03.1 Experimental Error
|
|
- Virginia Pearson
- 5 years ago
- Views:
Transcription
1 03.1 Experimental Error Problems: 15, 18, 20 Dr. Fred Omega Garces Chemistry 251 Miramar College 1
2 Making a measurement In general, the uncertainty of a measurement is determined by the precision of the measuring device. A 1-ml pipette with a graduation of 0.01mL with give an uncertainty of , or 10% of the smallest graduation (10% 0.01 =.001). A 100-ml graduated cylinder with 1-ml graduation will have an uncertainty of +0.1mL. For a 25-ml graduated cylinder with graduation of 0.2 ml, the uncertainty is +.02-ml (10% of 0.2 =.02). A 500 ml graduated cylinder with a 5mL graduation will have an uncertainty of +.5 ml. 2
3 Significant Digits and the different type of Uncertainties Number of Significant figures Implied uncertainty Relative uncertainty % Relative uncertainty % % % % 3
4 Significant Figures A measurement will always have some uncertainty based on the measuring device used. One of the best ways of indicating reliability is to give a confident interval of 90% or better. Another method is to report the absolute standard deviation or the coefficient of variation. A less satisfactory but common indicator of quality of the data is the significant figure convention. Significant figures in a number contains all the certain digits in the measurement and the first uncertain digit. The uncertainty in a measurement is the estimate reading between the graduation in a measuring device. An easy method to remember significant figures rule is as follows: Place the number in the center of the map. The presence (Pacific) or absence (Atlantic) of a decimal point determines which strategy is used Decimal Present (Pacific) For numbers with a decimal point present, draw a line starting from the Pacific to the first non-zero number, all digits shown including the nonzero number are significant. i.e., Place Number here Decimal Absent (Absence) For numbers with a decimal point absent, draw a line starting from the Atlantic (right) to the first non-zero number, all digits shown including the non-zero number are significant. i.e., Significant Figures 3 Significant Figures
5 Significant Digits and the different type of Uncertainties Number of Significant figures Implied uncertainty Relative uncertainty % Relative uncertainty % % % % 5
6 What is the difference between Precision & Significant Figures What is the difference between significant figures and precision? In the examples shown, which number has the fewest significant figures and which is the least precise?. Fewest Significant figures Least precise a) 123 vs b) 1.23 vs c) vs d) 30 vs
7 Significant Figures in Arithmetic Math operation & significant figures Addition and Subtraction: Uncertainty of answer (Significant figures of answer) is limited to the value with the least precise value (number with fewest digit after decimal place Least precise Answ: = 105. Multiplication and division: Uncertainty of answer (Significant. Figure) is limited to the value with the fewest significant figures. Fewest number of significant figures S. F. 2 S. F. Logarithms and Antilogarithms: Generally when a number expressed in exponential notation, i.e.., , 10 is the base (base-10) and 6 is the exponent. This number contains 3 significant figures. The log of this number is is the characteristic and it correspond to the exponent of the number, is the mantissa and it represents the precision of the number. Since the original number contains 3-significant figures, the final logarithm answer should have the mantissa rounded to three digits S. F. Answer with 2 s.f. Log 10 ( ) = characteristic mantissa 7
8 Significant Figures in Graphs Graph format is based on information the graph is to portray. Qualitative information. Quantitative: These graph show trend and Graph needs to show precise value that may be used to make prediction. must be read within specific significant figures. At minimum, the graph must have tick mark on both axis it would be best to display graph on a grid. Calibration Curve for 50-ml Buret 8
