Scientific & Chemical Fundamentals

Precision & Accuracy/ Density

Dr. Ron Rusay

Spring 2008

© Copyright 2003-2008 R.J. Rusay© Copyright 2003-2008 R.J. Rusay

01_09

(c)(b)(a)

Precision & Accuracy

QUESTIONS: 1) Rank the images from best to worst precision.1) Rank the images from best to worst precision.

2) Rank the images from best to worst accuracy. 2) Rank the images from best to worst accuracy. c > b > ac > b > a

c > a > bc > a > b

QUESTIONTwo Chem 120 students are each drinking a soft drink after class. The volumes of both containers are respectively listed as 375 milliliters. Philip remarks that the law requires bottlers to be very precise. Susan correctly responded:

1. If precision were the only requirement, bottlers could claim any volume as long as it was always very nearly thesame volume.

2. Since precision is a requirement, bottlers have to get exactly 375 mL in every can.

3. Bottlers must have a precise average of all of the containers in a case of soft drinks equal to 375 mL.

4. If there were a difference of no more than +/- 1 mL between containers, the bottlers can sell their beverage.

ANSWERChoice 1 best fits what scientists define as precise. High precision measurements may have closeness to a set goal (such as 375 mL in a can) but precision always means closeness within a set of measurements. If the volumes of 100 containers were within a range of 294 to 295 mL the volumes would be precise, but not accurately 375 mL.

Section 1.4: Uncertainty in Measurement

Precision & AccuracyNumerical Data

a) b) c)

9.52 8.40 7.958.36 8.35 8.007.29 8.42 8.058.34 8.36 7.95

__________ __________ __________Average

a) b) c)

9.52 8.40 7.958.36 8.35 8.007.29 8.42 8.058.34 8.36 7.95

__________ __________ __________Average 8.378 8.383 7.988

Round Off 8.38 8.38 7.99

a) b) c)deviation deviation deviation

9.52 -1.14 8.40 -0.02 7.958.36 0.02 8.35 0.03 8.007.29 1.09 8.42 -0.04 8.058.34 0.04 8.36 0.02 7.95

__________ __________ __________Average 8.378 0.573 8.383 0.028 7.988

Round Off 8.38 +/- 0.57 8.38 +/- 0.03 7.99

Absolute value ( all of the - become +)

0.04-0.01-0.060.04

0.038

+/- 0.04

QUESTION

A)A) Precision: a > c > bPrecision: a > c > b B) Precision: b > c > aB) Precision: b > c > a

C) Precision: a = b > cC) Precision: a = b > c D) Precision: a > b > cD) Precision: a > b > c

Average Average Average

a) b) c)

8.38 8.38 7.99

average average average

deviation deviation deviation

a) b) c)

+/- 0.57 +/- 0.03 +/- 0.04

Rank the relative precision of the three sets of data: Rank the relative precision of the three sets of data: a), b) and c).The accepted value is 8.08.a), b) and c).The accepted value is 8.08.

Answer:Answer:

QUESTION

A)A) Accuracy: a > c > bAccuracy: a > c > b B) Accuracy: b > c > aB) Accuracy: b > c > a

C)C) Accuracy: c > a = b Accuracy: c > a = b D) Accuracy: a = b > cD) Accuracy: a = b > c

Average Average Average

a) b) c)

8.38 8.38 7.99

average average average

deviation deviation deviation

a) b) c)

+/- 0.57 +/- 0.03 +/- 0.04

Rank the relative accuracy of the three sets of data: Rank the relative accuracy of the three sets of data: a), b) and c).The accepted value is 8.08.a), b) and c).The accepted value is 8.08.

Answer:Answer:

DensityLab: pp. 105-110: WKS: pp.151-152

• Density = Mass / Volume [g/mL or g/cm3; g/L]

• Least dense man-made solid substance: Aerogel, D = 3.025 x 10-3 g/cm3

http://eetd.lbl.gov/ECS/aerogels/aerogels.htm

http://stardust.jpl.nasa.gov/spacecraft/aerogel.html

• Dair = 1.22 x 10-3 g/cm3 (1.22 g/L)

• Densest known substance: a White Dwarfhttp://antwrp.gsfc.nasa.gov/apod/ap961203.html

1.0 teaspoon = 3.0 T; D = ? g/cm3 (1 tsp = 4.93 mL; 1 mL = 1 cm3 )

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© Copyright 1998-2007 R.J. Rusay

QUESTIONWhich 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 cm3? (The density of solid salt is 2.16 g/cm3.) Report your choice and report the grams of the more massive sample.

1. Sample two; 1.08 grams2. Sample two; 4.32 grams3. Sample one; 2.35 grams4. Sample one; 2.350 grams

ANSWERChoice 2 provides the accurate mass for 2.00 cm3 of salt. This mass is larger than the 2.35 gram sample. Be sure to solve for the mass of a sample from its density and volume by multiplying 2.00 cm3 × 2.16 g/cm3.

Section 1.8: Density

Densities of Various Common Substances* at 20° C

QUESTIONThe volume of a sample can be obtained from its density and mass. If the mass of a sample of acid from a battery were 5.00 grams and the density was 1.2 g/mL, what would you report in mL and with the proper number of significant digits, as the sample volume?

1. 6.0 mL2. 6.00 mL3. 4.2 mL4. 4.17 mL

ANSWERChoice 3 shows the correct volume for 5.00 grams of this sample. First, be sure to use the correct solution for solving volume from mass and density (V = m/D). Then recall that the significant digit pattern for dividing measurements is to retain the same number of significant digits in the answer as the least number in any of the related measurements.

Section 1.8: Density