1. Measurements in Chemistry Precise measurements are essential in chemistry.

2. Part 1 Recording Data

3. Types of Observations and Measurements We make QUALITATIVE observations of reactions — changes in color and physical state.We make QUALITATIVE observations of reactions — changes in color and physical state. We also make QUANTITATIVE MEASUREMENTS, which involve numbers.We also make QUANTITATIVE MEASUREMENTS, which involve numbers.

4. Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 4 Nature of Measurement Measurement – quantitative observation consisting of two parts:  Number  Scale (unit)  Examples:  20 grams  6.63 × 10 -34  6.63 × 10 -34 joule·seconds 1.3

5. Chemistry: An Integrated Approach, 3 rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved Precision and Accuracy in Measurements Precision – how closely repeated measurements approach one another Accuracy – closeness of measurement to “true” (accepted) value Darts are close together, but they aren’t “bullseyes”. Darts are close together, and are “bullseyes”.

6. Chemistry: An Integrated Approach, 3 rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved 6 of 33 Precision and Accuracy in Measurements In the real world, we never know whether the measurement we make is accurate We make repeated measurements, and strive for precision We hope (not always correctly) that good precision implies good accuracy

7. Chemistry: An Integrated Approach, 3 rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved 7 of 33 Uncertainty in Measurement In recording measurements, the numbers should be written in a way that reflects the precision of the measuring device. Significant figures – all known digits, plus the first uncertain (estimated) digit.

8. Chemistry: An Integrated Approach, 3 rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved 8 of 33 Significant Figures What is the length of the cylinder?

9. Chemistry: An Integrated Approach, 3 rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved 9 of 33 Significant figures The cylinder is 6.3 cm…plus a little more The next digit is uncertain; 6.36? 6.37? We use three significant figures to express the length of the cylinder.

10. Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 10 Measurement of Volume Using a Buret 1.4

11. Part 2 Counting Significant Figures

12. Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 12 I. Rules for Counting Significant Figures Nonzero integers always count as significant figures: 3456 g has 4 sig figs 1.5

13. Counting Significant Figures Number of Significant Figures 38.15 cm___ 5.6 ft___ 65.6 lb___ 122.55 m 122.55 m___

14. Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 14 2. Rules for Counting Significant Figures (continued) Leading zeros do not count as significant figures: 0.048 g has 2 sig figs 1.5

15. Leading Zeros Number of Significant Figures 0.008 mm____ 0.0156 oz____ 0.0042 lb____ 0.000262 mL 0.000262 mL ____

16. Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 16 3. Rules for Counting Significant Figures (continued) Captive zeros always count as significant figures: 16.07 has 4 sig figs 1.5

17. Captured Zeros Number of Significant Figures 50.8 mm____ 2001 min____ 0.702 lb____ 0.00405 m____ 0.00405 m________

18. Copyright © Houghton Mifflin Company. All rights reserved. Chapter 1 | Slide 18 4. Rules for Counting Significant Figures Trailing zeros are significant only if the number contains a decimal point: 9.300 m has 4 sig figs 150 m 2 sig figs 1.5

19. Trailing Zeros Number of Significant Figures 25,000 in. ____ 25,000 in. ____ 200. yr____ 200. yr____ 48,600 gal____ 48,600 gal____ 25,005,000 g ____

20. Learning Check A. Which answers contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 10 5 1) 535 2) 535,000 3) 5.35 x 10 5

21. Learning Check In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 and 22.00 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000

22. Part 3 Calculations with Significant Figures

23. Significant Numbers in Calculations A calculated answer cannot be more precise than the measuring tool. A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from Significant figures are needed for final answers from 1) adding or subtracting 1) adding or subtracting 2) multiplying or dividing

24. Chemistry: An Integrated Approach, 3 rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved 24 of 33 Significant figures in calculated results Addition and Subtraction – Use the same number of decimal places in the result as the data with the fewest decimal places. 49.146 m + 72.13 m – 9.1434 m = ? = 112.1326 m (calculator) = 112.13 m (two decimal places)

25. Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 26.54 answer 26.5 one decimal place

26. Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.83) 257 B. 58.925 - 18.2= 1) 40.725 2) 40.733) 40.7

27. Chemistry: An Integrated Approach, 3 rd ed., Hill & Petrucci. ©2002 Prentice Hall. All rights reserved 27 of 33 Significant figures in calculated results Multiplication and division – Use the same number of significant figures in the result as the data with the fewest significant figures. 1.827 m x 0.762 m= 1.392174 m 2 (calculator) = 1.39 m 2 (three sig. fig.) 453.6 g / 21 people= 21.6 g/person (calculator) = 21.60 g/person (four sig. fig.) (Question: why didn’t we round to 22 g/person?)

28. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.32) 11 3) 0.041

29. Scientific Notation Scientific notation is simply a method for expressing, and working with, very large or very small numbers. The number 567000 in scientific notation is written as exponent 5.67 x 10 5 coefficient base

30. Practice Problems http://www.fordhamprep.org/gcurran/sho/sh o/review/rev25a.htm http://www.fordhamprep.org/gcurran/sho/sh o/review/rev25a.htm Do A#3

31. Metric Prefixes http://www.allaboutcircuits.com/vol_5/chpt_1/10.html http://www.allaboutcircuits.com/vol_5/chpt_1/10.html

32. Converting Units-Dimensional Analysis Problem: Convert 20 in/s into ft/min Given 12in = 1 ft and 1 min = 60 s Step 1. Express what you are given and what units you want. Step 2. Insert the required conversion factors to change between units Step 3. Cancel units where you can, and solve the math. http://www.mathsisfun.com/measure/metric-system.html Convert 400 ft/ml to mile/L

33. Examples: IMP: You must have the converting factors Example 1. A student determines that the density of a certain material is 4.46 kg/cm 3. What would be the density of this material in g/L? converting factor 1000 cm 3 = 1L Example 2. Imagine that water is leaking from a container, at a rate of 1.2 ml/hour. If this rate does not change, how many liters of water will be lost in a week? Converting factors 1 L = 1000 ml Example 3. Change 6.34 km/h to m/s Practice the following worksheet a, then do A#4 http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson24.htm