SCIENTIFIC MEASUREMENT

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1 SCIENTIFIC MEASUREMENT

2 QUANTITATIVE MEASUREMENTS Described with a value (number) & a unit (reference scale) Both the value and unit are of equal importance!! NO NAKED NUMBERS!!!!!!!!!!

3 QUANTITATIVE MEASUREMENTS - Derived vs. Measured Measured acquired directly from a measuring instrument. EX: ruler, balance, scale, graduated cylinder Derived calculated or determined from Measured values using formulas EX: area of a square or circle, volume of a cylinder, density of an object

4 QuanVtaVve Measurements 1) Temperature Celcius (CenVgrade) C Freezing Point of water Fahrenheit F Freezing Point of water Kelvin SI Unit of temperature with 0 0 K absolute zero, and K equal to the triple point of water (the point at which all three phases of water are at equilibrium) Kelvin = 0 C Celcius = K Farenheit = 0 C(1.8 F/1 0 C) C = F - 32 (1 0 C/1.8 F) 2) Time Fundamental unit is..seconds

5 QuanVtaVve Measurements 3) Volume 3- D space that macer occupies Liquids are defined (measured) or derived solids - - regular shapes formulas (derived value) - - irregular shapes displacement of another liquid, usually water gases formulas (derived values) SI UNIT IS 1 LITER Meters X Meters X Meters = 1 m3 = 1000 liters OR.1m X.1m X.1m =.001 m 3 1 = 1000ml = 1 liter

6 4) Mass macer weight the gravitavonal pull on an object (related to its mass) SI Units UNITS OF MASS: Gram (g) 5) Density Mass/Volume A derived quanvty Units: Grams/cm 3

7 Reporting Measurements Using significant figures Report what is known with certainty Add ONE digit of uncertainty (esvmavon) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

8 Practice Measuring cm 4.5 cm cm 4.54 cm cm 3.0 cm Timberlake, Chemistry 7 th Edition, page 7

9 Measurements in the Lab:! 1. If the glassware is marked every 10 mls, the volume you record should be in mls. (Example A) 2. If the glassware is marked every 1 ml, the volume you record should be in tenths of mls. 3. If the glassware is marked every 0.1 ml, the volume you record should be in hundredths of mls. (Example B) Example A 30 ml 20 ml 10 ml 30-mL beaker: the volume you write in your lab report should be 13 ml Example B 0 ml 1 ml 2 ml Buret marked in 0.1 ml: you record volume as 0.67 ml

Standard lab balance are trustworthy to the nearest milligram (0.001g) measurement: 25.

10 Cheap balance measurements are trustworthy to the nearest gram. Measurement = 25 g, so implied precision is +/- 1g. Standard lab balance are trustworthy to the nearest milligram (0.001g) measurement: g, so implied precision is +/ g The analyvcal balance is very precise. Measurements are trustworthy to the nearest 0.1mg. Measurement: implied precision: +/-.0001g

11 How good are the measurements? ScienVsts use two word to describe how good the measurements are Accuracy- how close the measurement is to the actual value Precision- how well can the measurement be repeated

12 Good Data is concerned with Accuracy vs. Precision in measurement Good accuracy Good precision Poor accuracy Good precision Random errors: reduce precision Poor accuracy Poor precision Systematic errors: reduce accuracy

13 Differences Accuracy can be true of an individual measurement or the average of several Precision requires several measurements before anything can be said about it

14 Let s use a golf analogy

15 Accurate? No Precise? Yes 10

16 Accurate? Yes Precise? Yes 12

17 Precise? No Accurate? Maybe? 13

18 Accurate? Yes Precise? We cant say! 18

19 Accurate? Yes Precise? We cant say! 18

20 Accurate? Yes Precise? We cant say! 18

21 Accuracy Precision Resolution 3 not accurate, not precise accurate, not precise not accurate, precise accurate and precise accurate, low resolution time offset [arbitrary units] subsequent samples

22 Significant figures Using proper significant figures in measured and calculated values conveys a sense of precision to the reader and defines a limit of error in the value.

