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The Numerical Side of Chemistry

The Numerical Side of Chemistry. Chapter 2. Types of measurement. Quantitative - use numbers to describe 4 feet 100 ْ F Qualitative - use description without numbers extra large Hot. Scientists prefer. Quantitative- easy check Easy to agree upon, no personal bias

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The Numerical Side of Chemistry

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  1. The Numerical Side of Chemistry Chapter 2

  2. Types of measurement • Quantitative- use numbers to describe • 4 feet • 100 ْF • Qualitative- use description without numbers • extra large • Hot

  3. Scientists prefer • Quantitative- easy check • Easy to agree upon, no personal bias • The measuring instrument limits how good the measurement is

  4. How good are the measurements? • Scientists 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

  5. 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 • examples

  6. Let’s use a golf analogy

  7. Accurate? Precise?

  8. Accurate? Precise?

  9. Accurate? Precise?

  10. In terms of measurement • Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. • Were they precise? • Were they accurate?

  11. Precision Grouping of measurements Need to have several measurements Repeatability Can have precision without accuracy Accuracy How close to true value Can use one measurement or many Can have accuracy without precision Summary of Precision Vs. Accuracy

  12. Significant Figures

  13. 1 2 3 4 5 Significant figures (sig figs) • How many numbers mean anything • When we measure something, we can (and do) always estimate between the smallest marks.

  14. Significant figures (sig figs) • The better marks, the better we can estimate. • Scientist always understand that the last number measured is actually an estimate 1 2 3 4 5

  15. Sig Figs • What is the smallest mark on the ruler that measures 142.15 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 zeroes count. • All other numbers count

  16. Which zeros count? • Those at the end of a number before the decimal point don’t count • 1000 • 1000000000 • 12400 • If the number is smaller than one, zeroes before the first number don’t count • 0.045 • 0.123 • 0.00006

  17. Which zeros count? • Zeros between other sig figs COUNT. • 1002 • 1000000003 • zeroes at the end of a number after the decimal point COUNT • 45.8300 • 56.230000 • If they are holding places, they don’t. • If they are measured (or estimated) they do

  18. Sig Figs • Only measurements have sig figs. • Counted numbers are exact • A dozen is exactly 12 • A a piece of paper is measured 11 inches tall. • Being able to locate, and count significant figures is an important skill. • YOU MUST KNOW ALL THE SIG FIG RULES !!!!

  19. A number is not significant if it is: • A zero at the beginning of a decimal number ex. 0.0004lb, 0.075m • A zero used as a placeholder in a number without a decimal point ex. 992,000,or 450,000,000 A number is a S.F. if it is: •Any real number ( 1 thru 9) • A zero between nonzero digits ex. 2002g or 1.809g • A zero at the end of a number or decimal point ex. 602.00ml or 0.0400g Summary of Significant Figures

  20. Learning Check 2 • How many sig figs in the following measurements? • 458 g_____ • 4085 g_____ • 4850 g______ • 0.0485 g_____ • 0.004085 g_____ • 40.004085 g______

  21. Learning Check 2 Con’t • 405.0 g______ • 4050 g_______ • 0.450 g_______ • 4050.05 g______ • 0.0500060 g______

  22. Scientific Notation

  23. Problems • 50 is only 1 significant figure • if it really has two, how can I write it? • A zero at the end only counts after the decimal place • Scientific notation • 5.0 x 101 • now the zero counts.

  24. Purposes of Scientific Notation • Express very small and very large numbers in a compact notation. • 2.0 x 108 instead of 200,000,000 • 3.5 x 10-7 instead of 0.00000035 • Express numbers in a notation that also indicates the precision of the number. • What is meant if two cities are said to be separated by a “distance of 3,000 miles”?

  25. What Do We Mean by 3,000 miles? • A distance between 2,999 and 3,001 miles? • A distance between 2,990 and 3,010 miles? • A distance between 2,900 and 3,100 miles? • A distance between 2,000 and 4,000 miles?