9 Systematic Errors Errors that have definite values and have assignable cause. These errors lead to bias in measurement techniques. Types of systematic errors- Instrument errors - poor calibration of instrument, glassware at extreme temperatures, voltage instability. Method errors - Incomplete conversion of sample for analysis Personal errors - poor experimental techniques, prejudice Result of systematic error lead to constant or proportional errors in each measurment. 9
10 Random Errors Random or indeterminate errors lead to repeated inconsistency even though systematic errors have been minimized. The randomness indicates that the errors are unpredictable and have null expected value, that is measurements are scattered about the true value, and tend to have null arithmetic mean when a measurement is repeated several times with the same instrument. All measurements are prone to random error. Origin of random errors are caused by unpredictable fluctuations in the readings of a measurement apparatus, or in the experimenter's interpretation of the instrumental reading; these fluctuations may be in part due to interference of the environment with the measurement process. These errors cannot be eliminated, but can be reduce by careful measurements and better experimental design. 10
11 Terms Mean, ; the sum of the replicated measurement divided by the x number of measurements in the set. Also known as arithmetic mean or average Medium - The middle result when the data is arranged in order of increasing values or decreasing values. Precision - reproducibility of measurement, closeness of results. Terms indicative of precision (function of deviation from mean)- standard deviation variance coefficient of variation 11
12 Precision versus accuracy Errors in Experiments measurements Analysis1; High precision and high accuracy Analysis2; Poor precision but high accuracy Analysis3: High precision but poor accuracy Analysis4: Poor precision and poor accuracy 12
13 Absolute and Relative Error Absolute Error (a.u.); E = x i - x t, This error is the uncertainty associated with a measurement. For example if a measurement is taken to be mol, then the absolute error is This error is also referred to as the difference between measured value (x i ) from the true value (x t ). This can be positive or negative. Relative Error (r.u.); E = [ (x i x t ) /x t ] * 100 This is the absolute error compared to the measurement. In general the relative uncertainty is dimensionless but it can be express in terms of percent relative error (% or pph) or in ppt (parts per thousand) 13
14 Detecting Errors Systematic error are found and corrected by calibration. Personal error minimized by care and self-discipline (do not rush the procedure). Use reliable standard reference materials. Use independent analytical method Run blank determination Vary sample size 14
15 Significant Digits and the different type of Uncertainties Number of Significant figures Implied uncertainty Relative uncertainty % Relative uncertainty % % % % 15
16 Propagation of Uncertainty from Random Errors Addition and Subtraction Calc. A.U then R.U ( ± 0.03) e ( ± 0.02) e ( ± 0.02) e ( ± e 4 ) The absolute uncertainty (AU), e 4 can be determined by the following: e 4 = e 1 ( ) 2 + ( e 2 ) 2 + ( e 3 ) 2 e 4 = ( 0.03) 2 + ( 0.02) 2 + ( 0.02) 2 = Relative uncertainty (RU) e x 100 = x 100 = 1. 3 % Multiplication and Division Calc. R.U then A.U ( ± 0.03) x 1.89 ( ± 0.02) 0.59 ( ± 0.02) = ± e 4 convert a.u. to percent r.u ( ± 1. 7 %) x 1.89 ( ± 1. 1 %) 0.59 ( ± 3. 4 %) = ± e 4 take % r.u. and determine root sum square to find e 4 %e 4 = %e 1 ( ) 2 + (%e 2 ) 2 + (%e 3 ) 2 (%e 4 is the percent r.u. of the answer) %e 4 = 1. 7 % ( ) 2 + ( 1. 1 %) 2 + ( 3. 4 %) 2 = 4. 0 % AU 100 = RU reults Mixed Operation 1.Carry out Addition- Subtraction w/ AU 2. Convert error to RU [1.76 ( ± 0.03) ( ± 0.02)] = ±? 1.89 ( ± 0.02) Addition Subraction first, and determine a.u. [1.76 ( ± 0.03) ( ± 0.02)] = e a.u. e a.u. = (.03) 2 + (.02) 2 = ± Simplifying and determining e r.u. for each measurment 1.17 ( ± 0.036) 1.89 ( ± 0.02) = ± e 0 r.u. convert a.u. to r.u. for answer, e a.u. e r.u ( ± 3. 1 %) = ± 3. 3 % 1.89 ( ± 1. 1 %) solving for AU: AU = result RU 100 convert e r.u. to e a.u. for answer AU = 3. 3 x = AU = Answer: ± AU ± 4. 0 % RU = Answer ± AU ± 3. 3 % RU 16