23 Measurements in the Lab:! The number of SFs in a measured value is equal to the number of known digits plus one uncertain digit. 23 C 22 C 21 C 23 C 22 C 21 C you record 21.6 C you record C

24 Significant Figures What is the smallest mark on the ruler that measures cm? 142 cm? 140 cm? Here there s a problem, does the zero count or not? They needed a set of rules to decide which zeros count. (Non- zeros always count)

25 Rule one SIG FIG Rules All non zero numbers are significant! PRACTICE g 2 g 6.4 g g

26 Rule two SIG FIG Rules All zeros between significant figures are significant So if the zeros are sandwiched or embedded in the number they ARE significant PRACTICE» 5004 g» g» g» g

27 Rule three SIG FIG Rules All trailing zeros to the right of the decimal ONLY are significant Those at the end of a number without the decimal point don t count PracVce» g» g» g» g» g» g

28 Which zeros count? If the number is smaller than one, zeros before the first number don t count g Zeros between other sig figs do g zeroes at the end of a number arer the decimal point do count g If they are holding places, they don t g If measured (or esvmated) they do count

29 Another way to figure it out If the number has a decimal in it: Find the first non zero from the LEFT That is the first significant figure in the number, and all digits arer (as you move toward the right) ARE significant PRACTICE:» g» g» g» g» g

30 If the number does NOT have a decimal in it: Find the first non zero from the RIGHT That is the first significant figure in the number, and all digits arer (as you move toward the ler) ARE significant. PracVce» g» g» g» g

31 Sig Figs Only measurements have sig figs. Counted numbers are exact Ex: A dozen is exactly 12 Number of students in this classroom Unit conversions in most cases will be considered exact numbers Ex: 1 milliliter is exactly.001 of a liter 100 cenvmeters is exactly 1 meter

32 Sig figs. How many sig figs in the following measurements? 458 g g 4850 g g g g

33 Sig Figs g 4050 g g g g Next we learn the rules for calculavons

34 Calculations Involving Measured Data! ü Addition/Subtraction: " ü The answer contains the same number of digits to the right of the decimal as that of the measurement with the fewest number of decimal places.! g g g 28.3 g 3 SFs g g g 0.10 g 2 SFs ü Calculators do NOT know these rules. Itʼs up to you to apply them!!

35 For example 1. First line up the decimal places Then do the adding 3. Count the sig figs in the decimal portion of each addend. 4. Round your answer to the place value of the addend with the least number of decimal places

36 Rounding rules look at the number to the right of place you are rounding to. If it is 0 to 4 don t change it If it is 5 to 9 make it one bigger round to four sig figs to three sig figs to two sig figs to one sig fig

37 PracVce 4.8 g g 520 cm cm m m 6.0 x 10 2 L x 10 3 L 5.4 ml ml 6.7 g g 500 cm cm 6.0 x 10-2 mg x 10-3 mg

38 MulVplicaVon and Division Same number of sig figs in the answer as the least in the quesvon 3.6 g x 653 g g is the answer you would get in your calculator 3.6 has 2 s.f. 653 has 3 s.f. So your answer can only have 2 s.f. You must round to 2 sig figs and your answer is 2400 g

39 Multiplying or Dividing Measured Data! ü answer contains the same number of SFs as the measurement with the fewest SFs.! 25.2 m x 6.1 m = m (on my calculator) = 1.5 x 10 2 m (correct answer) 25.2 g = g g = 7.31 g (correct answer) (6.626 x )(3 x 10 8 ) = x 10-2 (on my calculator) 6.48 x = 0.03 (correct answer)

40 MulVplicaVon and Division Same rules for division pracvce 4.5 g / g 4.5 m x m L x.043 L mg / 1983 mg g / 714 g

41 Problems 50 is only 1 significant figure, but if I actually measured or esvmated the ones place value to be 0, it really has two significant figures. How can I write it? A zero at the end only counts arer the decimal place So, I can use ScienVfic notavon 5.0 x 10 1 now the zero counts.

