scientific & chemical fundamentals applications: precision & accuracy density dr. ron rusay...
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Scientific & Chemical Fundamentals
Applications:Precision & Accuracy
Density
Dr. Ron Rusay
Refer to Lab Manual & Worksheets
01_09
(c)(b)(a)
Precision
QUESTION: Rank the images from best to worst precision.Rank the images from best to worst precision.
A) a > b > cA) a > b > c B) b > c > a C) c > a > b D) c > b > a B) b > c > a C) c > a > b D) c > b > a
01_09
(c)(b)(a)
Precision
Answer: Rank the images from best to worst precision.Rank the images from best to worst precision.
A) a > b > cA) a > b > c B) b > c > a C) c > a > b B) b > c > a C) c > a > b D) c > b > a D) c > b > a
01_09
(c)(b)(a)
Accuracy
QUESTION:
Rank the images from best to worst accuracy. Rank the images from best to worst accuracy.
A) a > b > cA) a > b > c B) b > c > a C) c > a > b D) c > b > a B) b > c > a C) c > a > b D) c > b > a
01_09
(c)(b)(a)
Accuracy
Answer:
Rank the images from best to worst accuracy. Rank the images from best to worst accuracy.
A) a > b > cA) a > b > c B) b > c > a B) b > c > a C) c > a > b C) c > a > b D) c > b > a D) c > b > a
QUESTIONTwo 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:
• If precision were the only requirement, bottlers could claim any volume as long as it was always very nearly the same volume.
• Since precision is a requirement, bottlers have to get exactly 375 mL in every can.
• Bottlers must have a precise average of all of the containers in a case of soft drinks equal to 375 mL.
• If there were a difference of no more than +/- 1 mL between containers, the bottlers can sell their beverage.
AnswerTwo 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:
• If precision were the only requirement, bottlers could claim any volume as long as it was always very nearly the same volume.
• Since precision is a requirement, bottlers have to get exactly 375 mL in every can.
• Bottlers must have a precise average of all of the containers in a case of soft drinks equal to 375 mL.
• If there were a difference of no more than +/- 1 mL between containers, the bottlers can sell their beverage.
Precision & Accuracy (The Following Measured Data is for Volume in mL)
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
The melting point of pure benzoic acid is 122°C. Data The melting point of pure benzoic acid is 122°C. Data obtained by four students in a laboratory experiment are obtained by four students in a laboratory experiment are shown below. Which student’s data are precise but not the shown below. Which student’s data are precise but not the most accurate?most accurate?
A) Student AA) Student A B) Student BB) Student B
C) Student CC) Student C D) Student DD) Student D
QUESTION
The melting point of pure benzoic acid is 122°C. Data The melting point of pure benzoic acid is 122°C. Data obtained by four students in a laboratory experiment are obtained by four students in a laboratory experiment are shown below. Which student’s data are precise but not the shown below. Which student’s data are precise but not the most accurate?most accurate?
A) Student AA) Student A B) Student BB) Student B
C) Student CC) Student C D) Student DD) Student D
Answer
Precision (Average Deviation vs. Standard Deviation)
http://en.wikipedia.org/wiki/Standard_deviation
The distribution of data (individual data points) in a set The distribution of data (individual data points) in a set is not considered by the Average Deviation. Standard is not considered by the Average Deviation. Standard Deviation, which Deviation, which is the square root of the data set’s
variance relative to its average (mean), is commonly relative to its average (mean), is commonly used to do this.used to do this.
Precision (Standard Deviation)
http://en.wikipedia.org/wiki/Standard_deviation
Standard Deviation Standard Deviation is the square root of the data set’s variance relative to its average (mean). Mathematically: relative to its average (mean). Mathematically:
Where σ Where σ is the Standard Deviation, μ is the data’s is the data’s average (mean), N is the total number of data points, average (mean), N is the total number of data points,
and xand xii is the individual data point. is the individual data point.
