1 / 21

Data Analysis

Data Analysis. Applying Mathematical Concepts to Chemistry. Scientific Notation. concise format for representing extremely large or small numbers Requires 2 parts: Number between 1 and 9.99999999 … (coefficient) Power of ten (exponent) Examples:

cargan
Download Presentation

Data Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Data Analysis Applying Mathematical Concepts to Chemistry

  2. Scientific Notation • concise format for representing extremely large or small numbers • Requires 2 parts: • Number between 1 and 9.99999999…(coefficient) • Power of ten (exponent) • Examples: • 6.02 x 1023 = 602,000,000,000,000,000,000,000 • 2.0 x 10 -7 m = 0.0000002 m See Appendix C R63 for instructions on how to properly calculate numbers in scientific notation with a calculator

  3. Scientific Notation CalculationsAddition and Subtraction • Additional and Subtraction • In order to add or subtract numbers that are expressed in scientific notation, the exponents must be the same. • If the exponents are different, it always helps to convert the number with the smaller exponent to a number with the larger exponent. Don’t worry about having a proper coefficient – you won’t  • Once the exponents are equal, add or subtract the coefficients and attach the larger exponent. • Being able to perform scientific notation calculations without a calculator is a great skill to have. It gives you’re the power to evaluate if you made a computational mistake.

  4. Scientific Notation CalculationsMultiplication and Division • Multiplication. • Multiply the coefficients and add the exponents • If the calculated coefficient is 10 or greater, move the decimal to the left and increase the exponent. In order to multiply or divide numbers that are expressed in scientific notation, the exponents DO NOT have to be the same. • Division • Divide the coefficients and add the exponents • If the calculated coefficient is less than 10, move the decimal to the right and increase the exponent.

  5. Accuracy vs Precision • Precision- closeness of measurements to each other • Accuracy- closeness of measurements to the target value • Error - difference between measured value and accepted value

  6. Percent Error Example: In order to calibrate a balance a 5.0g mass standard (accepted) was placed on the balance. The output registered 4.8g

  7. Measurement precision • Measurements are limited in by the precision of the instrument used to measure

  8. Significant DIGITS in measurement Significant digits in measurement include all of the digits that are known and plus one measure (the last digit) of uncertainty • Read one place past the instrument 52.7 • If a measurement is observed on one of the graduated lines, you must add a zero at the end of the number to indicate that degree of precision 50.0 Always read the volume of a liquid in a graduated cylinder from the bottom of the meniscus

  9. Recognizing Significant Digits • 1. Nonzero digits are always significant (543.21 5SF) • 2. Zeros between non-zeros are significant (1003 4SF) • 3. Zeros to the right of a decimal and a nonzero are significant (32.06200 7SF) • 4. Placeholder zeros are not significant 0.01g 1 SF 1000.g 4 SF 1000g 1 SF 1000.0g 5 SF • 5. Counting numbers and constants have infinite significant figures 5 people (infinite SF) Relax There are only two situations where zeros are not significant. Evaluate the zeros in any number first. If they are all significant then every digit in your number is significant.

  10. 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 A CALCULATED ANSWER CANNOT BE MORE PRECISE THAN THE LEAST PRECISE MEASUREMENT FROM WHICH IT WAS CALCULATED

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

  12. Rule for Adding/Subtracting • Round answer to least “precise” original operator. • Example 1001.2345 =1000 990 - 12 978 = 980

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

  14. Units of Measure • SI Units- scientifically accepted units of measure: • Know: • Length • Mass • Temperature • Time

  15. The Metric System G M K h da (base unit) d c m m n p

  16. Metric Practice • 623.19 hL= __________ L • 102600 nm = ___________cm • 0.025 kg = ___________mg • Online Powers of 10 Demonstration: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/ G M K h da (base unit) d c m m n p 62319 0.01026 25000

  17. Temperature Conversions • Degrees Celsius to Kelvin • Tkelvin=Tcelsius + 273 • Kelvin to Degrees Celsius • Tcelsius=Tkelvin - 273

  18. Derived Quantities - Volume The volume of an irregularly shaped object can be determined by displacing its volume Volume- amount of space an object takes up (ex: liters) • V = l x w x h • 1 cm3 = 1 mL by definition

  19. Derived Quantities- Density • Density- ratio of the mass of an object to its volume • Density = mass/volume • D= g/mL • Density depends on the composition of matter, no the amount of matter

  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 The Affect of Temperature on Volume • General Rules • Fit page • Even scale • Best fit/trendline • Informative Title • Labeled Axes with units

More Related