42 SCIENTIFIC NOTATION Based on Powers of 10 Technique Used to 1. Express Very Large or Very Small Numbers 2. Reduce likely- hood of errors 3. Compare Numbers Wricen in ScienVfic NotaVon First Compare Exponents of 10 (order of magnitude) Then Compare Numbers

43 SCIENTIFIC NOTATION Numbers that are very small The electrical charge on one electron: = X C

44 Or numbers that are very big!! The mass of the moon: 73,600,000,000,000,000,000,000 kg = 7.36 X kg

45 SCIENTIFIC NOTATION WriVng Numbers in ScienVfic NotaVon 1 Locate the Decimal Point 2 Move the decimal point just to the right of the non- zero digit in the largest place The new number is now greater than one but less than ten 3 MulVply the new number by 10 n where n is the number of places you moved the decimal point 4 Determine the sign on the exponent, n If the decimal point was moved ler, n is + If the decimal point was moved right, n is If the decimal point was not moved, n is 0

46 PracVce wrivng in scienvfic notavon = 4.66 x = 5.3 x ,000,000,000 = 1.23 x 10 11

47 SCIENTIFIC NOTATION WriVng Numbers in Standard Form 1 Determine the sign of n of 10 n If n is + the decimal point will move to the right If n is the decimal point will move to the ler 2 Determine the value of the exponent of 10 Tells the number of places to move the decimal point 3 Move the decimal point and rewrite the number

48 PracVce wrivng in standard form 4.50 X 10 7 mm = 45,000,000 mm 8.08 X g = g 4.0 X 10 1 m = 40 m X 10 0 L= L

49 Comparison of English and SI Units 1 inch 2.54 cm 1 inch = 2.54 cm Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 119

50 ConverVng measurements We use a method called dimensional analysis, also referred to as factor label method or train tracks

51 PROBLEM SOLVING STEPS n n n n n n n n Read problem IdenVfy data Make a unit plan from the inival unit to the desired unit Select conversion factors Change inival unit to desired unit Cancel units and check Do math on calculator Give an answer using significant figures

52 How many minutes in 2.5 hours? 2.5 hr X 60min/1 hr = 150 min By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers! 2.5 hr 60min = 150min 1hr Conversion factor

53 You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 $ X 4 quarters/1 $ = 29 quarters Set up railroad tracks 7.25$ 4 quarters = 29 quarters 1$ Conversion Factor

54 WHAT S WRONG WITH THIS? How many seconds in 1.4 days? 1.4 day X 1 day/24 hr X 60 min/1 hr X 60 sec/1 min Set up the railroad tracks 1.4day 1day 60min 60sec = 24hr 1hr 1 min

55 Can you figure it out? You're throwing a pizza party for 15. Each person may eat 4 slices. How much is the pizza going to cost you? You call the pizza place and learn that each pizza will cost $14.78 and will be cut into 12 slices. You have budgeted $70 for your party. Do you have enough money?

56 What units do you begin with? I know I have 15 acendees at the party What do I need to know? How much will the party cost me? So I am beginning with 15 people and need to know how much money the party will cost SO Begin with 15 people and I need to find dollars party party

57 MulVply by factors equivalent to ONE unvl you have solved your problem. Think about how you converted fracvons in elementary school.. ½ a pie is equivalent to how many 1/8s of a pie ½ X 4/4 (equivalent to one) = 4/8

58 15 people 4 slices 1 pizza $14.78 party 1 people 12 slices 1 pizza Now cancel the units MulVply across the top of the train tracks $ MulVpy across the bocom of the train tracks 12 parves Now divide = $73.90/party YOUR OVERBUDGET!

59 What about Square and Cubic units? Use the conversion factors you already know, but when you square or cube the unit, don t forget to cube the number also! Best way: Square or cube the ENTIRE conversion factor Example: Convert 4.3 cm 3 to mm cm 3 (10 mm/ 1 cm) 3 = 4.3 cm 3 X 10 3 mm 3 / 1 3 cm 3 = 4300 mm 3

Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed.

Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed. by Steven S. Zumdahl, Donald J. DeCoste University of Illinois Chapter 2 Measurements and Calculations