Precision & AccuracyProvide the Standard Deviation
(The Following Measured Data is for Volume in mL)
Standard Standard Standard
deviation deviation deviation
+/- 0.91 +/- 0.03 +/- 0.05
+/- 0.57 (Avg. Dev) +/- 0.03 (Avg. Dev) +/- 0.04
Reporting Results
Example: Chem 120 VAT Survey ResultsV A T34 28 28
34 24 22
28 22 30
30 28 18
32 26 15
36 32 18
26 30 23
30 32 18
36 22 32
28 26 22
22 24 28
32 22 18
35 6 35
36 26 34
30 26 28
34 20 26
30 30 26
32 28 24
28 24 22
30 22 16
28 34 28
25 24 26
32 30 3834 22 24
34 26 22
34 28 14
28 28 16
32 20 24
34 30 18
40 24 22
34 32 24
32 28 23
30 24 20
24 24 22
32 22 24
36 14 26
34 28 28
28 32 16
22 21 30
38 24 32
26 22 20
38 22 24
32 22 24
28 26 38
32 24 28
34 28 24
30 28 21
32 30 32
32 26 24
26 30 26
28 22 30
26 28 30
30 22 14
32 26 26
30 12 38
28 30 30
22 26 22
30 22 26
28 28 32
32 26 28
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.
Reporting Results
Example: Chem 120 VAT Survey Results
V A TAVG 31 25 25STDev 4 5 6Max 40 34 38Min 22 6 14
Can you use a spreadsheet?
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
Standard Standard Standard
deviation deviation deviation
a) b) c)
+/- 0.91 +/- 0.03 +/- 0.05
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 mL.a), b) and c). The accepted value is 8.08 mL.
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
Standard Standard Standard
deviation deviation deviation
a) b) c)
+/- 0.91 +/- 0.03 +/- 0.05
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 mL.a), b) and c). The accepted value is 8.08 mL.
Answer:Answer:
DensityDensity = Mass / Volume [g/mL or g/cm3; g/L]
Refer to Lab Manual/Worksheets
• One of the densest substances: a White Dwarfhttp://antwrp.gsfc.nasa.gov/apod/ap961203.html
1.0 teaspoon = 3.0 T (metric tons);
Calculate its density:
D = ? g/cm3
(1 tsp = 4.93 mL; 1 mL = 1 cm3; 1 metric ton = 1,000 kg )
D = ? g/cm3
1
DensityDensity = Mass / Volume [g/mL or g/cm3; g/L] (kg/m3)
Refer to Lab Manual/Worksheets
White Dwarfhttp://antwrp.gsfc.nasa.gov/apod/ap961203.html
D = 610,000 g/cm3 ( 6.1 x 10 5 g/cm3 )
1
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 106 g/cm3
DensityDensity = Mass / Volume [g/mL or g/cm3; g/L]
Refer to Lab Manual/Worksheets
White Dwarfhttp://antwrp.gsfc.nasa.gov/apod/ap961203.html
D = 610,000 g/cm3 ( 6.1 x 10 5 g/cm3 )
Densityastro= ? kg/m3
1
The density of a Neutron star (pulsar) is 3.7×1017 to 5.9×1017 kg/m3 (~ 3 ×1014 times the density of
our Sun)
How many times denser a Neutron Star versus a White Dwarf?
DensityDensity = Mass / Volume [g/mL or g/cm3; 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 yd3.
• When filled with Aerogel, the total weight of Aerogel is ~ 1100 lbs. What is the density of Aerogel?
• D = ? g/cm3
• D = 3.0 x 10-3 g/cm3
1
•D = ? g/L
DensityDensity = Mass / Volume [g/mL or g/cm3; 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/ft3
• Which is less dense Aerogel or Aerographite?
• D = ? g/cm3
1
A metal sample is hammered into a rectangular sheet A metal sample is hammered into a rectangular sheet with an area of 31.2 ftwith an area of 31.2 ft22 and an average thickness of and an average thickness of 2.30 2.30 ×× 10 10−−66 cm. If the mass of this sample is 0.4767 g, cm. If the mass of this sample is 0.4767 g, predict the identity of the metal. predict the identity of the metal.
The density of the metal is shown in parenthesis. The density of the metal is shown in parenthesis. Useful information: 1 in = 2.54 cmUseful information: 1 in = 2.54 cm
A) Aluminum (2.70 g/cmA) Aluminum (2.70 g/cm33)) B) Copper (8.95 g/cmB) Copper (8.95 g/cm33))
C) Gold (19.3 g/cmC) Gold (19.3 g/cm33)) D) Zinc (7.15 g/cmD) Zinc (7.15 g/cm33))
QUESTION
A metal sample is hammered into a rectangular sheet A metal sample is hammered into a rectangular sheet with an area of 31.2 ftwith an area of 31.2 ft22 and an average thickness of and an average thickness of 2.30 2.30 ×× 10 10−−66 cm. If the mass of this sample is 0.4767 g, cm. If the mass of this sample is 0.4767 g, predict the identity of the metal. predict the identity of the metal.