17 Summary of Rules for Propagation of Uncertainty Propagation of Random Errors using various math operation. 17
18 Real Rules of Significant Figures The first digit of the absolute uncertainty, a.u. is the last digit in the answer. In multiplication and division Add an extra digit when the answer is between 1 & 2 Consider 82/80 = 1.0 if rules of S.F. is followed. It is better to write an answer of 1.02 showing that the uncertainty is in the order of 1%. A value of 1.0 suggest uncertainty is in order of 10% which is larger than actual uncertainty in the original data. 18
19 Calculation Molarity Example 3.20 The concentration of HCl can be precisely determined by reaction with sodium carbonate. 2 HCl (aq) + Na 2 (s) g 2Na + (aq) + 2Cl - (aq) + H 2 O (s) + CO 2 (g) If g of Na 2 (FM ) required ml of HCl, what is the molarity of HCl and the a.u.? 1 mol Na ( ± ) g Na mol HCl 1 = M HCl ± a.u. ( ± ) g Na 2 1 mol Na 2 ( ± ) L convert a.u. to percent r.u. convert measured a.u. to measured percent r.u. 1 mol Na ( ± % ) g Na mol HCl 1 = M HCl ± %e ( ± %) g Na 2 1 mol Na 2 ( ± % )ml determine % r.u. of each measurement and determine root sum square to find answer e r.u. %e 4 = (%e 1 ) 2 + (%e 2 ) 2 + (%e 3 ) 2 = ( %) 2 + ( %) 2 + ( %) 2 = % (This is the percent r.u. of the answer) ( ± % ) g Na 2 1 mol Na 2 2 mol HCl 1 ( ± %) g Na 2 1 mol Na 2 ( ± % )ml = HCl ± 0.17 % 6 3 Converte e r.u. of answer and convert to e a.u. of anaswer A.U. = Results (R.U.) 100 = = Molarity HCl = with r.u. = % 19
20 Calculation Molarity Example 3.20 The concentration of HCl can be precisely determined by reaction with sodium carbonate. 2 HCl (aq) + Na 2 (s) g 2Na + (aq) + 2Cl - (aq) + H 2 O (s) + CO 2 (g) If g of Na 2 (FM ) required ml of HCl, what is the molarity of HCl and the a.u.? 1 mol Na ( ± ) g Na mol HCl 1 = M HCl ± a.u. ( ± ) g Na 2 1 mol Na 2 ( ± ) L convert a.u. to percent r.u. convert measured a.u. to measured percent r.u. 1 mol Na ( ± % ) g Na mol HCl 1 = M HCl ± %e ( ± %) g Na 2 1 mol Na 2 ( ± % )ml determine % r.u. of each measurement and determine root sum square to find answer e r.u. %e 4 = (%e 1 ) 2 + (%e 2 ) 2 + (%e 3 ) 2 = ( %) 2 + ( %) 2 + ( %) 2 = % (This is the percent r.u. of the answer) ( ± % ) g Na 2 1 mol Na 2 2 mol HCl 1 ( ± %) g Na 2 1 mol Na 2 ( ± % )ml = HCl ± 0.17 % 6 3 Converte e r.u. of answer and convert to e a.u. of anaswer A.U. = Results (R.U.) 100 = = Molarity HCl = with r.u. = % 20
21 Propagation of Systematic Uncertainty Uncertainty in Atomic Mass- The error in the atomic mass is not mainly from random error but from isotopic variation in samples of elements from various source samples which is found to be / g/mol Consider the atomic weight of O, the error in the mass approximates a rectangular distribution. There is an equal probability of fining the atomic mass of oxygen between and The standard deviation for this distribution is called the standard uncertainty, + a/ 3. For oxygen the standard uncertainty is / 3 =
22 Propagation of Systematic Uncertainty Uncertainty in Molar MassWhat is the uncertainty of the molar mass? Consider the molar mass of O2, the error in the molar mass is for two oxygen, the lower limit would be *2 = The upper limit would be *2 = Therefore for O2, the mass would be ( )/2 = ± The uncertainty of mass therefore for one atom is /2 = , which means for n atoms, the standard uncertainty is n * ± Thus for n = 2, (2* ± ) = For systematic uncertainty, the uncertainty is added per each term. Consider the molar mass of C2H6O, ethanolatomic mass of C = ± / 3 = ± Atomic mass of H = ± / 3 = ± Atomic mass of O = ± / 3 = ± C: 2( ± ) = ± (2* ) = ± H: 6( ± ) = ± (6* ) = ± O: 1( ± ) = ± (1* ) = ± ± e ± e4, e4 = ( )½ = Molar mass C2H5OH = ± g/mol 22
