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Chapter 2 Standards of Measurement

Chapter 2 Standards of Measurement. Objectives: Understand Mass and Weight (2.1) Identify the metric units of measurement (2.6) Explain what causes uncertainty in measurements (2.7, 2.8 – 2.12) Learn how to use significant digits and scientific notation (2.2 – 2.5) Dimensional Analysis (2.8)

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Chapter 2 Standards of Measurement

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  1. Chapter 2Standards of Measurement Objectives: • Understand Mass and Weight (2.1) • Identify the metric units of measurement (2.6) • Explain what causes uncertainty in measurements (2.7, 2.8 – 2.12) • Learn how to use significant digits and scientific notation (2.2 – 2.5) • Dimensional Analysis (2.8) • Density (2.12)

  2. The Metric System (2.6)The International System of Units • Standards of measurement • Base units (7) – see Table 2.2 (pg 20) • MASS: kilogram (kg) • LENGTH: meter (m) • TIME: second (s) • COUNT, QUANTITY: mole (mol) • TEMPERATURE: Kelvin (K) • ELECTRIC CURRENT: ampere (A) • LUMINOUS INSTENSITY: candela (cd)

  3. The Metric System • Derived Units: • AREA: square meter, m2 • VOLUME: cubic meter, m3 • ENERGY: joule, J • FORCE: newton, N • PRESSURE:pascal, Pa • POWER: watt, W • VOLTAGE: volt, V • FREQUENCY: hertz, Hz • ELECTRIC CHARGE: coulomb, C

  4. The Metric System • Metric Prefixes – make base unit larger or smaller • Table 2.1 – must know bolded prefixes • Based on 10 • Math method vs. “Stairs”

  5. Conversion Practice • Convert a volume of 12 microliters into centiliters • Express a distance of 15 meters in kilometers • Convert 83 cm into meters • Which is the longer amount of time, 1351 ps or 1.2 ns? • Convert 16 dL into L Answer: 0.0012 cL Answer: 0.015 km Answer: 0.83 m Answer: 1351 ps (1.2 ns = 1200 ns) Answer: 1.6 L

  6. Uncertainty in Measurement • Why are digits in measurements uncertain? • Instruments never completely free of flaws • Always involves estimation • Choose the right instrument for the job • May be estimated for you (electronic scales) • Scale is marked but you estimate the in-between

  7. Uncertainty in Measurement • Precision: getting the same result again and again under same conditions • Accuracy: close to accepted value

  8. Significant Digits • All digits known with certainty plus one final digit which is uncertain (or estimated) • All non-zeros are significant (143.34) • A zero is significant when : • It is between nonzero digits (2004) • It is at the end of a number that includes a decimal point (23.560) • A zero is not significant when: • It is before the first nonzero digit (0.25) • It is at the end of a number without a decimal point (2500)

  9. Significant Digits - PRACTICE How many significant digits? • 54.23 • 23.00005 • 0.0004 • 35000 • 0.000504 • 45.623200 • 5,000,000 • 4,000,000.1 • ANSWERS: • 4 sig figs • 7 • 1 • 2 • 3 • 8 • 1 • 8

  10. Significant Digits - Calculations • Addition and Subtraction • Round answer to have final digit in the SAME PLACE as the last digit in the LEAST ACCURATE MEASUREMENT • 1.21 + 5.002 + 10. = 16.212 becomes 16 • 34.5 + 12.45 + 23.0505 = • 186.31 + 11.1 = • 12.0231 + 3.86 = • 0.100012 + 120. = • 1200 + 12 + 15 + 0.5 = 70.0005 becomes 70.0 197.41 becomes 197.4 15.8831 becomes 15.88 120.100012 becomes 120. 1227.5 becomes 1200