The density of the metal is shown in parenthesis. The density of the metal is shown in parenthesis. Useful information: 1 in = 2.54 cmUseful information: 1 in = 2.54 cm
A) Aluminum (2.70 g/cmA) Aluminum (2.70 g/cm33)) B) Copper (8.95 g/cmB) Copper (8.95 g/cm33))
C) Gold (19.3 g/cmC) Gold (19.3 g/cm33)) D) Zinc (7.15 g/cmD) Zinc (7.15 g/cm33))
Answer
Densities of Various Common Substances* at 20° C
DensityDensity = Mass / Volume [g/mL or g/cm3; g/L]
Refer to Lab Manual/Worksheets
• How many pounds of air are there in PS 275? It has a volume of ~220 yd3.
• Dair = 1.22 x 10-3 g/cm3 (1.22 g/L)
• Mass = Density x Volume
• Mass = 450 lbs
1
Reporting Results
V A T34 28 28
34 24 22
28 22 30
30 28 18
32 26 15
36 32 18
26 30 23
30 32 18
36 22 32
28 26 22
22 24 28
32 22 18
35 6 35
36 26 34
30 26 28
34 20 26
30 30 26
32 28 24
28 24 22
30 22 16
28 34 28
25 24 26
32 30 3834 22 24
34 26 22
34 28 14
28 28 16
32 20 24
34 30 18
40 24 22
34 32 24
32 28 23
30 24 20
24 24 22
32 22 24
36 14 26
34 28 28
28 32 16
22 21 30
38 24 32
26 22 20
38 22 24
32 22 24
28 26 38
32 24 28
34 28 24
30 28 21
32 30 32
32 26 24
26 30 26
28 22 30
26 28 30
30 22 14
32 26 26
30 12 38
28 30 30
22 26 22
30 22 26
28 28 32
32 26 28
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.
Reporting Results
Chem 120 VAT Survey Results
V A TAVG 31 25 25STDev 4 5 6Max 40 34 38Min 22 6 14
Should V=40 and A=6 be eliminated from the Data set and
the Average recalculated?
METHOD 1: METHOD 3:
Stack of 10 Pennies NEW or OLD? Indivdual Penny NEW or OLD?
Height Diameter Mass Density Height Diameter Mass Density
(mm) (mm) (g) g/cm3 DEV (mm) (mm) (g) g/cm3 DEV
13.1 17.1 19.7483 1.2 18.9 2.0085
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 Working Calculated Average
REPORTED AVERAGE Correct # of REPORTED AVERAGE Correct # of
AVG DEV. significant AVG DEV. significant
STD DEV digits STD DEV digits
ACCURACY % ACCURACY %
METHOD 2: METHOD 4:
Stack of 10 Pennies NEW or OLD? Indivdual Penny NEW or OLD?
Volume Mass Density Volume Mass Density
(mL) (g) g/cm3 DEV (mL) (g) g/cm3 DEV
4.1 29.5854 0.35 2.6525
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 7.0100
7.0194 6.3005
7.8600 8.8995
Working Calculated Average Working Calculated Average
REPORTED AVERAGE Correct # of REPORTED AVERAGE Correct # of
AVG DEV. significant AVG DEV. significant
STD DEV digits STD DEV digits
ACCURACY % ACCURACY %
Reporting Results: Wednesday Lab
Q-Test, Standard Deviation & 10% Test (Avg. Dev.)
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.) Select the most massive sample and its mass in grams.
A. Sample two; 1.08 gramsB. Sample two; 4.32 gramsC. Sample one; 2.35 gramsD. Sample one; 2.350 grams
AnswerWhich 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.) Select the most massive sample and its mass in grams.
A. Sample two; 1.08 gramsB. Sample two; 4.32 gramsC. Sample one; 2.35 gramsD. Sample one; 2.350 grams
The mass of sample two is obtained from its density and volume by multiplying 2.00 cm3 × 2.16 g/cm3.
QUESTIONThe 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?
• 6.0 mL• 6.00 mL• 4.2 mL• 4.17 mL
AnswerThe 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?
• 6.0 mL• 6.00 mL• 4.2 mL• 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.