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• ### measurements

1. 1. Ch 100: Fundamentals for Chemistry
2. 2. What is Chemistry?• Chemistry is considered to be the central science• Chemistry is the study of matter• Matter is the “stuff” that makes up the universe• The fundamental questions of Chemistry are: • How can matter be described? • How does one type of matter interact with other types of matter? • How does matter transform into other forms of matter?
3. 3. Types of Observations• Qualitative Descriptive/subjective in nature Detail qualities such as color, taste, etc. Example: “It is really warm outside today”• Quantitative Described by a number and a unit (an accepted reference scale) Also known as measurements Example: “The temperature is 85oF outside today”
4. 4. Ch 100: Fundamentals for Chemistry Chapter 1: Measurements
5. 5. UNITS OF MEASUREMENTMeasurements are quantitative information.A measurement is more than just a number, evenin everyday life.Suppose a chef were to write a recipe like“1 salt, 3 sugar, 2 flour.”The cooks could not use the recipe without moreinformation.They need to know UNITS.
6. 6. Quantities• A measurement represents a quantity  something that has size or amount• Measurement and quantity NOT the same• 1 liter  liter is unit of measurement, volume is a quantity• Almost every measurement requires a number AND a unit
7. 7. Measurements• Described with a value (number) & a unit (reference scale)• Both the value and unit are of equal importance!!• The value indicates a measurement’s size (based on its unit)• The unit indicates a measurement’s relationship to other physical quantities
8. 8. Measurement SystemsThere are 3 standard unit systems we will focus on: 1. United States Customary System (USCS)  formerly the British system of measurement  Used in US, Albania, and a couple others  Base units are defined but seem arbitrary (e.g. there are 12 inches in 1 foot) 2. Metric  Used by most countries  Developed in France during Napoleon’s reign  Units are related by powers of 10 (e.g. there are 1000 meters in 1 kilometer) 3. SI (L’Systeme Internationale)  a special set of metric units  Used by scientists and most science textbooks  Not always the most practical unit system for lab work
9. 9. Related Units in the Metric System• All units in the metric system are related to the fundamental unit by a power of 10• The power of 10 is indicated by a prefix• The prefixes are always the same, regardless of the fundamental unit
10. 10. Metric Prefixes
11. 11. Units & Measurement• When a measurement has a specific unit (i.e. 25 cm) it can be expressed using different units without changing its meaning• Example: » 25 cm is the same as 0.25 m or even 250 mm• The choice of unit is somewhat arbitrary, what is important is the observation it represents
12. 12. Basic Quantities and SI Units 1. SI units 2. Base and derived quantities 3. Prefixes
13. 13. S.I. UNITS• Le system International d’unites• A modification of the older French metric system.
14. 14. Base Units Base units are considered sobecause they are not derivedfrom any pre-existing number orformula. We need to be able todiscuss things like distance,temperature and time, and wedo so by agreeing to a reliabledefinition of some basic (base!)facts.
15. 15. THE BASE QUANTITIES & UNITSQUANTITY UNIT SYMBOLmass kilogram kglength metre mtime second selectric current ampere (amp) Athermodynamic kelvin Ktemperatureamount of mole molsubstanceluminous intensity candela cd
16. 16. EXAMPLES OF DERIVED UNITS QUANTITY UNIT DERIVED UNIT frequency hertz (Hz) s-1 speed m s-1 m s-1 acceleration m s-2 m s-2 force newton (N) kg m s-2 energy joule (J) kg m2 s-2 power watt (W) kg m2 s-3 electric charge coulomb (C) Aspotential difference volt (V) kg m2 s-3 A-1electrical resistance ohm (Ω) kg m2 s-3 A-2specific latent heat J kg-1 K-1 m2 s-2 K-1
17. 17. The more commonly used prefixespeta P 1015tera T 1012giga G 109mega M 106kilo k 103deci d 10-1centi c 10-2milli m 10-3micro μ 10-6nano n 10-9pico p 10-12femto f 10-15atto a 10-18
18. 18. Mass and WeightMass: the measure of the quantity or amount ofmatter in an object. The mass of an object does notchange as Its position changes.Weight: A measure of the gravitational attraction ofthe earth for an object. The weight of an objectchanges with its distance from the center of the earth. Sample Calculations Involving Masses How many mg are in 2.56 kg? (2.56 kg)(103 g)(103mg) = 2.56 x 106 mg (1 kg) ( 1 g)
19. 19. Volume• The units for volume are given by (units of length)3. i.e., SI unit for volume is 1 m3.• A more common volume unit is the liter (L) 1 L = 1 dm3 = 1000 cm3 = 1000 mL.• We usually use 1 mL = 1 cm3. Sample Calculations Involving Volumes How many mL are in 3.456 L? (3.456 L)(1000 mL) = 3456 mL L How many ML are in 23.7 cm3? (23.7 cm3)( 1 mL )( 1 L_ _)(106 ML) (1 cm3)(1000 mL)( 1L ) = 23 700 ML = 2.37 x 10 4 ML
