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Chemistry Math Concepts: Accuracy, Precision, Scientific Notation

Explore applying mathematical concepts in chemistry, understanding accuracy vs. precision, SI units, significant figures, and more. Practice conversions, learn about density, and graphing data to analyze relationships. Discover temperature scales, perform calculations, and calculate percent error effectively.

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Chemistry Math Concepts: Accuracy, Precision, Scientific Notation

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  1. Data Analysis Applying Mathematical Concepts to Chemistry

  2. Accuracy- closeness of measurements to the target value Error- difference between measured value and accepted value (absolute value) Precision- closeness of measurements to each other Accuracy vs Precision

  3. Units of Measure • SI Units- scientifically accepted units of measure: • Know: • Length • Volume (m3) • Mass • Density (g/mL) • Temperature • Time

  4. The Metric System

  5. Metric Practice • 623.19 hL = __________ L • 1026 mm = ___________cm • 0.025 kg = ___________mg • Online Powers of 10 Demonstration: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

  6. Good Info to Know • Volume- amount of space an object takes up (ex: liters) • V = l x w x h • 1 cm3 = 1 mL by definition

  7. More Good Info to Know • Mass is different from weight • Mass ≠ Weight • Mass= measure of the amount of matter in an object • Weight= force caused by the pull of gravity on an object • ***Mass is constant while weight varies depending on the location of an object***

  8. Scientific Notation • concise format for representing extremely large or small numbers • Requires 2 parts: • Number between 1 and 9.99999999… • Power of ten • Examples: • 6.02 x 1023 = 602,000,000,000,000,000,000,000 • 2.0 x 10 -7 m = 0.0000002 m • Use calculator to solve problems on p. 788-789

  9. Significant Figures • Measurements are limited in their sensitivity by the instrument used to measure

  10. Estimating Measurements • Read one place past the instrument • 35.0 mL is saying the actual measurement is between 34.9 and 35.1 mL

  11. Why Significant Figures? • Measurements involve rounding • Multiplying/dividing or adding/subtracting measurements can not make them more accurate • Provide a way to tell how sensitive a measurement really is… • 5 ≠ 5.0 ≠ 5.00 ≠ 5.000

  12. Recognizing Significant Digits • 1. Nonzero digits are always significant • 543.21 meters has 5 significant figures • 2. Zeros between nonzeros are significant • 505.05 liters has 5 sig figs • 3. Zeros to the right of a decimal and a nonzero are significant • 3.10 has 3 sig figs

  13. Recognizing Sig Figs • 4. Placeholder zeros are not significant • 0.01g has one sig fig • 1000g has one sig fig • 1000.g has four sig figs • 1000.0g has five sig figs • 5. Counting numbers and constants have infinite significant figures • 5 people has infinite sig figs

  14. Rule for Multiplying/Dividing Sig Figs • Multiply as usual in calculator • Write answer • Round answer to same number of sig figs as the lowest original operator • EX: 1000 x 123.456 = 123456 = 100000 • EX: 1000. x 123.456 = 123456 = 123500

  15. Practice Multiplying/Dividing • 50.20 x 1.500 • 0.412 x 230 • 1.2x108 / 2.4 x 10-7 • 50400 / 61321

  16. Rule for Adding/Subtracting • Only place values where all measurements being added/subtracted have sig figs are utilized • EX: 1000 + 1.2345 1000

  17. Practice Adding/Subtracting • 100.23 + 56.1 • .000954 + 5.0542 • 1.0 x 103 + 5.02 x 104 • 1.0045 – 0.0250

  18. Derived Quantities- Density • Density- how much matter is in the volume an object takes up. • Density = mass/volume • D= g/mL

  19. Determining Density • Mass- measure in grams with balance • Volume- • Regular shaped object: measure sides and use volume formula • EX: rectangle  V= l x w x h • Irregular shaped object: water displacement

  20. Density by Water Displacement • Fill graduated cylinder to known initial volume • Add object • Record final volume • Subtract initial volume from final volume • Record volume of object

  21. Graphing Data How Does Volume Impact Temperature? • General Rules • Fit page • Even scale • Best fit/trendline • Informative Title • Labeled Axes

  22. Temperature Scales

  23. Degrees Celsius to Kelvin Tkelvin=Tcelsius + 273 EX: 25 °C = ? K Tkelvin=25 +273=298K Kelvin to Degrees Celsius Tcelsius=Tkelvin - 273 EX: 210 K = ? °C Tc= 273–210= -63°C Temperature Conversions

  24. Percent Error • %error = (accepted-experimental) x 100 accepted • EX: The measured mass is 5.0g. It was predicted that the accepted value should have been 6.0 g. • % error = 6.0g-5.0g x 100 = 16.7% 6.0g

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