23 Propagation of Systematic Uncertainty Multiple deliveries from Pipette- Consider a 25-mol Class-A volumetric pipette which is certified by manufacturer to deliver mol. The range therefore for a reading is to ml. For volumetric glassware the Triangular distribution is followed for the standard deviation, or + a/ 6 The standard uncertainty (std dev) for the pipet is therefor a/ 6 = +.03/ 6 = ml. From the triangular distribution, there is zero probability that a volume will fall out side of ml. If the pipette is un-calibrated and used four times to deliver 100mL, then the standard uncertainty (std dev) = + 4 x = ml and not + [ ] 1/2 or std dev = ml. This is due to systematic error Calibration of the pipette on the other hand, eliminates systematic errors. Calibration improves certainty by removing systematic error. For example consider a calibrated pipet that delivers a mean value of with a standard deviation ml (0.006 ml is random error). Using the pipet to deliver 4 times gives an uncertainty + [ ] 1/2 or ml. An un-calibrated pipet will give an uncertainty of 4 aliquots as 4 x ml = ml. Calibrated pipet volume: ml Un-calibrated pipet volume: mL 23
24 Summary Every measurement is influence by many uncertainties that produce a scattering of results. It is not easy to estimate the reliability of the experimental data, but sources of error must be identified whenever possible so that the results can be stated with confidence. The true value of a measurement is never really known exactly. 24
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 informationHarris: 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 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 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 informationSection 3 Using Scientific Measurements. Look at the specifications for electronic balances. How do the instruments vary in precision?
Lesson Starter Look at the specifications for electronic balances. How do the instruments vary in precision? Discuss using a beaker to measure volume versus using a graduated cylinder. Which is more precise?
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationAccuracy: An accurate measurement is a measurement.. It. Is the closeness between the result of a measurement and a value of the measured.
Chemical Analysis can be of two types: Chapter 11- Measurement and Data Processing: - : Substances are classified on the basis of their or properties, such as - : The amount of the sample determined in
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 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 informationAnalytical Chemistry. Course Philosophy
Analytical Chemistry Definition: the science of extraction, identification, and quantitation of an unknown sample. Example Applications: Human Genome Project Lab-on-a-Chip (microfluidics) and anotechnology
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 information(Significant Digits are in BOLD type and the non-significant digits are underlined)
Name Per. Date Significant Digits Worksheet Significant digits (or significant figures) are used to represent the accuracy of a measurement. In a measurement the significant digits represent all the reliable
More informationPHYS 2211L - Principles of Physics Laboratory I Propagation of Errors Supplement
PHYS 2211L - Principles of Physics Laboratory I Propagation of Errors Supplement 1. Introduction. Whenever two or more quantities are measured directly in order to indirectly determine the value of another,
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 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 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 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 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 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 informationUnit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific
Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific notation in calculations. Significant figures - consist of
More informationEvery time a measurement is taken, we must be aware of significant figures! Define significant figures.
