Chapter 2: Analyzing Data

# Chapter 2: Analyzing Data

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## Chapter 2: Analyzing Data

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1. CHEMISTRY Matter and Change Chapter 2: Analyzing Data

2. Table Of Contents CHAPTER2 Section 2.1 Units and Measurements Section 2.2 Scientific Notation and Dimensional Analysis Section 2.3 Uncertainty in Data Section 2.4 Representing Data Click a hyperlink to view the corresponding slides. Exit

3. Units and Measurements SECTION2.1 • Define SI base units for time, length, mass, and temperature. • Explain how adding a prefix changes a unit. • Compare the derived units for volume and density. mass: a measurement that reflects the amount of matter an object contains

4. Units and Measurements SECTION2.1 base unit second meter kilogram kelvin derived unit liter density Chemists use an internationally recognized system of units to communicate their findings.

5. Units and Measurements SECTION2.1 Units • Système Internationale d'Unités (SI) is an internationally agreed upon system of measurements. • A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.

6. Units and Measurements Units and Measurements SECTION2.1 SECTION2.1 Units (cont.)

7. Units and Measurements SECTION2.1 Units (cont.)

8. Units and Measurements SECTION2.1 Units (cont.) • The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom. • The SI base unit for length is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second. • The SI base unit of mass is the kilogram (kg), about 2.2 pounds

9. Units and Measurements SECTION2.1 Units (cont.) • The SI base unit of temperature is the kelvin(K). • Zero kelvin is the point where there is virtually no particle motion or kinetic energy, also known as absolute zero. • Two other temperature scales are Celsius and Fahrenheit.

10. Temperature Conversions

11. Units and Measurements SECTION2.1 Derived Units • Not all quantities can be measured with SI base units. • A unit that is defined by a combination of base units is called a derived unit.

12. Units and Measurements SECTION2.1 Derived Units (cont.) • Volume is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3).

13. Units and Measurements SECTION2.1 Derived Units (cont.) • Density is a derived unit, g/cm3, the amount of mass per unit volume. • The density equation is density = mass/volume.

14. Density Problems

15. Section Check SECTION2.1 Which of the following is a derived unit? A.yard B.second C.liter D.kilogram

16. Section Check SECTION2.1 What is the relationship between mass and volume called? A.density B.space C.matter D.weight

17. Scientific Notation and Dimensional Analysis SECTION2.2 • Express numbers in scientific notation. • Convert between units using dimensional analysis. quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on

18. Scientific Notation and Dimensional Analysis SECTION2.2 scientific notation dimensional analysis conversion factor Scientists often express numbers in scientific notation and solve problems using dimensional analysis.

19. Scientific Notation and Dimensional Analysis SECTION2.2 Scientific Notation • Scientific notation can be used to express any number as a number between 1 and 10 (known as the coefficient) multiplied by 10 raised to a power (known as the exponent). • Carbon atoms in the Hope Diamond = 4.6 x 1023 • 4.6 is the coefficient and 23 is the exponent.

20. Scientific Notation and Dimensional Analysis SECTION2.2 Scientific Notation (cont.) • Count the number of places the decimal point must be moved to give a coefficient between 1 and 10. • The number of places moved equals the value of the exponent. • The exponent is positive when the decimal moves to the left and negative when the decimal moves to the right. 800 = 8.0  102 0.0000343 = 3.43  10–5

21. Scientific Notation and Dimensional Analysis SECTION2.2 Scientific Notation (cont.) • Addition and subtraction • Exponents must be the same. • Rewrite values to make exponents the same. • Ex. 2.840 x 1018 + 3.60 x 1017, you must rewrite one of these numbers so their exponents are the same. Remember that moving the decimal to the right or left changes the exponent. 2.840 x 1018 + 0.360 x 1018 • Add or subtract coefficients. • Ex. 2.840 x 1018 + 0.360 x 1017 = 3.2 x 1018

22. Scientific Notation and Dimensional Analysis SECTION2.2 Scientific Notation (cont.) • Multiplication and division • To multiply, multiply the coefficients, then add the exponents. Ex. (4.6 x 1023)(2 x 10-23) = 9.2 x 100 • To divide, divide the coefficients, then subtract the exponent of the divisor from the exponent of the dividend. Ex. (9 x 107) ÷ (3 x 10-3) = 3 x 1010 Note: Any number raised to a power of 0 is equal to 1: thus, 9.2 x 100 is equal to 9.2.