  11. Significant Digits - Calculations • Multiplication and Division • The answer has as many sig figs as the number with the fewest sig figs • 14.8 x 3.1 = 45.88 becomes 46 • 18.2 x 3.0 = • 52/1.5 = • 321.868783 x 1 = • 2400 x 2.123 = • 15000/12.354 = 54.6 becomes 55 34.66666 becomes 35 321.868783 becomes 300 5095.2 becomes 5100 1214.181641 becomes 1200

  12. Scientific Notation • Convenient way of writing very large or very small numbers and showing only significant figures • Number between 1 & 10 with a power of ten • 5120 becomes 5.12 x 103 • Move decimal point in original number to make number 1-10 • Move left = +; move right = -

  13. Scientific Notation Practice 1.23 x 105 • 123,000 = • 0.000045 = • 23.45 = • 0.0000000003 = • 1,000,000 = 4.5 x 10-5 2.345 x 101 3 x 10-10 1 x 106

  14. Scientific Notation • Adding and subtracting • Numbers must be the SAME POWER • 1.4 x 104 + 2.1 x 105 (must change to 21.0 x 104) and then = 2.24 x 104 • 3.2 x 103 + 1.8 x 102 = 3.38 x 103

  15. Scientific Notation • Multiplying • Add exponents • (2.0 x 103) x (3.0 x 104) = 6.0 x 107 • Dividing • Subtract exponents • (8.2 x 108) x (4.1 x 104) = 2.0 x 104

  16. Types of Measurements • Mass – amount of matter in a body • Expressed in grams, kilograms, etc. • Does not change • Weight – measure of earth’s gravitational attraction for that object • Expressed in same units • Changes with location (position on earth or distance from earth)

  17. Types of Measurements • Volume – the amount of space occupied by matter • Cubic meter or liter • Many instruments to measure • Temperature – measure of the intensity of heat (figure 2.6) • Kelvin • Degrees Celsius • Degress Farenheit

  18. Conversion Factors • Enable movement between metric system and “English” system • See back cover of book and Appendix III • Common conversions you should memorize • 1 inch = 2.54 cm • 1 mile = 1.609 km • 1 kg = 2.20 pounds • 1 mL = 1 cm3 • 0 K = -273.15 0C • 0F = 1.8(0C) + 32

  19. Dimensional Analysis(Problem Solving) • Remember: ALWAYS use UNITS OF MEASUREMENT in your work!!! • A technique of converting between units • Same system (metrics) • Different systems (inches to meters) • Chemical equations….later chapters…

  20. Dimensional Analysis(Problem Solving) • Conversion Factors: ratio derived from the equality between 2 different units 3 feet = 1 1 dollar = 1 1 yard 4 quarters • CF can be written either way 1 minute = 1 60 seconds = 1 60 seconds 1 minute

  21. The “t” method Dimensional Analysis(Problem Solving) unit given unit wanted = unit wanted unit given Conversion Factor Example: How many liters are in 125.6 gallons? 125.6 gallons 3.785 Liters = 1 gallon 475.4 L

  22. Dimensional Analysis(Problem Solving) Dimensional Analysis(Problem Solving) How many seconds are in 4.15 hours? 4.15 hours 60 minutes 60 seconds = 1 hour 1 minute 14900 s If a student needs 1.5 mL of water, how many cups does he need? 1.5 mL 1 L 1 gal 4 qts 4 cups = 1000 mL 3.785 L 1 gal 1 qt 0.0063 cups

  23. Common ratio used in chemistry Physical property of a substance Mass/volume D = m v SI units: kg/m3 Solid g/cm3 Liquid g/mL Gas g/L Density Can change due to temperature and/or pressure changes

  24. Density • Find the density of a piece of metal with a volume of 2.7 cm3 and a mass of 10.8 g. • D = m • v = 10.8 g 2.7 cm3 = 4.0 g/cm3 2. Determine the mass of an object with a density of 0.24 g/cm3 and a volume of 2 cm3. SIG FIGS!!! m = d x v = 0.24 g/cm3 x 2 cm3 = 0.48 0.5 g

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