SCHM 103: FUNDAMENTALS OF CHEMISTRY Ch. 2: Numerical Side of Chemistry Types of data collected in experiments include: Qualitative: Quantitative: Making Measurements Whenever a piece of data is collected,
More informationAppendix A: Significant Figures and Error Analysis
1 Appendix A: Significant Figures and Error Analysis Every measurement of a physical quantity contains some amount of uncertainty or error. We often speak of a certain number or measurement as being precise
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 informationAppendix F. Treatment of Numerical Data. I. Recording Data F-1
Treatment of umerical Data I. Recording Data When numerical data are recorded, three kinds of information must be conveyed: the magnitude of the number, how well the number is known, and the units used
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 informationDimensional Analysis, SI Units & Significant figures
Dimensional Analysis, SI Units & Significant figures WHAT IS CHEMISTRY The study of matter, its composition, structure, properties, and the changes it undergoes & energy changes associated with it. Scientific
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 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 informationCHAPTER 2: SCIENTIFIC MEASUREMENTS
CHAPTER 2: SCIENTIFIC MEASUREMENTS Problems: 1-26, 37-76, 80-84, 89-93 2.1 UNCERTAINTY IN MEASUREMENTS measurement: a number with attached units To measure, one uses instruments = tools such as a ruler,
More informationChemistry 11. Unit 2: Introduction to Chemistry. Measurement tools Graphing Scientific notation Unit conversions Density Significant figures
Chemistry 11 Unit 2: Introduction to Chemistry Measurement tools Graphing Scientific notation Unit conversions Density Significant figures Book 1: Measuring and Recording Scientific Data Name: Block: 1
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 informationMeasurements. October 06, 2014
Measurements Measurements Measurements are quantitative observations. What are some kinds of quantitative observations you might make? Temperature Volume Length Mass Student A and Student B measured the
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 informationChemistry 11. Measuring and Recording Scientific Data. Measurement tools Graphing Scientific notation Unit conversions Density Significant figures
Chemistry 11 Measuring and Recording Scientific Data Measurement tools Graphing Scientific notation Unit conversions Density Significant figures Name: Block: Measuring and Recording Significant Data SI
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 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 informationIntroduction to Uncertainty and Treatment of Data
Introduction to Uncertainty and Treatment of Data Introduction The purpose of this experiment is to familiarize the student with some of the instruments used in making measurements in the physics laboratory,
More informationCHEM Chapter 1
CHEM 1110 Chapter 1 Chapter 1 OVERVIEW What s science? What s chemistry? Science and numbers Measurements Unit conversion States of matter Density & specific gravity Describing energy Heat and its transfer
More informationScientific Measurement
Scientific Measurement A quantity is anything having a measurable size or amount For Example: 5 But 5 what? A unit assigns value to a measured quantity For Example: 5 ft, 5 gal, 5 sec, 5 m, 5 g. Base Units
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 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 informationINTRODUCTORY CHEMISTRY Concepts and Critical Thinking
INTRODUCTORY CHEMISTRY Concepts and Critical Thinking Sixth Edition by Charles H. Corwin Scientific Measurements by Christopher Hamaker 1 Uncertainty in Measurements A measurement is a number with a unit
More informationUsing Scientific Measurements
Section 3 Main Ideas Accuracy is different from precision. Significant figures are those measured precisely, plus one estimated digit. Scientific notation is used to express very large or very small numbers.
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 informationsee page 8 of these notes )
UNIT 1 Note Packet INTRODUCTION TO CHEMISTRY Name: METRICS AND MEASUREMENT In the chemistry classroom and lab, the metric system of measurement is used, so it is important to know what you are measuring,
More informationChapter 2 Math Skills
Chapter 2 Math Skills 2.1 Measurements Measurement number with a unit Units are very important o A student wouldn t ask a teacher Could you please hand me 6? The student would instead ask, Could you please
More informationHW #1: 1.42, 1.52, 1.54, 1.64, 1.66, 1.70, 1.76, 1.78, 1.80, 1.82, 1.84, 1.86, 1.92, 1.94, 1.98, 1.106, 1.110, 1.116
Chemistry 121 Lecture 3: Physical Quantities Measuring Mass, Length, and Volume; Measurement and Significant Figures; Scientific Notation; Rounding Review Sections 1.7-1.11 in McMurry, Ballantine, et.
