1. Scientific Measurement

2. Importance of Measurement Qualitative & Quantitative Measurements Qualitative: SubjectiveSubjective ObservationalObservational DescriptiveDescriptive Non-numericalNon-numerical Quantitative: ObjectiveObjective Expressible as a quantityExpressible as a quantity NumericalNumerical Has specific unitsHas specific units

3. Scientific Notation Number written as product of 2 numbers A coefficientA coefficient 10 raised to a power10 raised to a power 36,000 written as 3.6 X 10 4     coefficient 10 to power of 4 coefficient 10 to power of 4 Coefficient is always between 1-10

4. Scientific Notation Make very large /small numbers user- friendly Avagadro’s Number (number of molecules /mole) 602,000,000,000,000,000,000,000 602,000,000,000,000,000,000,000 6.02 X 10 23 6.02 X 10 23

5. Scientific Notation Coefficient is always between 1-10 If number is >10 Exponent is positiveExponent is positive # places decimal moved to left# places decimal moved to left 4,870,000 = 4.87 X 10 6 If number is < 1 exponent is negativeexponent is negative # placed decimal moved to right# placed decimal moved to right 0.00000487 = 4.87 X 10 -6

6. Scientific Notation To multiply in Scientific Notation Multiply the coefficientsMultiply the coefficients Add the exponentsAdd the exponents (3.5 X 10 4 ) X (2.0 X 10 3 ) = 7.0 X 10 7 (3.5 X 10 4 ) X (2.0 X 10 -8 ) = 7.0 X 10 -4 (3.5 X 10 -4 ) X (2.0 X 10 -8 ) = 7.0 X 10 -12

7. Scientific Notation To divide in Scientific Notation Divide the coefficientsDivide the coefficients Subtract the exponent of denominator from exponent of numeratorSubtract the exponent of denominator from exponent of numerator (7.0 X 10 8 )  (2.0 X 10 3 ) = 3.5 X 10 5 (7.0 X 10 4 )  (2.0 X 10 -8 ) = 3.5 X 10 12 (7.0 X 10 -4 )  (2.0 X 10 8 ) = 3.5 X 10 -12 (7.0 X 10 -4 )  (2.0 X 10 -8 ) = 3.5 X 10 4

8. Scientific Notation Addition & Subtraction Make the exponents the sameMake the exponents the same Add or subtract coefficientsAdd or subtract coefficients Exponent remains unchangedExponent remains unchanged (5.40 X 10 3 ) + (6.0 X 10 2 ) = (5.40 X 10 3 ) + (0.60 X 10 3 ) = 6.00 X 10 3

9. Accuracy& Precision Accuracy Closeness to true valueCloseness to true valuePrecision Ability to repeat a measurementAbility to repeat a measurement closeness of series of measurements to each othercloseness of series of measurements to each other

10. ErrorError Indicator of accuracy &/or precision of a measurementIndicator of accuracy &/or precision of a measurement Error = experimental value - accepted value accepted value = assumed or known correct value experimental value = measured value

11. Percent Error Percent error: a measure of relative error Error = experimental value - accepted value % error = (  error  /accepted value) x 100 Why would you want to know the error associated with an instrument or a procedure? Allows assessment of accuracyAllows assessment of accuracy

12. Percent Error ex. thermometer measures BP of H 2 O at sea level as 99.2 O C error = 100 O C - 99.2 O C = 0.8 O C % error = (0.8 O C /100 O C) X 100 % = 0.8 % If same thermometer gave BP of unknown liquid as 85 O C,If same thermometer gave BP of unknown liquid as 85 O C, True BP is 85 O C + 0.8 % or 85 + 0.68 O C = 85.7 O CTrue BP is 85 O C + 0.8 % or 85 + 0.68 O C = 85.7 O C

13. Significant Figures A calculated answer cannot be more accurate than the measurements used to make the calculation.

14. Significant Figures ex. density = mass/volume Given: mass = 10.0 g & volume = 53.0 cm 3 By calculator: density = 1.886792452 g/cm 3 Implies we know the density accurately to the nearest 1 millionth of a g/cm 3 Instrument accuracy: 0.1g and 0.1 cm 3

15. Example 5.45 cm 9.85 cm Use calculator to determine area Implies can measure to nearest.0001 cm 9.85 cm x 5.45 cm = 53.6825 cm 2 Can only estimate to.01 cm Round 53.6825 cm 2 to 53.7 cm 2

16. Known digits + 1 estimated digit 0 1 2 3 4 5 6 7 8 9 10 cm scale 9 1 2 3 4 5 6 7 8 9 10 mm indicated between cm On cm scale Know: 9 cm Est: 9.8 cm 2 sig. figures With mm scale Know: 8 mm Est: 8.5 mm 3 sig. figures Final measure: 9.85 cm

