Chapter 2 Measurements and Calculations

1. Chapter 2Measurements and Calculations

2. Chapter Outline • Expressing numbers in scientific notation • Unit systems (3) • What chemists commonly measure • How to take measurements • Uncertainty in measurements • Significant Figures – brief introduction • Rules for rounding off • Converting between units • Temperature scales • Density

3. Quantitative Observations • A quantitative observation generally includes a number and a unit. • Record three quantitative observations about yourself.

4. Scientific Notation • Goal: to express numbers in scientific notation and as ordinary decimal numbers • Scientific notation • A number between 1 and less than 10 multiplied by 10 raised to an exponent. • Examples • Why is scientific notation useful? • Review powers of 10

5. Scientific Notation • Express each of the following in scientific notation: 53,000 350 0.0025 0.0000050

6. Scientific Notation • Express each of the following as an ordinary decimal number 3.2 x 103 1.8 x 10-2 5.03 x 105 2.3 x 108

7. Unit Systems • English system • Used in United States • Metric system • Used in science • International system (SI) • Based on the metric system UNITS MATTER! See page 19

8. Unit Systems • English System • Used in U.S. • Little logic to the units • Examples

9. Unit Systems • Metric System • Developed in the late 1700’s and adopted after the French Revolution • A base (or fundamental) unit is defined for each quantity measured • The size of the base unit can be modified by adding a prefix

10. Metric System Quantity Base unit Symbol

11. Unit Systems - meteric • Metric Prefixes, see page 19

12. Unit Systems • Using prefixes • Base unit = meter • Kilometer = km = _________ m

13. Unit Systems • International System (SI) • Adopted in 1960 • Internationally agreed upon set of units • Used in industry • Some use in science • See page 18

14. What chemists measure • Length – distance between 2 points • Metric base = ____________ • 1 inch = 2.54 cm exactly • Other commonly used multiples: • km • cm • mm • mcm • nm

15. Mass and Weight • Mass – quantity of matter present • Base unit: __________ • Measure on a balance • Weight – measure of gravitational pull on an object • Base unit: • Measure on a scale

16. Volume • Volume – amount of three dimensional space occupied by an object • SI base = meter3 • Metric base = Liter • Liter = 10 cm x 10 cm x 10 cm • mL = ________ = ___________

17. CUBIC METER

18. Measuring Volume • Measuring Volume of a “block” • Volume = length x height x width • Volume of an irregularly shaped object • Use water displacement

19. Taking measurements • Use a measuring device to take measurements • All measurements recorded include some degree of uncertainty • A properly taken measurement includes one estimated digit

20. Taking measurements • Measuring devices have units marked on them • When taking a measurement you record: • All known digits • those marked on the measuring device • One estimated digit • Estimated digit is 1/10 the smallest marked unit on the measuring device

21. Taking measurements • Graduated cylinder example Thermometer example

22. Significant Figures • The last digit recorded in a measurement is estimated/uncertain. • The numbers recorded in a measurement are called the significant figures. • When measurements are used in calculations the answer to the calculation is rounded off so that the last digit is also an estimate.

23. Significant Figures - Goals • Your goal is to: • Record all measurements correctly • Recognize the estimated digit • Define the term significant figures • State the number of significant figures in a measurement you take. • Round answers to calculations as instructed

24. Rounding Off • If the first digit to be removed is: • 5 or greater then the preceding digit is increased by 1 (round up) • Less than 5 then the preceding digit remains the same (round down)

25. Rounding Off • Round 1345.493 to: • 2 decimal places • 1 decimal place • The 1’s (ones) • The 10’s (tens) • The 100’s (hundreds)

26. Converting Between Units • Metric to Metric Conversions • See board for the staircase method • Using dimensional analysis to convert between units.

27. Converting Between Units, Practice! • Miles  km • Pounds  grams  kg • mL  fluid ounces • M  cm  inches

28. Density • Density – the amount of matter present in a given volume of a substance • Density = mass of an object volume of object

29. Density Units • The mass of the object is expressed in grams and the volume is expressed in: • mL or cm3 for solids and liquids • L for gases • Density units: • g/mL or g/cm3 – solids and liquids • g/L - gases • Other: Pounds/foot3(English system)

30. Density • Density of water is ~ 1g/mL at room temperature. • What is the approximate mass of water in a 0.5 L water bottle? • What is the volume of 150 grams of water?

31. Density • Objects with a density greater than 1g/mL sink in water. • Objects with a density less than 1g/mL float in water.

32. Density • The density of the elements can be found on the periodic table. • Examples: • The density of compounds must be looked up in reference “books”.

33. Density • Calculating density from data • In class experiment

34. Density • Rearrange the density equation to solve for volume and mass: Volume = Mass =

35. Density Calculations • Calculate the mass, in grams and in pounds, of a gold brick • see board for the dimensions of the gold brick

36. Density Calculations • Calculate the volume, in ml, of my gold cross • Mass of cross: 4.5 g • Round your answer to 2 decimal places

37. Temperature Temperature Scales (3) • Fahrenheit • Celsius • Kelvin

38. Temperature

39. Temperature Conversions TK = TC = TF =

40. Temperature Conversions • Shark fishing example • Convert room temperature to: • 0 C and K • Sauna example