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 informationNumbers and Uncertainty
Significant Figures Numbers and Uncertainty Numbers express uncertainty. Exact numbers contain no uncertainty. They are obtained by counting objects (integers) or are defined, as in some conversion factors
More informationCh. 2 Notes: ANALYZING DATA MEASUREMENT NOTE: Vocabulary terms are in boldface and underlined. Supporting details are in italics.
Ch. 2 Notes: ANALYZING DATA MEASUREMENT NOTE: Vocabulary terms are in boldface and underlined. Supporting details are in italics. I. Units and Measurement - Metrics A. The International System of Units
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 informationCHEM 121 Introduction to Fundamental Chemistry. Summer Quarter 2008 SCCC. Lecture 2
CHEM 121 Introduction to Fundamental Chemistry Summer Quarter 2008 SCCC Lecture 2 Could Stephanie, Liqingqing, Huong, Sophia and Yumiko see me after class for a few minutes. Thanks. Matter, Measurements
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 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 information7.5 MULTIPLYING DECIMALS
7.5 MULTIPLYING DECIMALS MEASUREMENT REVIEW AND EXTENSION Knowing the number of significant figures is critical in scientific measurement. Every measuring tool has a level or degree of precision and this
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 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 informationTools of Chemistry. Measurement Scientific Method Lab Safety & Apparatus
Tools of Chemistry Measurement Scientific Method Lab Safety & Apparatus Scientific Notation Scientific Notation a number described as a power of 10 (used for very large or small numbers) 1000 = 1 X 10
More informationMATH HANDBOOK. Handbook. Math
MATH HANDBOOK ematics is a language used in science to express and solve problems. Calculations you perform during your study of chemistry require arithmetic operations, such as addition, subtraction,
More informationNumbers and Data Analysis
Numbers and Data Analysis With thanks to George Goth, Skyline College for portions of this material. Significant figures Significant figures (sig figs) are only the first approimation to uncertainty and
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 informationNotes: Measurement and Calculation
Name Chemistry-PAP Per. I. The Basics of Measurement Notes: Measurement and Calculation A. Measurement Most provide quantitative information, but because they are obtained experimentally, they are inexact.
More informationMethods and Tools of Physics
Methods and Tools of Physics Order of Magnitude Estimation: Essential idea: Scientists aim towards designing experiments that can give a true value from their measurements, but due to the limited precision
More informationPHYSICS 30S/40S - GUIDE TO MEASUREMENT ERROR AND SIGNIFICANT FIGURES
PHYSICS 30S/40S - GUIDE TO MEASUREMENT ERROR AND SIGNIFICANT FIGURES ACCURACY AND PRECISION An important rule in science is that there is always some degree of uncertainty in measurement. The last digit
More informationSignificant Figures, Precision and Accuracy, and Dimensional Analysis
Significant Figures, Precision and Accuracy, and Dimensional Analysis 1 I. SIGNIFICANT FIGURES - In chemistry, when do we need to worry about the digits reported in a number? 1. Significant Figure Rules
More informationAllows us to work with very large or small numbers more easily. All numbers are a product of 10.
