 # Scientific Measurement

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Scientific Measurement

Objectives Understand how to calculate percentage error.
Understand the concepts of accuracy and precision. Explain how precision lead to accuracy.

Accuracy 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?

Precision precision: consistency of results
precise results: mL, 45.8 mL, 45.9 mL, 45.9 mL not 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: cm less precise: 3.6 cm

Accuracy and Precision
A tool with better precision usually results in greater accuracy… less estimation is required, so… 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?
7,052,155,751 people = very precise value 7,052,000,000 people = not as precise significant figures: measured values that imply precision Which zeros are significant and which 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: mL = 2 SF Ending zeros after decimal are significant: g = 4 SF Placeholder zeros are not significant: people = 2 SF Easily counted whole items, defined values, and whole #s in equations have unlimited significant figures: 13 cats min = 60 sec C = 2pr (all are exact!)

How many significant figures?
49.4 cm 0.023 s 7000 bison 22 students 9.08 g 1.030 mL 0.40 m kg 1 ft = 12 in 3 2 1 unlimited 4

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 = m2 = 36 m2 45.67 g / 12.8 mL = 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 m = ? 4.5 +9.18 13.68 = 13.7 m g – 9.25 g = ? 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
Which of the following are measurements? 12 grams pounds 4.5 mL 3.1415 measurement: includes value and unit mass: amount of matter grams (g) use a balance nearest 0.01 g MASS IS NOT WEIGHT! weight is the force of gravity length: measure of distance centimeters (cm) nearest 0.1 cm with ruler 42.3 cm

Volume volume: amount of 3-D space cubic centimeters (cm3) for solids
milliliters (mL) for liquids # cm3 = # mL use a graduated cylinder or graduated flask +/- 0.1 mL (using meniscus) volume = 52.7 mL # mL water = # g water ONLY TRUE FOR WATER! 1.00 L water = 1.00 kg water

Temperature temperature: measures particle
vibrational motion (faster = hotter) degrees Celsius (oC) or Kelvin (K) measure to nearest 1oC # oC = # K # K = # oC absolute zero: coldest temperature, all particle motion stops 0 K = -273oC

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 M mega = 106 k kilo = 103 c centi = 10-2
m milli = 10-3 m micro = 10-6 Use the prefix scale to move the decimal point… M ● ● k ● ● unit ● c m ● ● m 145 mm 14.5 cm = ? mm 34.6 mL = ? L L 4.57 kg = ? g 4570 g

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 density: mass per volume (g/cm3 or g/mL)
All samples of a substance (at same conditions) 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?

Density 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 V = 5.11 cm3

Density What is the mass of a 12.5 cm3 piece of iron?
Look up the density on your periodic table! m = 98.3 g

Thickness of Aluminum Foil Lab
Question: How much thicker is “heavy duty” aluminum foil than “regular” aluminum foil? We can use density to help answer this question. Measure the mass, length, and width of a sheet of each type of foil. The density will be the same for each. The thickness (h) can be calculated and compared.

Vernier Calipers = 1.23 cm This line shows that the length
is a little more than 1.2 cm The 3rd line on vernier scale aligns with scale above