20. 20. DensityDensity - The mass of a unit volume of a material. density = mass/volumeWhat is the density of a cubic block of wood that is 2.4 cm on each side and has a mass of 9.57 g? volume = [2.4 cm x 2.4 cm x 2.4 cm] density = (9.57 g)/(13.8 cm3) = 0.69 g/cm3 = 0.69 g/mLNote that 1 cm3 = 1 mL
21. 21. Temperature 21
22. 22. Temperature Conversions: K = oC + 273.15273 K = 0 oC373 K = 100 oC o C = 5 (oF – 32) 9 o F = 9 (oC) + 32 5 32 oF = 0 oC212 oF = 100 oC
23. 23. TemperatureKelvin Scale Used in science. Same temperature increment as Celsius scale. Lowest temperature possible (absolute zero) is zero Kelvin. Absolute zero: 0 K = -273.15oC.Celsius Scale Also used in science. Water freezes at 0oC and boils at 100oC. To convert: K = oC + 273.15.Fahrenheit Scale Not generally used in science. Water freezes at 32oF and boils at 212oF.Converting between Celsius and Fahrenheit 5 9 ° = (° - 32 ) C F ° = (° ) +32 F C 9 5
24. 24. Sample Calculations Involving TemperaturesConvert 73.6oF to Celsius and Kelvin temperatures. o C = (5/9)(oF - 32) K = oC + 273.15 Memorizeo C = (5/9)(73.6oF - 32) = (5/9)(41.6) = 23.1oC K = 23.1oC + 273.15 = 296.3 K
25. 25. Measurement & Uncertainty• A measurement always has some amount of uncertainty• Uncertainty comes from limitations of the techniques used for comparison• To understand how reliable a measurement is, we need to understand the limitations of the measurement
26. 26. Exact numbers vs. Measured numbers  Exact numbers are numbers that are defined  Infinite number of significant figures present in exact numbers  Zero uncertainty  Measured numbers are an estimated amount – dependent on the measuring tool  Limited number of significant figures present in measured numbers  Always some uncertainty in the measurement
27. 27. Significant Figures• Significant figures are used to distinguish truly measured values from those simply resulting from calculation.• Significant figures determine the precision of a measurement.• Precision refers to the degree of subdivision of a measurement.
28. 28. Significant Figures• Significant figures in a measurement are of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated
29. 29. Why do significant figures matter?  Show how precisely the data has been measured  Greater number of significant figures means the measuring tool is more precise  Incorrectly adding more significant figures makes it seem that you have more precision than truly exists  Not having enough significant figures makes it seem that you have less precision than the measuring tools provided What do significant figures nottell us? • If a measurement is truly accurate
30. 30. Rules for Counting Significant Figures• Nonzero integers are always significant• Exact numbers have an unlimited number of significant figures• Zeros ….. The problem
31. 31. Rules for Determining Significant Zeros Rule Examples1. Zeros appearing between nonzero digits a. 40.7 L has three sig figsare significant. b. 87,009 km has five sig figs2. Zeros appearing in front of all nonzero a. 0.095897 m has five sig figsdigits are NOT significant. b. 0.0009 kg has one sig fig3. Zeros at the end of a number and to the a. 85.00 g has four sig figsright of a decimal point are significant. b. 9.000000000 mm has ten sig figs4. Zeros at the end of a number but to the a. 2000 m may contain from one to fourleft of a decimal point may or may not be sig figs, depending on how many zerossignificant. If a zero has not been are placeholders. For measurementsmeasured or estimated but is just a given in this text, assume that 2000 mplaceholder, it is not significant. A decimal has one sig fig.point placed after zeros indicates they are b. 2000. m contains four sig figs, indicatedsignificant. by the presence of the decimal point
32. 32. No decimal point2 sig figs Zeros are not significant! Decimal Point All digits including zeros to the left of The decimal are significant. 6 sig figs
33. 33. All figures are Significant 4 sig figs Zeros between Non zeros are significantAll figures are Significant 5 sig figs Zero to the Right of the Decimal are significant
34. 34. 3 sig figs Zeros to the right of The decimal with no Non zero values Before the decimal Are not significant5 sig figs Zeros to the right of the decimal And to the right of non zero values Are significant
35. 35. Sample ProblemHow many significant figures are in each of the following measurements?a. 28.6 gthreeb. 3440. cmfourc. 910 mtwod. 0.046 04 Lfoure. 0.006 700 0 kgfive
36. 36. Practice Problems1. Determine the number of significant figures ineach of the following.