  26. What Do We Mean by 3,000 miles? • Without a context, we don’t know what is meant. In each case above, the colored digit is the largest one that is uncertain. As you ascend from bottom to top, the uncertainty decreases and the numbers become increasingly precise. • Scientific notation will allow us to express these quantities (all are “three thousand”) with the precision or uncertainty being explicit.

  27. First Things First… • Power-of-ten exponential notation is central to scientific notation. • To start, you should review powers of ten and make sure that you understand the exponential notation and can covert it to standard notation.

  28. How to Handle Significant Figs and Scientific Notation When Doing Math

  29. Adding and subtracting with sig figs • The last sig fig in a measurement is an estimate. • Your answer when you add or subtract can not be better than your worst estimate. • You have to round it to the least place of the measurement in the problem

  30. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example • First line up the decimal places Then do the adding Find the estimated numbers in the problem. 34.33 This answer must be rounded to the tenths place

  31. What About Rounding? • look at the number behind the one you’re rounding. • If it is 0 to 4 don’t change it • If it is 5 to 9 make it one bigger • round 45.462 to four sig figs • to three sig figs • to two sig figs • to one sig fig

  32. Practice • 4.8 + 6.8765 • 520 + 94.98 • 0.0045 + 2.113 • 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28 • 6.7 - .542 • 500 -126 • 6.0 x 10-2 - 3.8 x 10-3

  33. Multiplication and Division • Rule is simpler • Same number of sig figs in the answer as the least in the question • 3.6 x 653 • 2350.8 • 3.6 has 2 s.f. 653 has 3 s.f. • answer can only have 2 s.f. • 2400

  34. Multiplication and Division • Same rules for division • practice • 4.5 / 6.245 • 4.5 x 6.245 • 9.8764 x .043 • 3.876 / 1983 • 16547 / 714

  35. The Metric System An easy way to measure

  36. Measuring • The numbers are only half of a measurement • It is 10 long • 10 what. • Numbers without units are meaningless.

  37. The Metric System • Easier to use because it is a decimal system • Every conversion is by some power of 10. • A metric unit has two parts • A prefix and a base unit. • prefix tells you how many times to divide or multiply by 10.

  38. The SI System •The SI system has seven base units from which all others are derived. Five of them are showed here

  39. SI Units (Con’t) • These prefixes indicate decimal fractions or multiples of various units

  40. Derived Units

  41. Derived Units • SI units are used to derive the units of other quantities. • Some of these units express speed, velocity, area and volume…. • They are either base units squared or cubed, or they define different base units

  42. Volume • calculated by multiplying • L x W x H (for a square) • π x r2 x H (for a cylinder) • (for a sphere) • Basic SI unit of volume is the cubic meter (m3 ). • Smaller units are sometimes employed ex. cm3, dm3 …. • Volume is more commonly defined by liter (L).

  43. Mass • weight is a force, is the amount of matter. • 1gram is defined as the mass of 1 cm3 of water at 4 ºC. • 1000 g = 1000 cm3 of water • 1 kg = 1 L of water

  44. Temperature Scales

  45. Measuring Temperature 0ºC • Celsius scale. • water freezes at 0ºC • water boils at 100ºC • body temperature 37ºC • room temperature 20 - 25ºC

  46. Measuring Temperature 273 K • Kelvin starts at absolute zero (-273 º C) • degrees are the same size • C = K -273.15 • K = C + 273.15 • Kelvin is always bigger. • Kelvin can never be negative.

  47. At home you like to keep the thermostat at 72 F. While traveling in Canada, you find the room thermostat calibrated in degrees Celsius. To what Celsius temperature would you need to set the thermostat to get the same temperature you enjoy at home ? • °C = 5/9 ( °F-32) °F = 9/5 (°C ) +32 K = °C + 273.15 Temperature Conversions

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