Chapter Two

1. Fundamentals of General, Organic & Biological Chemistry Chapter Two Measurements in Chemistry

2. Stating a Measurement • In every measurement, a number is followed by aunit. • Observe the following examples of measurements:number + unit35 m 0.25 L 225 lb 3.4 hr

3. The Metric System (SI) The metric system is • A decimal system based on 10. • Used in most of the world. • Used by scientists and in hospitals.

4. Units in the Metric System In the metric and SI systems, a basic unit identifies each type of measurement:

5. Length Measurement • In the metric system, length is measured in meters using a meter stick. • The metric unit for length is the meter (m).

6. Volume Measurement • Volume is the space occupied by a substance. • The metric unit of volume is the liter (L). • The liter is slightly bigger than a quart. • A graduated cylinder is used to measure the volume of a liquid.

7. Mass Measurement • The mass of an object is the quantity of material it contains. • A balance is used to measure mass. • The metric unit for mass is the gram (g).

8. Learning Check In each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume. ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g Aspirin. ____ D. A bottle contains 1.5 L of water.

9. Solution In each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume. 2 mass A. A bag of tomatoes is 4.6 kg. 1 lengthB. A person is 2.0 m tall. 2 massC. A medication contains 0.50 g Aspirin. 3 volumeD. A bottle contains 1.5 L of water.

10. Learning Check Identify the measurement that has a metric unit. A. John’s height is 1) 1.5 yards 2) 6 feet 3) 2 meters B. The volume of saline in the IV container is 1) 1 liter 2) 1 quart 3) 2 pints C. The mass of a lemon is 1) 12 ounces 2) 145 grams 3) 0.6 pounds

11. Solution A. John’s height is 3) 2 meters B. The volume of saline in the IV container is 1) 1 liter C. The mass of a lemon is 2) 145 grams

12. Scientific Notation • A number in scientific notation contains a coefficient and a power of 10. coefficient power of ten coefficient power of ten 1.5 x 102 7.35 x 10-4 • Place the decimal point after the first digit. Indicate the spaces moved as a power of ten. 52 000 = 5.2 x 104 0.00378 = 3.78 x 10-3 4 spaces left 3 spaces right

13. Learning Check Select the correct scientific notation for each. A. 0.000 008 1) 8 x 106 2) 8 x 10-6 3) 0.8 x 10-5 B. 72 000 1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4

14. Solution Select the correct scientific notation for each. A. 0.000 008 2) 8 x 10-6 B. 72 000 1) 7.2 x 104

15. Learning Check Write each as a standard number. A. 2.0 x 10-2 1) 200 2) 0.023) 0.020 B. 1.8 x 105 1) 180 000 2) 0.0000183) 18 000

16. Solution Write each as a standard number. A. 2.0 x 10-2 3) 0.020 B. 1.8 x 105 1) 180 000

17. Measured Numbers • You use a measuring tool to determine a quantity such as your height or the mass of an object. • The numbers you obtain are called measured numbers.

18. Reading a Meter Stick . l2. . . . l . . . . l3 . . . . l . . . . l4. . cm • To measure the length of the blue line, we read the markings on the meter stick. The first digit 2 plus the second digit 2.7 • Estimating the third digit between 2.7–2.8 gives a final length reported as 2.75 cm or 2.76 cm

19. Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise precise but not accurate not accurate & not precise Chapter 01 Slide 19

20. Mass of a Tennis Ball good accuracy good precision

21. Mass of a Tennis Ball good accuracy poor precision

22. Mass of a Tennis Ball poor accuracy poor precision

23. Known + Estimated Digits • In the length measurement of 2.76 cm, • the digits 2 and 7 are certain (known). • the third digit 5(or 6) is estimated (uncertain). • all three digits (2.76) are significant including the estimated digit.

24. Learning Check . l8. . . . l . . . . l9. . . . l . . . . l10. . cm What is the length of the red line? 1) 9.0 cm 2) 9.03 cm 3) 9.04 cm

25. Solution . l8. . . . l . . . . l9. . . . l . . . . l10. . cm The length of the red line could be reported as 2) 9.03 cm or 3) 9.04 cm The estimated digit may be slightly different. Both readings are acceptable.