37. 37. Measurements & Significant Figures• To indicate the uncertainty of a single measurement scientists use a system called significant figures• The last digit written in a measurement is the number that is considered to be uncertain• Unless stated otherwise, the uncertainty in the last digit is ±1
38. 38. Scientific Notation• Technique Used to Express Very Large or Very Small Numbers• Based on Powers of 10• To Compare Numbers Written in Scientific Notation First Compare Exponents of 10 (order of magnitude) Then Compare Numbers
39. 39. Scientific Notation• In scientific notation, numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.• Ex. 65,000 km in scientific notation is• 6.5 x 104 km
40. 40. Scientific numbers use powers of 10
41. 41. RULE 1 As the decimal is moved to the left Any number to the The power of 10 increases one Zero power = 1value for each decimal place moved
42. 42. RULE 2As the decimal is moved to the right Any number to the The power of 10 decreases one Zero power = 1value for each decimal place moved
43. 43. RULE 3When scientific numbers are multiplied The powers of 10 are added
44. 44. RULE 4When scientific numbers are divided The powers of 10 are subtracted
45. 45. RULE 5When scientific numbers are raised to powers The powers of 10 are multiplied
46. 46. RULE 6Roots of scientific numbers are treated as fractional powers. The powers of 10 are multiplied
47. 47. RULE 7When scientific numbers are added or subtractedThe powers of 10 must be the same for each term. Powers of 10 are Different. Values Cannot be added ! Move the decimal And change the power Of 10 Power are now the Same and values Can be added.
48. 48. Writing Numbers in Scientific Notation 1 Locate the Decimal Point 2 Move the decimal point to the right of the non-zero digit in the largest place  The new number is now between 1 and 10 3 Multiply the new number by 10n  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 left, n is +  If the decimal point was moved right, n is –  If the decimal point was not moved, n is 0
49. 49. Example• 0.000 12 mm = 1.2 × 10−4 mm• Move the decimal point four places to the right and multiply the number by 10−4• 1. Determine M by moving the decimal point in the original number to the left or the right so that only one nonzero digit remains to the left of the decimal point.• 2. Determine n by counting the number of places that you moved the decimal point. If you moved it to the left, n is positive. If you moved it to the right, n is negative.
50. 50. Writing Numbers in Standard Form1 Determine the sign of n of 10n If n is + the decimal point will move to the right If n is – the decimal point will move to the left2 Determine the value of the exponent of 10 Tells the number of places to move the decimal point3 Move the decimal point and rewrite the number
51. 51. Rules for Rounding Off• If the digit to be removed • is less than 5, the preceding digit stays the same • is equal to or greater than 5, the preceding digit is increased by 1• In a series of calculations, carry the extra digits to the final result and then round off• Don’t forget to add place-holding zeros if necessary to keep value the same!!
52. 52. Addition or Subtraction• When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. 25.1 g + 2.03 g = 27.13 g 27.1 g
53. 53. The numbers in these positions are not zeros, they are unknown The sum of an unknown number and a 6 is not valid. The same is trueThe answer is rounded to the For the 2position of least significance
54. 54. Multiplication and Division• For multiplication and division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. = 0.360094451 g/mL = 0.360 g/mL
55. 55. Uncertainty,Precision & Accuracyin Measurements
56. 56. Definitions Accuracy and Precision …sound the same thing… …is there a difference??
57. 57. ACCURACYMEANS HOW CLOSE A MEASUREMENT IS TO THE TRUE VALUE PRECISION REFERS TO THE DEGREE OFSUBBDIVISION OF THE MEASUREMENT
58. 58. Accuracy• Accuracy is the extent to which a measurement approaches the true value.• Accurate means "capable of providing a correct reading or measurement." A measurement is accurate if it correctly reflects the size of the thing being measured.
59. 59. Precision• Precision measures the reproducibility of your value.• Precise means “repeatable, reliable, getting the same measurement each time.”
60. 60. Accuracy & Precision• Accuracy is how close to the accepted value.• Precision is how close a series of measurements are to each other.
61. 61. Accuracy & Precision (cont.)
62. 62. Accuracy & Precision (cont.)• Students collected density data for powered sucrose.• The accepted density is 1.59 g/cm 3. Density Data Collected by Three different Students Student A Student B Student C Trial 1 1.54 g/cm3 1.40 g/cm3 1.70 g/cm3 Trial 2 1.60 g/cm3 1.68 g/cm3 1.69 g/cm3 Trial 3 1.57 g/cm3 1.45 g/cm3 1.71 g/cm3 Average 1.57 g/cm3 1.51 g/cm3 1.70 g/cm3
63. 63. 1-5 Summary• What is the difference between accuracy and precision?
64. 64. Precision and AccuracyAccuracy – how close a measurement is to the true oraccepted valueTo determine if a measured value is accurate, you wouldhave to know what the true or accepted value for thatmeasurement is – this is rarely known!Precision – how close a set of measurements are toeach other; the scatter of repeated measurementsabout an average.We may not be able to say if a measured value is accurate,but we can make careful measurements and use goodequipment to obtain good precision, or reproducibility.
65. 65. Precision and AccuracyA target analogy is often used to compare accuracy andprecision. accurate precise not accurate & but & precise not accurate not precise