17. Significant Figures 1. Every nonzero digit is significant 2. 0s between nonzero digits are significant (ex 30.45, 50.0024) 3. Leftmost 0s in front of nonzero digits are not significant (ex 0.45, 0.0024) 4. 0s at the end of a number after a decimal point are significant (ex 24.00, 3.200)

18. Significant Figures 5. Rightmost 0s at end of number (left of understood decimal point) are not significant (ex 300) 6. Unlimited significant figures a) counting (ex 15 rats) b) defined quantities (ex 1 hr = 60 min)

19. Significant Figures 3 3 5 5 123 meters 0.123 meters 40,506 meters 9.8000 X 10 4 meters

20. Significant Figures 3 Unlimited 4 2 30.0 meters 22 meter sticks 0.07080 meters 98,000 meters

21. Significant Figures in Calculations 1. Determine the number of significant figures in the answer 2.Round the answer to that number of significant figures

22. Count that number of figures from left a) if next digit is  5,  the last significant digit by 1 b) if next digit is < 5, last significant digit stays the same To round to a given number of significant figures

23. Practice Rounding Round the following to 4 sig figures: 52.5341 4 < 5 52.53 52.5361 6  5 52.54 0.023005 5  5 0.02301 2,382,900 9  5 2,383,000 1.023005 0 < 5 1.023

24. Determining Number of Significant Figures Addition & Subtraction Round to number of decimal places as measurement with least number of sig figures after decimalRound to number of decimal places as measurement with least number of sig figures after decimal

25. Ex: Addition 213.0872 +5.34 +5.34 Need 2 digits after decimal point Need 2 digits after decimal point 218.42 218.42 1 st digit after 2 is a 7, 7>5 1 st digit after 2 is a 7, 7>5 Final answer is 218.43 Final answer is 218.43 218.4272  2 significant figures after decimal point

26. Determining Number of Significant Figures Multiplication & Division Round to same number of sig figures as measurement with least number of significant figuresRound to same number of sig figures as measurement with least number of significant figures

27. Ex: multiplication 23.0872 23.0872 x5.21 x5.21 Can have 3 sig figures 120.284312  3 sig figures  6 sig figures 120.284321 1 st digit after 0 is a 2, 2<5 Final answer is 120 No, must rewrite as 1.20 x 10 2 ?

28. International System of Units (SI) Based on metric system. Know: length = mlength = m volume = m 3volume = m 3 mass = kgmass = kg density = g/cm 3 = g/mLdensity = g/cm 3 = g/mL temperature = Ktemperature = K Common prefixes & metric relationships Tables 3.2 - 3.5 pp 64-67

29. The Seven SI Base Units Physical QuantityName of UnitSymbol MassKilogram kg LengthMeter m TimeSecond s Electric currentAmpere A TemperatureKelvin K Luminous intensity Candela cd Quantity of substance Mole mol Required for Chem A & B

30. SI Prefixes Factor Prefix Symbol 10 18 exa E 10 15 petaP 10 12 teraT 10 9 gigaG 10 6 mega M 10 3 kilo k 10 2 hecto h 10 1 deka da MUST KNOW

31. SI Prefixes Factor Prefix Symbol 10 -1 deci d 10 -2 centi c 10 -3 milli m 10 -6 micro  10 -9 nano n 10 -12 pico p 10 -15 femto f 10 -18 atto a MUST KNOW

32. Density Density = mass/ volume Physical characteristic Can be used for identification Commonly given as g/cm 3 at 20 O C solids and liquidsg/cm 3 at 20 O C solids and liquids g/L at 20 O C gasesg/L at 20 O C gases Why specify temperature? As temp , volume ,  density 

33. Determining Density mass = 10.000 gmass = 10.000 g volume = 53.0 cm 3volume = 53.0 cm 3 density = m/vdensity = m/v = 1.88679 g/cm 3 53.0 = 3 significant figures53.0 = 3 significant figures Round to 3 significant figuresRound to 3 significant figures density = 1.89 g/cm 3density = 1.89 g/cm 3

34. Specific Gravity Specific gravity = density of substance  density of H 2 O Density of H 2 O is  1 1.000000 g/ml at 3.98 O C (0.997 g/ml at 25 O C) Specific gravity of substance  density of substance

35. Specific Gravity Units of density = g/cm 3 What are units of specific gravity? No units substance g/cm 3 water g/cm 3

36. Hydrometer Liquid Reading Hydrometer Measures specific gravity of liquidsMeasures specific gravity of liquids

37. Temperature Degree of hotness or coldness Celsius scale BP of H 2 O = 100 O C (at sea level) MP of H 2 O = 0 O C

38. Kelvin Scale 0 K = absolute 0 0 K = absolute 0 0 K = absence of heat 0 K = -273 O C K = O C + 273 O C = K - 273