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The numerical side of chemistry

The numerical side of chemistry. Chapter 2. Outline. Precision and Accuracy Uncertainty and Significant figures Zeros and Significant figures Scientific notation Units of measure Conversion factors and Algebraic manipulations. Accuracy and Precision. Precision and Accuracy.

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The numerical side of chemistry

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  1. The numerical side of chemistry Chapter 2

  2. Outline • Precision and Accuracy • Uncertainty and Significant figures • Zeros and Significant figures • Scientific notation • Units of measure • Conversion factors and Algebraic manipulations

  3. Accuracy and Precision

  4. Precision and Accuracy • Accuracyrefers to the agreement of a particular value with the truevalue. • Precisionrefers to the degree of agreement among several measurements made in the same manner. Precise but not accurate Precise AND accurate Neither accurate nor precise

  5. Types of Error • Random Error(Indeterminate Error) - measurement has an equal probability of being high or low. • Systematic Error(Determinate Error) - Occurs in the same directioneach time (high or low), often resulting from poor technique or incorrect calibration. This can result in measurements that are precise, but not accurate.

  6. Uncertainty in Measurement • A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. • Measurements are performed with • instruments • No instrument can read to an infinite • number of decimal places

  7. Nature of Measurement Measurement - quantitative observation consisting of 2 parts • Part 1 - number • Part 2 - scale (unit) • Examples: • 20grams • 34.5 mL • 45.0 m

  8. Significant figures or significant digits • Digits that are not beyond accuracy of measuring device • The certain digits and the estimated digit of a measurement

  9. 245 0.04 0.040 1000 10.00 0.0301 103 3 significant digits 1 significant digit 2 significant digits 1 significant digit 4 significant digit 3 significant digit 3 significant digit Rules

  10. Rules for Counting Significant Figures - Details • Nonzero integersalways count as significant figures. • 3456has • 4sig figs.

  11. Rules for Counting Significant Figures - Details • Zeros • -Leading zeros do not count as • significant figures. • 0.0486 has • 3 sig figs.

  12. Rules for Counting Significant Figures - Details • Zeros • -Captive zeros always count as • significant figures. • 16.07 has • 4 sig figs.

  13. Rules for Counting Significant Figures - Details • Zeros • Trailing zerosare significant only if the number contains a decimal point. • 9.300 has • 4 sig figs.

  14. Rules for Counting Significant Figures - Details • Exact numbershave an infinite number of significant figures. • 1 inch = 2.54cm, exactly

  15. Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000  2 sig figs

  16. Rules for Significant Figures in Mathematical Operations • Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. • 6.8 + 11.934 = • 18.734  18.7 (3 sig figs)

  17. Sig Fig Practice #2 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL

  18. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:# sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38 x 2.0 = • 12.76 13 (2 sig figs)

  19. Sig Fig Practice #3 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 5870 lb·ft 1818.2 lb x 3.23 ft 5872.786 lb·ft 2.9561 g/mL 2.96 g/mL 1.030 g ÷ 2.87 mL

  20. Why do we use scientific notation? • To express very small and very large numbers • To indicate the precision of the number • Use it to avoid with sig digs

  21. Scientific Notation In science, we deal with some very LARGE numbers: 1 mole = 602000000000000000000000 In science, we deal with some very SMALL numbers: Mass of an electron = 0.000000000000000000000000000000091 kg

  22. . 2 500 000 000 9 7 6 5 4 3 2 1 8 Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

  23. 2.5 x 109 The exponent is the number of places we moved the decimal.

  24. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10n

  25. 5.79 x 10-5 The exponent is negative because the number we started with was less than 1.

  26. Review: Scientific notation expresses a number in the form: M x 10n n is an integer 1  M  10

  27. SI measurement • Le Système international d'unités • The only countries that have not officially adopted SI are Liberia (in western Africa) and Myanmar (a.k.a. Burma, in SE Asia), but now these are reportedly using metric regularly • Metrication is a process that does not happen all at once, but is rather a process that happens over time. • Among countries with non-metric usage, the U.S. is the only country significantly holding out.The U.S. officially adopted SI in 1866. Information from U.S. Metric Association

  28. The Fundamental SI Units(le Système International, SI)

  29. Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard. For example, at one time the standard for length was the king’s foot. What are some problems with this standard?

  30. Derived SI units Physical quantity Name Abbreviation Volume cubic meter m3 Pressure pascal Pa Energy joule J

  31. Metric System • System used in science • Decimal system • Measurements are related by factors of 10 • Has one standard unit for each type of measurement • Prefixes are attached in front of standard unit

  32. Metric Prefixes • Kilo- means 1000 of that unit • 1 kilometer (km) = 1000 meters (m) • Centi- means 1/100 of that unit • 1 meter (m) = 100 centimeters (cm) • 1 dollar = 100 cents • Milli- means 1/1000 of that unit • 1 Liter (L) = 1000 milliliters (mL)

  33. SI Prefixes Common to Chemistry

  34. Metric Prefixes

  35. Metric Prefixes

  36. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

  37. Learning Check Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers

  38. How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 min 1 hr cancel 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!

  39. Steps to Problem Solving • Write down the given amount. Don’t forget the units! • Multiply by a fraction. • Use the fraction as a conversion factor. Determine if the top or the bottom should be the same unit as the given so that it will cancel. • Put a unit on the opposite side that will be the new unit. If you don’t know a conversion between those units directly, use one that you do know that is a step toward the one you want at the end. • Insert the numbers on the conversion so that the top and the bottom amounts are EQUAL, but in different units. • Multiply and divide the units (Cancel). • If the units are not the ones you want for your answer, make more conversions until you reach that point. • Multiply and divide the numbers. Don’t forget “Please Excuse My Dear Aunt Sally”! (order of operations)

  40. Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b) 244 cm c) 24.4 cm

  41. Solution A rattlesnake is 2.44 m long. How long is the snake in cm? b) 244 cm 2.44 m x 100 cm = 244 cm 1 m

  42. Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x ?? 1 day

  43. Wait a minute! What is wrong with the following setup? 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min

  44. Dealing with Two Units If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?

  45. 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 ENITRE conversion factor • Example: Convert 4.3 cm3 to mm3 ( ) 4.3 cm3 10 mm 3 1 cm 4.3 cm3 103 mm3 13 cm3 = = 4300 mm3

  46. Learning Check • A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (DHMO). How many cubic decimeters is that?

  47. Solution 1000 cm3 1 dm 3 10 cm ( ) = 1 dm3 So, a dm3 is the same as a Liter ! A cm3 is the same as a milliliter.

  48. Anders Celsius 1701-1744 Lord Kelvin (William Thomson) 1824-1907 Temperature Scales • Fahrenheit • Celsius • Kelvin

  49. 212 ˚F 100 ˚C 373 K 100 K 180˚F 100˚C 32 ˚F 0 ˚C 273 K Temperature Scales Fahrenheit Celsius Kelvin Boiling point of water Freezing point of water Notice that 1 Kelvin = 1 degree Celsius

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