Download - Scientific Measurement
Objectives
• Understand how to calculate percentage error.
• Understand the concepts of accuracy and precision.
• Explain how precision lead to accuracy.
Accuracy
100A
EAE %
accuracy: closeness to accepted value (true, actual)percentage error: represents accuracy
Sample Problems
• An automobile scale is used to measure the weight of a car. The true weight of the car is 3245 lbs, but the scale says 3238 lbs. What is the percentage error?• The same scale is used to measure the weight of a cat. The cat actually weighs 12 lbs, but the scale says 5 lbs. What is the % E?
100A
EAE %
Precisionprecision: consistency of results
precise results: 45.9 mL, 45.8 mL, 45.9 mL, 45.9 mLnot as precise: 46 mL, 48 mL, 51 mL, 45 mL
precision: number of significant figures in a measurement; depends on the quality of the measuring tool
more precise: 3.584 cm less precise: 3.6 cm
Accuracy and Precision
• A tool with better precision usually results in greater accuracy…1. less estimation is required, so…2. greater certainty = more accurate
Objectives
• Be able to determine the number of significant figures in a measurement.
• Be able to report the correct number of significant figures for a calculation.
Significant Figures
What is the world’s population?
7,052,000,000 people = not as precise7,052,155,751 people = very precise value
significant figures: measured values that imply precision
Which zeros are significant andwhich ones are not?
50 mL or 50.0 mL?
Sig Fig Rules
• Non-zero digits are always significant: 25.6 m = 3 SF• Zeros between SF are significant: 1026 g = 4 SF• Left-most zeros are not significant: 0.0042 mL = 2 SF• Ending zeros after decimal are significant: 45.30 g = 4 SF• Placeholder zeros are not significant: 44000 people = 2 SF• Easily counted whole items, defined values, and whole #s
in equations have unlimited significant figures: 13 cats 1 min = 60 sec C = 2r (all are exact!)
How many significant figures?
a. 49.4 cmb. 0.023 sc. 7000 bisond. 22 studentse. 9.08 gf. 1.030 mLg. 0.40 mh. 0.0007 kgi. 1 ft = 12 in
321unlimited3421unlimited
Calculations with Sig Figs
Multiplication and division: the reported answer should have the same number of SFs as the least precise measurement
13.4 m x 2.7 m = 36.18 m2 = 36 m2 45.67 g / 12.8 mL = 3.56796875 g/mL = 3.57 g/mL
You can use the removed digits to round if necessary.
Calculations with Sig Figs
Addition and subtraction: the answer should be rounded to the least precise decimal position
4.5 m + 9.18 m = ?
14.832 g – 9.25 g = ?
4.5+9.1813.68 = 13.7 m
14.832-9.25 5.582 = 5.58 g
Objectives
• Be able to define commonly used types of measurements used in chemistry.
• Be able to identify the units used in chemistry.• Be able to identify the types of instruments
used to make measurements.
Common Metric Measurements
• mass: amount of matter• grams (g)• use a balance • nearest 0.01 g
• length: measure of distance• centimeters (cm)• nearest 0.1 cm with ruler
42.3 cm
MASS IS NOT WEIGHT!weight is the force of gravity
measurement: includes value and unitWhich of the following are measurements?a. 12 grams b. pounds c. 4.5 mLd. 3.1415
Volume
# mL water = # g water ONLY TRUE FOR WATER!
• volume: amount of 3-D space• cubic centimeters (cm3) for solids• milliliters (mL) for liquids• # cm3 = # mL
volume = 52.7 mL
1.00 L water = 1.00 kg water
• use a graduated cylinder or graduated flask• +/- 0.1 mL (using meniscus)
Temperature
• temperature: measures particle vibrational motion (faster = hotter)• degrees Celsius (oC) or Kelvin (K)• measure to nearest 1oC
absolute zero: coldesttemperature, all particle motion stops0 K = -273oC
• # oC + 273 = # K• # K - 273 = # oC
Objectives
• Be familiar with Celsius and Kelvin temperature.
• Be able to make conversions between common prefixes used in the metric system.
• Understand the meaning of accuracy.• Be able to calculate percentage error.
Metric Prefixes
Use the prefix scale to move the decimal point…M ● ● k ● ● unit ● c m ● ●
M mega = 106 k kilo = 103
c centi = 10-2
m milli = 10-3
micro = 10-6
14.5 cm = ? mm 145 mm
4.57 kg = ? g 4570 g
34.6 mL = ? L 0.0346 L
Objectives
• Understand the concept of density in terms of a physical property.
• Be able to use the density equation to calculate density, mass, or volume.
Density
Vm
ddensity: mass per volume (g/cm3 or g/mL)
All samples of a substance (at sameconditions) will have an identical density.
If 3.00 cm3 of lead has a mass of 34.0 g, then 6.00 cm3 will have a mass of 68.0 g. What are their densities?
3cm
g3 11.3
3.00cm34.0g
d
3cm
g3 11.3
6.00cm68.0g
d
Density
Vm
d
If the density and either the mass or volume is known, then the other variable can be calculated.
What is the volume of a 45.8 g piece of copper? d = 8.96 g/cm3
dm
V
3cm
g8.9645.8g
V V = 5.11 cm3
Density
Vm
d Vdm
What is the mass of a 12.5 cm3 piece of iron? Look up the density on your periodic table!
3
cm
g 12.5cm7.86m 3 m = 98.3 g
Thickness of Aluminum Foil Lab
Vm
d hwlV
Question: How much thicker is “heavy duty” aluminum foil than “regular” aluminum foil?
We can use density to help answer this question.
hwlm
d
Measure the mass, length, and width of a sheet ofeach type of foil. The density will be the same for each.The thickness (h) can be calculated and compared.