Unit 1: Measurements Scientific Notation : Allows us to work with very large or small numbers more easily. All numbers are a product of 10. M x 10n M= signif. digit [ 1 < M < 10 ] n = an integer move the
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 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 informationChapter 2. Preview. Objectives Scientific Method Observing and Collecting Data Formulating Hypotheses Testing Hypotheses Theorizing Scientific Method
Preview Objectives Scientific Method Observing and Collecting Data Formulating Hypotheses Testing Hypotheses Theorizing Scientific Method Section 1 Scientific Method Objectives Describe the purpose of
More informationAccelerated Chemistry Study Guide What is Chemistry? (Chapter 1)
Accelerated Chemistry Study Guide What is Chemistry? (Chapter 1) Conversion factor Density Uncertainty Significant digits/figures Precision Accuracy Percent error September 2017 Page 1 of 32 Scientific
More informationChapter 2 - Measurements and Calculations
Chapter 2 - Measurements and Calculations 2-1 The Scientific Method "A logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating
More informationINTRODUCTORY CHEMISTRY Concepts and Critical Thinking Seventh Edition by Charles H. Corwin
Lecture INTRODUCTORY CHEMISTRY Concepts and Critical Thinking Seventh Edition by Charles H. Corwin Introduction to Chemistry by Christopher G. Hamaker Illinois State University Evolution of Chemistry The
More information1. Volume=amount of an object takes up Ways we can measure volume:
Chemistry Ms. Ye Name Date Block A physical property is something that can be measured or observed without changing the chemical composition of the substance. Mass, volume, and density or examples of physical
More informationErrors and Uncertainties in Chemistry Internal Assessment
Errors and Uncertainties in Chemistry Internal Assessment The treatment of errors and uncertainties is relevant in the internal assessment criteria of: data collection, aspect 1 (collecting and recording
More informationMath Without a Calculator for AP Chemistry
Math Without a Calculator for AP Chemistry Number Sense 6.02 1000 6.02 0.01 0.1 1000 0.02 1000 0.3 1000 0. 1000 Let fractions be your friends! Fraction Decimal Percent 3/ 0.80 Example: 3.00 1.2 3.00 6
More informationMath APPENDIX. Handbook. 1. Addition and subtraction. Math Handbook
APPENDIX CHAPTER AB ## Practice ASSESSMENT Problems ematics is a language used in science to express and solve problems. Use this handbook to review basic math skills and to reinforce some math skills
More informationThermodynamics of Borax Dissolution
Thermodynamics of Borax Dissolution Introduction In this experiment, you will determine the values of H, G and S for the reaction which occurs when borax (sodium tetraborate octahydrate) dissolves in water.
More informationPhysics 10 Scientific Measurement Workbook Mr. Proctor
Physics 10 Scientific Measurement Workbook Mr. Proctor Name: MEASUREMENT OF MATTER - Science 10 textbook reference pages 344-351 The Seven Fundamental Measurements (with units) in Physics are: meter (m)
More informationChem 321 Lecture 5 - Experimental Errors and Statistics 9/10/13
Chem 321 Lecture 5 - Experimental Errors and Statistics 9/10/13 Student Learning Objectives Experimental Errors and Statistics Calibration Results for a 2.0-mL Transfer Pipet 1.998 ml 1.991 ml 2.001 ml
More informationPhysics and Physical Measurement. Topic 1.2 The Realm of Physics Range of magnitudes of quantities in our universe
Physics and Physical Measurement Topic 1.2 The Realm of Physics Range of magnitudes of quantities in our universe Range of Magnitudes Scientists are more concerned with the order of magnitude rather than
More informationChemistry: The Study of Change Chang & Goldsby 12 th edition
Chemistry: The Study of Change Chang & Goldsby 12 th edition modified by Dr. Hahn Chapter 1 Example 1.4 Determine the number of significant figures in the following measurements: (a)478 cm (b)6.01 g end
More informationCHAPTER 2. Significant Figures
CHAPTER 2 Significant Figures A lever balance used to weigh a truckload of stone may be accurate to the nearest 100 kg, giving a reading of 15 200 kg, for instance. should be written in such a way that
More informationTopic 11: Measurement and data processing
Topic 11: Measurement and data processing 11.1 Uncertainty and error in measurement 11.2 Uncertainties in calculated results 11.3 Graphical techniques -later! From the syllabus Precision v. Accuracy The
More informationChem 222 #18 Ch 10, Review Mar 10, 2005
Chem 222 #18 Ch 10, Review Mar 10, 2005 Announcement Next Tuesday Review Class (Lecture note will be probably uploaded on this Saturday) Midterm Exam on the next Thursday this room in the same time (50
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 information