Measurements in Chemistry

1. Measurements in Chemistry Chapter 2 p. 36

2. Accuracy vs Precision Notes: Accuracy Adescriptionofhowcloseameasurementistothetruevalue. Precision Adescriptionofhowcloselyseveralmeasurementsofthesamequantityagreewithoneanother.

3. Accuracy vs Precision Accuracy A description of how close a measurement is to the true value. Precision A description of how closely several measurements of the same quantity agree with one another. See p. 55, Figure 16

4. 2.3 Accuracy vs. Precision Accuracy = a description of how close a measurement is to the true value e.g. If actual height of door = 210 cm Measurement A = 209 cm • Accurate  Measurement B = 195 cm  Inaccurate 

5. 2.3 Accuracy Accuracy is indicated by calculation of % error: % error = measured – actual x 100 actual

6. 2.3 Reproducibility • Important: measurements are performed more than once to ensure accuracy Precision = how closely several repeated measurements agree with one another

7. 2.3 Accuracy vs. Precision(See fig 16 p. 55) Which set of throws has low accuracy, but high precision?

8. 2.3 Sig Figs The number of significant figures in a number tells you how the measurement was made. e.g. beaker vs graduated cylinder

9. 2.3 Significant Figures We have three different kinds of balances in the lab: • 0.0 g (decigram) • 0.00 g (centigram) • 0.000 g (milligram) Read p. 56 paragraph 1 and 2.

10. 2.3 Significant Figures ‘meniscus’

11. 2.3 Measurement Volume = ? mL

12. 2.3 Significant Figures • How many sig figs should this measurement be made to?

13. 2.3 Significant Figures How many significant figures are there in the following measurements: • 304 g • 0.000405 g • 44.0 g Read Skills Toolkit p. 57 “Rules for Determining Significant Figures”

14. 2.3 Calculations with sig figs Multiplication and division Practice: 6.9 m x 11.4 m = ? How many sig figs? 2 sig figs ANS = 79 m2

15. 2.3 Calculations with sig figs Remember: your calculator is DUMB!! It does not understand sig figs! Do not just write down all the digits your calculator gives you. Think for yourself!!

16. 2.3 Calculations with sig figs Multiplication and division The answer must have the same number of sig figs…. as the measurement with the least number of sig figs Rounding!!! See Skills Toolkit p. 58 #1

17. 2.3 Calculations with Sig Figs Addition & Subtraction See Skills Toolkit p. 58 #2

18. Check For Understanding (CFU) Scratch paper work What is 0.0032 x 204.0 (written to the correct number of significant figures)? ANS = 0.6528? 0.65

19. Check For Understanding (CFU) Scratch paper work What is 0.204367 divided by 36? (written to the correct number of significant figures. Hint: how many SFs are in 0.204367? How many SFs in 36? So, how many sig figs in your answer?

20. 2.3 Sig Figs p. 67 # 20a-d, 23, 24

21. 2.3 Scientific Notation Read p. 62 What is the population of the United States? 300 000 000 people 3 x 108 people

22. 2.3 Scientific Notation rules The first part of the scientific notation is always a number between 1 and 10. 34 000 000 (to 2 SFs) = • 34 x 106 = INCORRECT • 0.34 x 108 = INCORRECT • 3.4 x 107 = CORRECT

23. 2.3 Scientific Notation rules • The second part of the scientific notation is a power of ten • Example: 104 = 10x10x10x10 = 10000 • The exponent = the number of places the decimal is moved

24. 2.3 Scientific Notation rules When to use scientific notation…… 745? Is not necessary to use scinotn 745 000? 0.000000745? Is necessary, b/c of all of those zeroes. Let’s do it

25. 2.3 Scientific Notation rules Convert 745 000 to scinotn If the decimal point is moved to the left…. the exponent is positive 745 000 = 7.45 x 105 = 7.45 x10x10x10x10x10 Note: If the number is large, the power of ten is positive (e.g. 105)

26. 2.3 Scientific Notation rules 745 000 = 7.45 x 105 Note: the magnitude of the number does not change; we are just re-writing it in a better way. Note: the exponent is not necessarily the number of zeroes in the figure. Note: the number of significant figures is now represented properly (to 3SFs)

27. 2.3 Scientific notation rules Charge of electron = 0.00000000000000000016 C If the decimal point is moved to the right…. the exponent is negative = 1.6 x 10-19 C Note: If the number is small, the power of ten is negative (e.g. 10-4)

28. 2.3 Scientific Notation Practice (scratch paper): a. Rewrite 13780 m in scientific notation b. Rewrite 4.21 x 10-5g in ordinary notation p. 67 # 30,31

29. 2.3 Scientific NotationLARGE NUMBERS Reminder: When converting from ordinary notation to scinotn…. for a POSITIVE exponent… move the decimal point to the LEFT. The opposite problem Convert 6.3 x 104 g to ordinary notation (‘long form’) = 6.3 x10x10x10x10 Move the decimal point 4 places to the RIGHT ANS = 63 000 g

30. 2.3 Scientific Notationsmall numbers Reminder: When converting from ordinary notation to scinotn…. for a NEGATIVE exponent… move the decimal point to the RIGHT. Problem Convert 6.3 x 10-4 g to ordinary notation (‘long form’) Move the decimal point to the LEFT ANS = 0.00063 g

31. Calculations with Scientific Notation See Skills Toolkit p. 62 #3 Multiplication: exponents are added (2.0 x 104) x (3.0 x 103) = (2.0 x 3.0) x (104 x 103) How many sig figs? = 6.0 x (104+3) = 6.0 x 107 Let’s try it in your scientific calculator.

32. Calculations with Scientific Notation See Skills Toolkit p. 62 #3 Multiplication: exponents are added (2.0 x 104) x (7.0 x 103) = (2.0 x 7.0) x (104 x 103) How many sig figs? = 14 x (104+3) = 14 x 107 = (1.4x10)x 107 = 1.4 x 108 Let’s try it in your scientific calculator.

33. Calculations with Scientific Notation See Skills Toolkit p. 62 #4 Division: exponents are subtracted (8.0 x 107) / (4.0 x 103) = (8.0 / 4.0) x (107/ 103) = 2.0 x (107-3) = 2.0 x 104 Let’s try it in your scientific calculator.

34. Calculations with Scientific Notation See Skills Toolkit p. 62 #4 Division: exponents are subtracted (2.0 x 104) / (8.0 x 103) = (2.0 / 8.0) x (104 / 103) = 0.25 x (104-3) = 0.25 x 101 = 2.5 Let’s try it in your scientific calculator.