Data Analysis for General Chemistry: Lab Procedures, Precision, and Uncertainty - Prof. Ra, Lab Reports of Chemistry

Download Data Analysis for General Chemistry: Lab Procedures, Precision, and Uncertainty - Prof. Ra and more Lab Reports Chemistry in PDF only on Docsity! 1 Data Analysis for General Chemistry Introduction Contact Information Dr. Randa Roland UCSC: 459-5486 Thimann 317 e-mail: roland@chemistry.ucsc.edu website: chemistry.ucsc.edu course homepage syllabus, powerpoints, etc. 2 General Procedures Come to lab on time and prepared
Complete prelab
Appropriate attire Lab writeups due the following lab session
Late lab penalty 25% off for each day late
All writeups must be turned in no matter what Makeup labs
Same week or following week only
See me and your TA Prelab includes: Title and date Definitions Answers to prelab questions Procedure* Data tables Prelabs are done PRIOR to lab in your notebook TA must sign off at start of lab session 5 Precision, Accuracy, Error Precision: reproducibility Accuracy: trueness Error: standard deviation (uncertainty) Accuracy vs. Precision Precise Not Accurate Better Accuracy Not Precise Precise Accurate 6 Types of Error 1 Systematic: Accuracy Trial Mass (g) 1 10.22 2 10.23 3 10.19 4 10.17 5 10.22 Mass of Water 9.90 10.00 10.10 10.20 10.30 1 2 3 4 5 Trial M as s (g ) Types of Error 2 Random: Reproducibility / precision Trial Mass (g) 1 10.02 2 10.03 3 9.99 4 9.97 5 10.02 Mass of Water 9.80 9.90 10.00 10.10 10.20 1 2 3 4 5 Trial M as s (g ) 1 Data Analysis for General Chemistry Introduction Contact Information Dr. Randa Roland UCSC: 459-5486 Thimann 317 e-mail: roland@chemistry.ucsc.edu website: chemistry.ucsc.edu course homepage syllabus, powerpoints, etc. 2 General Procedures Come to lab on time and prepared
Complete prelab
Appropriate attire Lab writeups due the following lab session
Late lab penalty 25% off for each day late
All writeups must be turned in no matter what Makeup labs
Same week or following week only
See me and your TA Prelab includes: Title and date Definitions Answers to prelab questions Procedure* Data tables Prelabs are done PRIOR to lab in your notebook TA must sign off at start of lab session 5 Precision, Accuracy, Error Precision: reproducibility Accuracy: trueness Error: standard deviation (uncertainty) Accuracy vs. Precision Precise Not Accurate Better Accuracy Not Precise Precise Accurate 6 Types of Error 1 Systematic: Accuracy Trial Mass (g) 1 10.22 2 10.23 3 10.19 4 10.17 5 10.22 Mass of Water 9.90 10.00 10.10 10.20 10.30 1 2 3 4 5 Trial M as s (g ) Types of Error 2 Random: Reproducibility / precision Trial Mass (g) 1 10.02 2 10.03 3 9.99 4 9.97 5 10.02 Mass of Water 9.80 9.90 10.00 10.10 10.20 1 2 3 4 5 Trial M as s (g ) 7 Reporting Data Average: ( ) n xxx x n21 +++ = K Standard deviation: ( ) ( ) ( ) 1-n x-xx-xx-x 2 n 2 2 2 1 +++ = K σ Examples of Precision  100 150 200  140 150 160  149 150. 151  149.5 150.0 150.5  149.9 150.0 150.1 and so on… Average: “150” Precision: very different 10 Significant Figures Which numbers are meaningful? 1. Mathematical 2. Standard Deviation Mathematical Sig. Figs. Multiplication/Division: Round answer to fewest sig. figs. Addition/Subtraction: Round answer to fewest decimal places. Standard deviation takes precedence over these rules. 11 Example 3 sig. figs./2 decimal places 4 sig. figs./2 decimal places Trial # Volume (mL) 1 10.00 2 9.99 3 10.03 Average 10.01 St. Dev. 0.02 Standard deviation takes precedence Report: 10.01 ± 0.02 mL Direct vs. Derived Values Direct: Measured /no calculations required Derived: Must be calculated from data How do we account for our uncertainty? 12 Uncertainty in Measuring Devices 0 1 2 Ruler 1.38 cm ± 0.01 cm Uncertainty in Measuring Devices Graduated cylinders 0.364 ± 0.001 mL 3.60 ± 0.01 mL 0.3 0.4 3 4 15 Multiplication 12.5 cm σ1 = 0.1 cm × 2.05 cm σ2 = 0.01cm 25.625 cm2 σ = ? Report: 25.6 ± 0.3 cm2 σ = 25.625 cm2 0.1 cm 12.5 cm 0.01 cm 2.05 cm + = 0.33 cm2 Division 12.5 g σ1 = 0.1 g 2.05 cm3 σ2 = 0.01cm 3 6.09756 g σ = ? cm3 Report: 6.10 ± 0.08 g/cm3 σ = 6.09756 g cm3 0.1 g 12.5 g 0.01 cm 2.05 cm + = 0.0785g/cm3 16 Example sidecirclecylinder LAV ×= diameter, d length, l ( ) ( )       ++±= ±±=== ldd ldldV ldldlrV ldd ld σσσππ σσ ππ π 22 222 44 44 Measured: diameter length Example Density = mass/Volume )()( )(4 4 2 2 ld m ld m ld m D σσπ σ π ±± ± ==       +++±= lddmld m ld m D lddm σσσσ ππ 22 44 diameter, d length, l Measured: mass diameter length 17 Density Calculation A 218.44 ± 0.01 g metal cylinder has diameter of 2.50 ± 0.01 cm and is 5.00 ± 0.01 cm long. What is the density of the metal?
Mass: 218.44 ± 0.01 g
Diameter: 2.50 ± 0.01 cm
Length: 5.00 ± 0.01 cm Volume = ¼πd2l Density = m/V Density of a Cylinder 32 90005.8 )00.5()50.2( )44.218(4 cm g cmcm g D == π       +++±= lddmld m ld m D lddm σσσσ ππ 22 44 Formula: Density: 20 Graphing / Visualizing Data Volume (mL) Mass (g) 5.00 4.93 10.00 9.62 15.00 14.99 20.00 21.02 25.00 24.89 30.00 29.77 Density of Water Density of Water y = 1.0028x 0 10 20 30 0.00 10.00 20.00 30.00 Volume (mL) M as s (g ) OHdensity mL g xx yy lope 2 0028.1s 12 12 == − − = Graphing For a plot of mass vs. volume y-axis: mass in g x-axis: volume in mL mL g density volume mass lope 00.1s === Density: linear relationship of mass to volume 21 Densities 22.4Os 19.3Au 10.5Ag 4.5Ti 3.51diamond 2.65quartz 1.00water 0.35wood Density (g/mL) Substance Increasing density = Increasing “heaviness”