Chapter 3 Scientific Measurement

Transcription

1 Chapter 3 Scientific Measurement Measurements 2 types: Qualitative measurements (words) Heavy, hot, or long Quantitative measurements (# s) & depend on: 1) Reliability of measuring instrument 2) Care w/ which it s read determined by YOU! Scientific Notation Coefficient raised to power 10 (ex. 1.3 x 10 7 ) Review: Textbook pages R56 & R57 1

2 Accuracy, Precision, and Error Necessary for reliable lab measurements Accuracy how close measurement is to true value Precision how close measurements to each other Reproducible For # s w/ decimal pt decimal place right-most digit is in Accuracy, Precision, and Error For # s w/o decimal pt...rightmost non-zero #

3 Precision and Accuracy Accuracy, Precision, and Error Accepted value based on reliable references (Density Table page 90) Experimental value - measured in lab 3

4 Accuracy, Precision, and Error Error = accepted value experimental value can be + or - Percent error = absolute value of error divided by accepted value, & multiplied by 100% % error = error accepted value NFL Flyovers 4:53 x 100% Significant Figures in Measurements Significant figures all known digits + one estimated digit Measurements must be recorded to correct # sig figs 4

5 Figure 3.5 Significant Figures - Page 67 Which measurement is the best? What is the measured value? What is the measured value? What is the measured value? Rules for Counting Sig Figs Non-zeros always count as sig figs: 3456 has 4 sig figs 5

6 Rules for Counting Sig Figs Zeros Leading zeroes do not count as sig figs: has 3 sig figs Rules for Counting Sig Figs Zeros Captive zeroes always count as sig figs: has 4 sig figs 6

7 Zeros Rules for Counting Sig Figs Trailing zeros significant only w/ written decimal point: has 4 sig figs Rules for Counting Sig Figs Two special situations have unlimited # sig figs: 1. Counted items a) 23 people, or 425 thumbtacks 2. Exactly defined quantities b) 60 minutes = 1 hour Big Sig Fig Gig (2:27) Mark Rosengarten 7

8 Sig Fig Practice #1 How many significant figures in the following? m 5 sig figs kg 4 sig figs 100,890 L 5 sig figs 3.29 x 10 3 s 3 sig figs These all come from some measurements cm 2 sig figs 3,200,000 ml 2 sig figs 5 dogs unlimited This is a counted value Sig Figs in Calculations answer cannot be more precise than least precise measurement. Sometimes, calculated values need rounded off 8

9 Rounding Calculated Answers Rounding Decide how many sig figs needed Round to that many digits, counting from the left Is next digit less than 5? Drop it. Is next digit 5+? Add 1 - Page 69 Be sure to answer the question completely! 9

10 Rounding Calculated Answers Addition and Subtraction answer rounded to same # decimal places as least # decimal places in problem - Page 70 10

11 Rounding Calculated Answers Multiplication and Division answer rounded to same # of sig figs as least # of sig figs in problem - Page 71 11

12 Rules for Sig Figs in Mathematical Operations Multiplication and Division: # sig figs in result = # in least precise measurement used in calculation x 2.0 = (2 sig figs) Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m m 2 23 m g 23.7 cm g/cm g/cm cm x cm cm cm m 3.0 s m/s 240 m/s lb x 3.23 ft lb ft 5870 lb ft g x 2.87 ml g/ml 2.96 g/ml 12

13 Rules for Sig Figs in Mathematical Operations Addition and Subtraction: # decimal places in result = # decimal places in least precise measurement = (3 sig figs) Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m m m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.39 cm L L L L lb lb lb lb ml ml 0.16 ml ml *Note the zero that has been added. 13

14 International System of Units p. 73 Measurements depend on units The standards of measurement of science is Metric System Why science uses the metrics 2:30 International System of Units Metric system now revised & named International System of Units (SI), (1960) multiples of 10 5 common base units in chemistry meter, kilogram, kelvin, second & mole 14

15 2 parts: Nature of Measurements Measurement - quantitative observation - Part 1 number Part 2 - unit Examples: 22 grams 3.55 x 10 3 moles International System of Units Sometimes, non-si units used Liter, Celsius, calorie Derived units joining units Speed = kilometers/hour (distance/time) Density = grams/ml (mass/volume) 15

16 Length SI basic unit - meter (m) distance btwn 2 objects use prefixes for larger/smaller units SI Prefixes Page 74 - Common to Chemistry Prefix Abbreviation Meaning Exponent Mega- M Million 10 6 Kilo- k thousand 10 3 Deci- d tenth 10-1 Centi- c hundredth 10-2 Milli- m thousandth 10-3 Micro- millionth 10-6 Nano- n billionth 10-9 Pico- P trillionth

17 Volume Space occupied by matter Calculated for solid length x width x height derived from units of length SI unit = cubic meter (m 3 ) Everyday unit = Liter (L), non-si (Note: 1mL = 1cm 3 ) Devices for Measuring Liquid Volume Graduated cylinders Pipets Burets Volumetric Flasks Syringes 17