23. Scientific Notation and Dimensional Analysis SECTION2.2 Dimensional Analysis • Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another. • A conversion factor is a ratio of equivalent values having different units.

24. Scientific Notation and Dimensional Analysis SECTION2.2 Dimensional Analysis (cont.) • Writing conversion factors • Conversion factors are derived from equality relationships, such as 1 dozen eggs = 12 eggs. • Percentages can also be used as conversion factors. They relate the number of parts of one component to 100 total parts.

25. Scientific Notation and Dimensional Analysis SECTION2.2 Dimensional Analysis (cont.) • Using conversion factors • A conversion factor must cancel one unit and introduce a new one.

26. Section Check SECTION2.2 What is a systematic approach to problem solving that converts from one unit to another? A.conversion ratio B.conversion factor C.scientific notation D.dimensional analysis

27. Section Check SECTION2.2 Which of the following expresses 9,640,000 in the correct scientific notation? A.9.64  104 B.9.64  105 C.9.64 × 106 D.9.64  610

28. Uncertainty in Data SECTION2.3 • Define and compare accuracy and precision. • Describe the accuracy of experimental data using error and percent error. • Apply rules for significant figures to express uncertainty in measured and calculated values. experiment: a set of controlled observations that test a hypothesis

29. Uncertainty in Data SECTION2.3 accuracy precision error percent error significant figures Measurements contain uncertainties that affect how a result is presented.

30. Uncertainty in Data SECTION2.3 Accuracy and Precision • Accuracy refers to how close a measured value is to an accepted value. • Precision refers to how close a series of measurements are to one another.

31. Uncertainty in Data SECTION2.3 Accuracy and Precision (cont.) • Erroris defined as the difference between an experimental value and an accepted value.

32. Uncertainty in Data SECTION2.3 Accuracy and Precision (cont.) • The error equation is error = experimental value – accepted value. • Percent errorexpresses error as a percentage of the accepted value.

33. Uncertainty in Data SECTION2.3 Significant Figures • Often, precision is limited by the tools available. • Significant figures include all known digits plus one estimated digit.

34. Uncertainty in Data SECTION2.3 Significant Figures (cont.) • Rules for significant figures • Rule 1: Nonzero numbers are always significant. • Rule 2: Zeros between nonzero numbers are always significant. • Rule 3: All final zeros to the right of the decimal are significant. • Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation. • Rule 5: Counting numbers and defined constants have an infinite number of significant figures.

35. Uncertainty in Data SECTION2.3 Rounding Numbers • Calculators are not aware of significant figures. • Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

36. Uncertainty in Data SECTION2.3 Rounding Numbers (cont.) • Rules for rounding • Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure. • Rule 2: If the digit to the right of the last significant figure is greater than 5, round up the last significant figure. • Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up the last significant figure.

37. Uncertainty in Data SECTION2.3 Rounding Numbers (cont.) • Rules for rounding (cont.) • Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up.

38. Uncertainty in Data SECTION2.3 Rounding Numbers (cont.) • Addition and subtraction • Round the answer to the same number of decimal places as the original measurement with the fewest decimal places. • Multiplication and division • Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.

39. Section Check SECTION2.3 Determine the number of significant figures in the following: 8,200, 723.0, and 0.01. A.4, 4, and 3 B.4, 3, and 3 C.2, 3, and 1 D.2, 4, and 1

40. Section Check SECTION2.3 A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error? A.20% B.–20% C.10% D.90%

41. Representing Data SECTION2.4 • Create graphics to reveal patterns in data. independent variable: the variable that is changed during an experiment • Interpret graphs. graph Graphs visually depict data, making it easier to see patterns and trends.

42. Representing Data SECTION2.4 Graphing • A graphis a visual display of data that makes trends easier to see than in a table.

43. Representing Data SECTION2.4 Graphing (cont.) • A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.

44. Representing Data SECTION2.4 Graphing (cont.) • Bar graphs are often used to show how a quantity varies across categories.

45. Representing Data SECTION2.4 Graphing (cont.) • On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.

46. Representing Data SECTION2.4 Graphing (cont.) • If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.