Scientific & Chemical
Fundamentals
Precision & Accuracy/ Density
Dr. Ron Rusay
Spring 2008
© Copyright 2003-2008 R.J. Rusay
Precision & Accuracy
(a)
(b)
(c)
QUESTIONS:
1) Rank the images from best to worst precision.
c>b>a
2) Rank the images from best to worst accuracy.
c>a>b
QUESTION
Two 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 the
same 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.
ANSWER
Choice 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 & Accuracy
Numerical Data
a)
b)
a)
9.5 2 9.52
8.3 6 8.36
7.2 9 7.29
8.3 4 8.34
___ ____
_____
____ ____
Averag eAvera ge
8.378
Roun d Off
Avera ge
Roun d Off
7.9 5 7.95
8.0 0 8.00
8.0 5 8.05
7.9 5 7.95
___ ____
_____
____ ____
7.988
8.38
7.99
9.52
8.36
7.29
8.34
__ ____ ____
8.378
b)
de vi atio n
-1.14
0.02
1.09
0.04
0.573
8.38 +/- 0.57
c)
8.4 0 8.40
8.3 5 8.35
8.4 2 8.42
8.3 6 8.36
___ ____
_____
____ ____
8.383
8.38
a)
c)
b)
8.40
8.35
8.42
8.36
__ ____ ____
8.383
c)
de vi atio n
-0.02
0.03
-0.04
0.02
0.028
8.38 +/- 0.0 3
Abs olute va lue ( all of the - becom e +)
de vi atio n
7.95
8.00
8.05
7.95
__ ____ ____
7.988
7.99
0.0 4
-0.0 1
-0.0 6
0.0 4
0.038
+/- 0.04
QUESTION
Rank the relative precision of the three sets of data:
a), b) and c).The accepted value is 8.08.
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
A) Precision: a > c > b
Answer:
B) Precision: b > c > a
C) Precision: a = b > c
D) Precision: a > b > c
QUESTION
Rank the relative accuracy of the three sets of data:
a), b) and c).The accepted value is 8.08.
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
A) Accuracy: a > c > b
Answer:
C) Accuracy: c > a = b
B) Accuracy: b > c > a
D) Accuracy: a = b > c
Density
Lab: pp. 105-110: WKS: pp.151-152
• Density = Mass / Volume [g/mL or g/cm ; g/L]
• Least dense man-made solid substance:
3
1
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
• D = 1.22 x 10 g/cm (1.22 g/L)
• Densest known substance: a White Dwarf
-3
air
3
http://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 )
© Copyright 1998-2007 R.J. Rusay
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
cm3? (The density of solid salt is 2.16 g/cm3.) Report your choice
and report the grams of the more massive sample.
1.
2.
3.
4.
Sample two; 1.08 grams
Sample two; 4.32 grams
Sample one; 2.35 grams
Sample one; 2.350 grams
ANSWER
Choice 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
QUESTION
The 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.
2.
3.
4.
6.0 mL
6.00 mL
4.2 mL
4.17 mL
ANSWER
Choice 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