18 Volume Changes! Volumes of a solid, liquid, or gas generally increases w/ temp More prominent for GASES Therefore, measuring instruments calibrated for specific temp usually 20 o C, which is about room temp Ex. Volumetric flask Units of Mass Mass - quantity of matter present Mass constant, regardless of location Weight - force of g - changes w/ location 18

19 Working with Mass SI unit - kilogram (kg) everyday unit is gram (g) measuring instrument: triple beam balance Units of Temperature Temp - measures how hot/cold object is. (Measured with a thermometer.) Heat moves from hi - low temp 2 temp scales: Celsius named after Anders Celsius Kelvin named after Lord Kelvin 19

20 Units of Temperature Celsius scale Water Freezing point = 0 o C Water Boiling point = 100 o C Kelvin scale does not use degree sign, just K absolute zero = 0 K (no negative values) formula to convert: K = o C Page 78 20

21 Units of Energy Energy - ability to do work, or produce heat energy can be measured 2 common units: 1) Joule (J) = SI unit of energy, named after James Prescott Joule 2) calorie (cal) = heat needed to raise 1g of water 1 o C Units of Energy Conversions btwn joules & calories carried out by using following relationship: 1 cal = J 21

22 Sec 3.3 Conversion factors A ratio of equivalent measurements Start with two things that are the same: one meter is one hundred centimeters write it as an equation 1 m = 100 cm Divide on each side of equation to come up with 2 ways of writing the number 1 Conversion factors 1 m = 100 cm 100 cm 100 cm 22

23 Conversion factors 1 m = 100 cm 1 Conversion factors 1 m = 100 cm 1 1 m = 100 cm 1 m 1 m 23

24 Conversion factors 1 m = 100 cm 1 1 = 100 cm 1 m Conversion factors unique way of writing the # 1 In same system they are defined quantities so unlimited number of sig figs big # small unit = small # big unit 100 cm = 1 m 24

25 Practice writing two possible conversion factors for the following: Between kilograms and grams between feet and inches using qt. = 1.00 L What are they good for? We can multiply by # one creatively to change units Question: 13 inches is how many yards? We know that 36 inches = 1 yard 1 yard = 1 36 inches 13 inches x 1 yard = 36 inches 25

26 What are they good for? We can multiply by a conversion factor to change the units. Problem: 13 inches is how many yards? Known: 36 inches = 1 yard. 1 yard = 1 36 inches 13 inches x 1 yard = 0.36 yards 36 inches Dimensional Analysis Method of analyzing & solving problems, by using units (dimensions) of measurement Dimension = unit (g, L, cm) Analyze = solve Using units to solve problems If units of answer correct, you probably did math correctly! 26

27 Dimensional Analysis provides alternative approach to problem solving, instead of with equation or algebra. ruler is 12.0 inches long. How long is it in cm? ( 1 inch = 2.54 cm) How long is this in meters? A race is 10.0 km long. How far is this in miles, if: 1 mile = 1760 yards 1 meter = yards p. 82 practice problem #28 How many minutes are there in exactly one week? 27

28 p. 83 practice problem # 30 An experiment requires that each student use an 8.5-cm length of magnesium ribbon. How many students can do the experiment if there is a 570- cm length of magnesium ribbon available? Converting Between Units measurements with one unit converted to equivalent measurement with another unit easily solved using dimensional analysis Sample: Express 750 dg in grams. Many complex problems are best solved by breaking the problem into manageable parts. 28

29 p. 84 practice problem #32 Using tables from this chapter, convert these: a km to meters b. 4.6 mg to grams c g to centigrams Converting Between Units Let s say you need to clean your car: 1) Start by vacuuming the interior 2) Next, wash the exterior 3) Dry the exterior 4) Finally, put on a coat of wax What problem-solving methods can help you solve complex word problems? Break the solution down into steps, and use more than one conversion factor if necessary 29

30 p. 85 practice problem # 34 (p. 30 in workbook) The radius of a potassium atom is nm. Express this radius in the unit centimeters. Converting Complex Units? Complex units are those that are expressed as a ratio of two units: Speed might be meters/hour Sample: Change 15 meters/hour to units of centimeters/second How do we work with units that are squared or cubed? (cm 3 to m 3, etc.) BONUS: Crash of Flight 143 see my webpage 30

31 - Page 86 Section 3.4 Density Which is heavier- a pound of steel or a pound of styrofoam? Most people answer steel, but the weight is exactly the same They are normally thinking about equal volumes of the two The relationship here between mass and volume is called Density 31

32 Density The formula for density is: mass Density = volume Common units are: g/ml, or g/cm 3, (or g/l for gas) Density is a physical property, and does not depend upon sample size A gold nugget has the same density as a gold bar - Page 90 Note temperature and density units 32

33 Density and Temperature What happens to the density as the temperature of an object increases? Mass remains the same Most substances increase in volume as temperature increases Thus, density generally decreases as the temperature increases Density and Water Water is an important exception to the previous statement. Over certain temperatures, the volume of water increases as the temperature decreases (You don t want your water pipes to freeze in the winter, right?) Why does ice float in liquid water? 33

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