5. Statistical Evaluation of Acid-Base Indicators 1 This experiment introduces you to the use of indicators and to the statistical concepts of mean, standard deviation, Grubbs test, F test, and t test.
More informationMeasurement. New Topics accuracy vs. precision rounding in chemistry significant figures determining uncertainty of a measurement % error moles - 1 -
Measurement Unit Description In this unit we will focus on the mathematical tools we use in science, especially chemistry the metric system and moles. We will also talk about how to gauge the accuracy
More informationExperimental Uncertainty (Error) and Data Analysis
E X P E R I M E N T 1 Experimental Uncertainty (Error) and Data Analysis INTRODUCTION AND OBJECTIVES Laboratory investigations involve taking measurements of physical quantities, and the process of taking
More informationGuide to the Expression of Uncertainty in Measurement (GUM)- An Overview
Estimation of Uncertainties in Chemical Measurement Guide to the Expression of Uncertainty in Measurement (GUM)- An Overview Angelique Botha Method of evaluation: Analytical measurement Step 1: Specification
More informationAnd how to do them. Denise L Seman City of Youngstown
And how to do them Denise L Seman City of Youngstown Quality Control (QC) is defined as the process of detecting analytical errors to ensure both reliability and accuracy of the data generated QC can be
More informationEngineering Fundamentals and Problem Solving, 6e. Chapter 6 Engineering Measurements
Engineering Fundamentals and Problem Solving, 6e Chapter 6 Engineering Measurements Chapter Objectives Determine the number of significant digits in a measurement Perform numerical computations with measured
More informationFor this lab, you will determine the purity of the aspirin by titration and by spectrophotometric analysis.
Introduction: ommercially prepared aspirin tablets are not considered 100% pure acetylsalicylic acid. Most aspirin tablets contain a small amount of binder which helps prevent the tablets from crumbling.
More informationFUNDAMENTAL CONCEPTS IN MEASUREMENT & EXPERIMENTATION (continued) Measurement Errors and Uncertainty:
FUNDAMENTAL CNCEPTS N MEASUREMENT & EXPERMENTATN (continued) Measurement Errors and Uncertainty: The Error in a measurement is the difference between the Measured Value and the True Value of the Measurand.
More informationMeasurement And Uncertainty
Measurement And Uncertainty Based on Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297, 1994 Edition PHYS 407 1 Measurement approximates or
More information3. Measurement Error and Precision
3.1 Measurement Error 3.1.1 Definition 3. Measurement Error and Precision No physical measurement is completely exact or even completely precise. - Difference between a measured value and the true value
More informationPART I: MEASURING MASS
Chemistry I Name Dr. Saulmon 2014-15 School Year Laboratory 1 Measuring Mass, Volume, and Temperature Monday, August 25, 2014 This laboratory is broken into three parts, each with its own introduction,
More informationExperiment 20-Acid-Base Titration: Standardization of KOH and Determination of the Molarity and/or Percent Composition of an Acid Solution
Experiment 20-Acid-Base Titration: Standardization of KOH and Determination of the Molarity and/or Percent Composition of an Acid Solution In this experiment, you will determine the molarity and percent
More informationCyanide, colorimetric, pyridine-pyrazolone
Cyanide, colorimetric, pyridine-pyrazolone Parameters and Codes: Cyanide, dissolved, I-1300-85 mg/l as CN): 00723 Cyanide, total, I-3300-85 (mgll as CN): 00720 Cyanide, total-in-bottom-material, dry wt,
More informationCalibration of Volumetric Glassware. Prepared by Allan Fraser May 2016 APPLICATION Note 1
Calibration of Volumetric Glassware Prepared by Allan Fraser May 2016 APPLICATION Note 1 TABLE OF CONTENTS TABLE OF CONTENTS... i LIST OF TABLES... ii 1. 2. 3. 4. 5. 6. 7. 8. Purpose... 1 Scope... 1 Principle...
More informationStatistical Analysis of Chemical Data Chapter 4
Statistical Analysis of Chemical Data Chapter 4 Random errors arise from limitations on our ability to make physical measurements and on natural fluctuations Random errors arise from limitations on our
More informationVolumetric Analysis: Analysis of antacid tablets Analysis of Cl - concentrations in IV solutions
Volumetric Analysis: Analysis of antacid tablets Analysis of Cl - concentrations in IV solutions OBJECTIVE: The goals of this experiment are to learn titration concepts and techniques. SKILLS: Titration,
More information