1. Scientific & Chemical Fundamentals Applications: Precision & Accuracy Density Dr. Ron Rusay Refer to Lab Manual & Worksheets

2. Precision QUESTION: Rank the images from best to worst precision. A) a > b > c B) b > c > a C) c > a > b D) c > b > a A) a > b > c B) b > c > a C) c > a > b D) c > b > a

3. Precision Answer: Rank the images from best to worst precision. A) a > b > c B) b > c > a C) c > a > b D) c > b > a A) a > b > c B) b > c > a C) c > a > b D) c > b > a

4. Accuracy QUESTION: Rank the images from best to worst accuracy. A) a > b > c B) b > c > a C) c > a > b D) c > b > a A) a > b > c B) b > c > a C) c > a > b D) c > b > a

5. Accuracy Answer: Rank the images from best to worst accuracy. A) a > b > c B) b > c > a C) c > a > b D) c > b > a A) a > b > c B) b > c > a C) c > a > b D) c > b > a

6. QUESTION Two Chem 120 students are each drinking a can of cranberry juice after class. The printed label indicates that the respective volume of both containers is 375 milliliters. Euna remarks that the Federal Trade Commision (FTC) requires bottlers to be very precise. Mike correctly responded: A. If precision were the only requirement, bottlers could claim any volume as long as it was always very nearly the same volume. B.Since precision is a requirement, bottlers have to get exactly 375 mL in every can. C.Bottlers must have a precise average of all of the containers in a case of soft drinks equal to 375 mL. D. If there were a difference of no more than +/- 1 mL between containers, the bottlers can sell their beverage.

7. Answer Two Chem 120 students are each drinking a can of cranberry juice after class. The printed label indicates that the respective volume of both containers is 375 milliliters. Euna remarks that the Federal Trade Commision (FTC) requires bottlers to be very precise. Mike correctly responded: A. If precision were the only requirement, bottlers could claim any volume as long as it was always very nearly the same volume. B.Since precision is a requirement, bottlers have to get exactly 375 mL in every can. C.Bottlers must have a precise average of all of the containers in a case of soft drinks equal to 375 mL. D. If there were a difference of no more than +/- 1 mL between containers, the bottlers can sell their beverage.

8. Precision & Accuracy (The Following Measured Data is for Volume in mL)

9. The melting point of pure benzoic acid is 122°C. Data obtained by four students in a laboratory experiment are shown below. Which student’s data are precise but not the most accurate? A) Student AB) Student B A) Student AB) Student B C) Student CD) Student D C) Student CD) Student D QUESTION

10. The melting point of pure benzoic acid is 122°C. Data obtained by four students in a laboratory experiment are shown below. Which student’s data are precise but not the most accurate? A) Student AB) Student B C) Student CD) Student D C) Student CD) Student D Answer

11. Precision (Average Deviation vs. Standard Deviation) http://en.wikipedia.org/wiki/Standard_deviation http://en.wikipedia.org/wiki/Standard_deviation The distribution of data (individual data points) in a set is not considered by the Average Deviation. Standard Deviation, which relative to its average (mean), is commonly used to do this. The distribution of data (individual data points) in a set is not considered by the Average Deviation. Standard Deviation, which is the square root of the data set’s variance relative to its average (mean), is commonly used to do this.square root variance

12. Precision (Standard Deviation) http://en.wikipedia.org/wiki/Standard_deviation http://en.wikipedia.org/wiki/Standard_deviation Standard Deviation relative to its average (mean). Mathematically: Standard Deviation is the square root of the data set’s variance relative to its average (mean). Mathematically:square root variance Where σ is the data’s average (mean), N is the total number of data points, and x i is the individual data point. Where σ is the Standard Deviation, μ is the data’s average (mean), N is the total number of data points, and x i is the individual data point.

13. Precision & Accuracy Provide the Standard Deviation (The Following Measured Data is for Volume in mL) Standard deviation +/- 0.91+/- 0.03+/- 0.05 +/- 0.57(Avg. Dev)+/- 0.03(Avg. Dev)+/- 0.04

14. Reporting Results Example: Chem 120 VAT Survey Results VAT 3428 342422 2822 30 2818 322615 363218 263023 303218 362232 282622 2428 322218 356 362634 302628 342026 30 26 322824 282422 302216 283428 252426 323038 342224 342622 342814 28 16 322024 343018 402422 343224 322823 302420 24 22 322224 361426 3428 3216 222130 382432 262220 382224 322224 282638 322428 342824 302821 323032 2624 263026 282230 262830 2214 3226 301238 2830 222622 302226 28 32 2628 What number best represent the respective VAT class result? Average of each. How much does the class vary in each? Standard Deviation of each, Maximum & Minimum of each.