26. Zero as a Measured Number . l3. . . . l . . . . l4. . . . l . . . . l5. . cm • The first and second digits are 4.5. • In this example, the line ends on a mark. • Then the estimated digit for the hundredths place is 0. • We would report this measurement as 4.50cm.

27. Exact Numbers • An exact number is obtained when you count objects or use a defined relationship.Counting objects2 soccer balls 4 pizzasDefined relationships1 foot = 12 inches 1 meter = 100 cm • An exact number is not obtained with a measuring tool.

28. Learning Check A. Exact numbers are obtained by 1. using a measuring tool 2. counting 3. definition B. Measured numbers are obtained by 1. using a measuring tool 2. counting 3. definition

29. Solution A. Exact numbers are obtained by 2. counting 3. definition B. Measured numbers are obtained by 1. using a measuring tool

30. Learning Check Classify each of the following as an exact (1) or a measured (2) number. A.__Gold melts at 1064°C. B.__1 yard = 3 feet C.__The diameter of a red blood cell is 6 x 10-4 cm. D.__There are 6 hats on the shelf. E.__A can of soda contains 355 mL of soda.

31. Solution Classify each of the following as an exact (1) or a measured(2) number. A. 2 A measuring tool is required. B. 1 This is a defined relationship. C. 2 A measuring tool is used to determine length. D. 1 The number of hats is obtained by counting. E. 2 The volume of soda is measured.

32. 2.4 Measurement and Significant Figures • Every experimental measurement, no matter how precise, has a degree of uncertainty to it because there is a limit to the number of digits that can be determined.

33. Chapter 01 0 1 2 3 4 Accuracy, Precision, and Significant Figures cm 1.7 cm < length < 1.8 cm length = 1.74 cm

34. Rules for determining significant figures • 1. Zeroes in the middle of a number are significant. 69.08 g has four significant figures, 6, 9, 0, and 8. • 2. Zeroes at the beginning of a number are not significant. 0.0089 g has two significant figure, 8 and 9. • 3.Zeroes at the end of a number and after the decimal points are significant. 2.50 g has three significant figures 2, 5, and 0. • 25.00 m has four significant figures 2, 5, 0, and 0.

35. 4. Zeroes at the end of a number and before an implied decimal points may or may not be significant. 1500 kg may have two, three, or four significant figures. Zeroes here may be part of the measurements or for simply to locate the unwritten decimal point.

36. Which of the following measurements has three significant figures? • 1,207 g • 4.250 g • 0.006 g • 0.0250 g • 0.03750 g

37. Which of the following measurements has three significant figures? • 1,207 g • 4.250 g • 0.006 g • 0.0250 g • 0.03750 g

38. Which of the following numbers contains four significant figures? • 230,110 • 23,011.0 • 0.23010 • 0.0230100 • 0.002301

39. Which of the following numbers contains four significant figures? • 230,110 • 23,011.0 • 0.23010 • 0.0230100 • 0.002301

40. 2.6 Rounding off Numbers • Often calculator produces large number as a result of a calculation although the number of significant figures is good only to a fewer number than the calculator has produced – in this case the large number may be rounded off to a smaller number keeping only significant figures.

41. Rules for Rounding off Numbers: • Rule 1 (For multiplicationand divisions): The answer can’t have more significant figures than either of the original numbers.

42. Rule 2 (For addition and subtraction): The answer should have minimum decimal places.

43. How many significant figures should be shown for the calculation? 1 2 3 4 5

44. How many significant figures should be shown for the calculation? 1 2 3 4 5

45. How many significant figures are there in the following number: 1.200 X 109? 4 3 2 1 Cannot deduce from given information.

46. Correct Answer: 4 3 2 1 Cannot deduce from given information. 1.200 109 Zeros that fall both at the end of a number and after the decimal point are always significant.

47. How many significant figures are there in the following summation: 2 3 4 5 6 6.220 1.0 + 125

48. Correct Answer: 2 3 4 5 6 6.220 1.0 + 125 132.220 In addition and subtraction the result can have no more decimal places than the measurement with the fewest number of decimal places.

49. How many significant figures are there in the result of the following multiplication: (2.54)  (6.2)  (12.000) 2 3 4 5

50. Correct Answer: 2 3 4 5 (2.54)  (6.2)  (12.000) = 188.976 = 190 In multiplication and division the result must be reported with the same number of significant figures as the measurement with the fewest significant figures.