15. Reporting Results Example: Chem 120 VAT Survey Results VAT AVG3125 STDev456 Max403438 Min22614 Can you use a spreadsheet?

16. QUESTION A) Precision: a > c > bB) Precision: b > c > a C) Precision: a = b > cD) Precision: a > b > c Average a)b)c) 8.38 7.99 Standard deviation a)b)c) +/- 0.91+/- 0.03+/- 0.05 Rank the relative precision of the three sets of data: a), b) and c). The accepted value is 8.08 mL. Answer:

17. QUESTION A) Accuracy: a > c > bB) Accuracy: b > c > a C) Accuracy: c > a = b D) Accuracy: a = b > c Average a)b)c) 8.38 7.99 Standard deviation a)b)c) +/- 0.91+/- 0.03+/- 0.05 Rank the relative accuracy of the three sets of data: a), b) and c). The accepted value is 8.08 mL. Answer:

18. Density Density = Mass / Volume [g/mL or g/cm 3 ; g/L] Refer to Lab Manual/Worksheets One of the densest substances: a White Dwarf http://antwrp.gsfc.nasa.gov/apod/ap961203.html 1.0 teaspoon = 3.0 T (metric tons); Calculate its density: D = ? g/cm 3 (1 tsp = 4.93 mL; 1 mL = 1 cm 3 ; 1 metric ton = 1,000 kg ) D = ? g/cm 3

19. Density Density = Mass / Volume [g/mL or g/cm 3 ; g/L] (kg/m 3 ) Refer to Lab Manual/Worksheets White Dwarf http://antwrp.gsfc.nasa.gov/apod/ap961203.html D = 610,000 g/cm 3 ( 6.1 x 10 5 g/cm 3 ) Our Sun will eventually become a white dwarf “butterfly”….. but not for ~5 billion years. A White Dwarf’s mass is comparable to our Sun's, but its volume is about a million times smaller; the average density is ~1,000,000 times greater than the Sun’s, approximately 1 x 10 6 g/cm 3

20. Density Density = Mass / Volume [g/mL or g/cm 3 ; g/L] Refer to Lab Manual/Worksheets White Dwarf http://antwrp.gsfc.nasa.gov/apod/ap961203.html D = 610,000 g/cm 3 ( 6.1 x 10 5 g/cm 3 ) Density astro = ? kg/m 3 The density of a Neutron star (pulsar) is 3.7×10 17 to 5.9×10 17 kg/m 3 (~ 3 ×10 14 times the density of our Sun) How many times denser a Neutron Star versus a White Dwarf?

21. Density Density = Mass / Volume [g/mL or g/cm 3 ; g/L] Refer to Lab Manual/Worksheets One of the least dense man-made solid substances: Aerogel http://eetd.lbl.gov/ECS/aerogels/aerogels.htm http://stardust.jpl.nasa.gov/spacecraft/aerogel.html PS 275 has a volume of ~220 yd 3. When filled with Aerogel, the total weight of Aerogel is ~ 1100 lbs. What is the density of Aerogel? D = ? g/cm 3 D = 3.0 x 10 -3 g/cm 3 D = ? g/L

22. Density Density = Mass / Volume [g/mL or g/cm 3 ; g/L] Refer to Lab Manual/Worksheets Aerographite is a synthetic foam consisting of a porous interconnected network of tubular carbon. It was first reported by researchers at the University of Kiel and the Technical University of Hamburg in Germany in a scientific journal in June 2012. It’s density is: D = 0.00112 lbs/ft 3 Which is less dense Aerogel or Aerographite? D = ? g/cm 3

23. A metal sample is hammered into a rectangular sheet with an area of 31.2 ft 2 and an average thickness of 2.30 × 10 −6 cm. If the mass of this sample is 0.4767 g, predict the identity of the metal. The density of the metal is shown in parenthesis. Useful information: 1 in = 2.54 cm A) Aluminum (2.70 g/cm 3 )B) Copper (8.95 g/cm 3 ) A) Aluminum (2.70 g/cm 3 )B) Copper (8.95 g/cm 3 ) C) Gold (19.3 g/cm 3 )D) Zinc (7.15 g/cm 3 ) C) Gold (19.3 g/cm 3 )D) Zinc (7.15 g/cm 3 ) QUESTION

24. A metal sample is hammered into a rectangular sheet with an area of 31.2 ft 2 and an average thickness of 2.30 × 10 −6 cm. If the mass of this sample is 0.4767 g, predict the identity of the metal. The density of the metal is shown in parenthesis. Useful information: 1 in = 2.54 cm A) Aluminum (2.70 g/cm 3 )B) Copper (8.95 g/cm 3 ) A) Aluminum (2.70 g/cm 3 )B) Copper (8.95 g/cm 3 ) C) Gold (19.3 g/cm 3 )D) Zinc (7.15 g/cm 3 ) C) Gold (19.3 g/cm 3 )D) Zinc (7.15 g/cm 3 ) Answer

25. Densities of Various Common Substances* at 20° C

26. Density Density = Mass / Volume [g/mL or g/cm 3 ; g/L] Refer to Lab Manual/Worksheets How many pounds of air are there in PS 275? It has a volume of ~220 yd 3. D air = 1.22 x 10 -3 g/cm 3 (1.22 g/L) Mass = Density x Volume Mass = 450 lbs

27. Reporting Results VAT 3428 342422 2822 30 2818 322615 363218 263023 303218 362232 282622 2428 322218 356 362634 302628 342026 30 26 322824 282422 302216 283428 252426 323038 342224 342622 342814 28 16 322024 343018 402422 343224 322823 302420 24 22 322224 361426 3428 3216 222130 382432 262220 382224 322224 282638 322428 342824 302821 323032 2624 263026 282230 262830 2214 3226 301238 2830 222622 302226 28 32 2628 What number best represent the respective VAT class result? Average of each. How much does the class vary in each? Standard Deviation of each, Maximum & Minimum of each.

28. Reporting Results Chem 120 VAT Survey Results VAT AVG3125 STDev456 Max403438 Min22614 Should V=40 and A=6 be eliminated from the Data set and the Average recalculated?

29. METHOD 1:METHOD 3: Stack of 10 PenniesNEW or OLD? Indivdual PennyNEW or OLD? HeightDiameterMassDensity HeightDiameterMassDensity (mm) (g)g/cm3DEV(mm) (g)g/cm3DEV 13.117.119.7483 1.218.92.0085 6.0215 6.3016 6.6985 6.8984 6.6905 7.0055 6.3495 7.7045 6.6806 5.7002 6.0294 6.1998 6.8811 6.0008 6.3789 5.7992 6.0800 7.5000 Working Calculated Average REPORTEDAVERAGE Correct # of REPORTEDAVERAGE Correct # of AVG DEV. significant AVG DEV. significant STD DEV digits STD DEV digits ACCURACY % % METHOD 2:METHOD 4: Stack of 10 PenniesNEW or OLD? Indivdual PennyNEW or OLD? VolumeMassDensity VolumeMassDensity (mL)(g)g/cm3DEV(mL)(g)g/cm3DEV 4.129.5854 0.352.6525 7.6015 9.2008 7.0585 6.8992 7.9802 7.9805 7.7998 7.1995 7.3600 6.7122 7.1006 6.1878 7.0100 7.0194 6.3005 7.8600 8.8995 Working Calculated Average REPORTEDAVERAGE Correct # of REPORTEDAVERAGE Correct # of AVG DEV. significant AVG DEV. significant STD DEV digits STD DEV digits ACCURACY % % Reporting Results: Wednesday Lab Q-Test, Standard Deviation & 10% Test (Avg. Dev.)

30. QUESTION Which would provide more grams of NaCl, sample one with a mass of 2,350 mg, or sample two, a solid with a volume of 2.00 cm 3 ? (The density of solid salt is 2.16 g/cm 3.) Select the most massive sample and its mass in grams. A. Sample two; 1.08 grams B. Sample two; 4.32 grams C. Sample one; 2.35 grams D. Sample one; 2.350 grams

31. Answer Which would provide more grams of NaCl, sample one with a mass of 2,350 mg, or sample two, a solid with a volume of 2.00 cm 3 ? (The density of solid salt is 2.16 g/cm 3.) Select the most massive sample and its mass in grams. A. Sample two; 1.08 grams B. Sample two; 4.32 grams C. Sample one; 2.35 grams D. Sample one; 2.350 grams The mass of sample two is obtained from its density and volume by multiplying 2.00 cm 3 × 2.16 g/cm 3.

32. QUESTION The volume of any material can be obtained from its density and mass. If the mass of a sample of acid from a battery were 5.00 grams and its density was 1.2 g/mL, what would the correct reported volume in mL with the proper number of significant digits? A.6.0 mL B.6.00 mL C.4.2 mL D.4.17 mL

33. Answer The volume of any material can be obtained from its density and mass. If the mass of a sample of acid from a battery were 5.00 grams and its density was 1.2 g/mL, what would the correct reported volume in mL with the proper number of significant digits? A.6.0 mL B.6.00 mL C.4.2 mL D.4.17 mL Volume from mass and density is V = m/D. Significant digits in the answer, which involves division in the calculation, is limited to the same number of significant digits as the least number in any of the values used in the calculation.