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Chapter 1

Chapter 1. Measurements in Chemistry. Setting the Stage - measurements. Measurements are a critical part of life, as well as chemistry Measurements consist of two parts – a number and a unit Mathematics is also a critical part of life and chemistry.

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Chapter 1

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  1. Chapter1 Measurements in Chemistry

  2. Setting the Stage - measurements Measurements are a critical part of life, as well as chemistry Measurements consist of two parts – a number and a unit Mathematics is also a critical part of life and chemistry Malone and Dolter - Basic Concepts of Chemistry 8e

  3. Setting a Goal - Part AThe Numbers Used in Chemistry • You will learn how to apply and manipulate measurements to produce scientifically meaningful outcomes Malone and Dolter - Basic Concepts of Chemistry 8e

  4. Objectives for Section 1-1 • To describe the difference between accuracy and precision • To determine the number of significant figures in a measurement Malone and Dolter - Basic Concepts of Chemistry 8e

  5. 1-1 The Numerical Value of a Measurement • A measurement determines the quantity, dimensions or extent of something • A unit is a definite quantity adapted to as a standard of measurement Malone and Dolter - Basic Concepts of Chemistry 8e

  6. Significant Digits or Figures • Significant digit – a digit that is either reliably known or estimated • We write numbers with digits, and assume that the last digit is uncertain • For example, in the number 1.23, there are three significant digits, and we assume that the last digit, the 3, is uncertain Malone and Dolter - Basic Concepts of Chemistry 8e

  7. Features of Measured Quantities • When we measure a number, there are physical constraints to the measurement • Instruments and scientists are not perfect, so the measurement is not perfect (i. e., it has error) • The error in the measurement is related to the accuracy and the precision of the measurement Malone and Dolter - Basic Concepts of Chemistry 8e

  8. Accuracy and Precision • Accuracy – how close the measurement is to the “true” value (of course we have to know what the “true” value is) • Precision - the degree to which the measurement is reproducible • We express precision through how we write the number – significant digits or figures Malone and Dolter - Basic Concepts of Chemistry 8e

  9. Accuracy and Precision Malone and Dolter - Basic Concepts of Chemistry 8e

  10. Two Accurate Shooters Malone and Dolter - Basic Concepts of Chemistry 8e

  11. Significant Digits • Any non-zero digit • A zero between two nonzero digits (907) • Zeroes to the right of a nonzero digit and to the right of the decimal point (8.0) Malone and Dolter - Basic Concepts of Chemistry 8e

  12. Non-Significant Digits • Zeroes to the left of the leftmost nonzero digit • 0.078 has two significant digits • Zeroes to the left of an implied decimal point may or may not be significant • 567 has an implied decimal point • in the number 450, we do not know if the zero is significant Malone and Dolter - Basic Concepts of Chemistry 8e

  13. Number 0.0014 0.610 70 70. 15217 Significant figures 2 3 1 or 2 2 5 Significant Digits - Examples Malone and Dolter - Basic Concepts of Chemistry 8e

  14. Objective for Section 1-2 • To perform arithmetic operations, rounding the answer to the appropriate number of significant figures Malone and Dolter - Basic Concepts of Chemistry 8e

  15. 1-2 Significant Figures and Mathematical Operations Addition and subtraction – answer is expressed to the same number of significant digits as the number in the calculation with the fewest digits to the right of the decimal point10.6871+1.4212.1071 = 12.11 Malone and Dolter - Basic Concepts of Chemistry 8e

  16. Significant Digits in Calculations • In multiplication or division, the answer is expressed to the same number of significant digits as the number with the fewest significant digits2.34  3.225 = 7.5465 = 7.55 Malone and Dolter - Basic Concepts of Chemistry 8e

  17. Significant Figures and Calculators • Calculators always express numbers and the results of calculations as if they were exact • e. g. 7.8/2.3 = 3.3913043 is displayed • is this realistic if 7.8 and 2.3 resulted from a measurement? • Calculators use far more digits than is possible in virtually all measurements in order to avoid round off error within the calculator Malone and Dolter - Basic Concepts of Chemistry 8e

  18. Rounding Off • If the digit to be dropped is less than 5, simply drop that digit (12.44 is rounded down to 12.4 • If the digit to be dropped is 5 or greater, increase the preceding digit by one (0.3568 is rounded up to 0.357, and 13.65 is rounded up to 13.7) Malone and Dolter - Basic Concepts of Chemistry 8e

  19. Operation 12.36 + 3.127 2.051 × 0.72 39.41 × 7.15 (4.68 x 1016)/ (9.1 x 10-5) Result 15.487  15.49 (4 sf) 1.47672  1.5 (2 sf) 281.782  282 (3 sf) 0.514 × 1021  5.14 × 1020  5.1 × 1020 (2 sf) Rounding Off - Examples Malone and Dolter - Basic Concepts of Chemistry 8e

  20. Objectives for Section 1-3 • To write very large or small measurements in scientific notation • To perform arithmetic operations involving scientific notation Malone and Dolter - Basic Concepts of Chemistry 8e

  21. 1-3 Expressing Large and Small Numbers: Scientific Notation • Numbers are expressed with one nonzero digit to the left of the decimal point multiplied by 10 raised to an appropriate power • The coefficient is the number with all of the appropriate significant digits • The exponent is the power of ten the mantissa is multiplied by Malone and Dolter - Basic Concepts of Chemistry 8e

  22. Scientific Notation Format Malone and Dolter - Basic Concepts of Chemistry 8e

  23. Scientific Notation and Calculators • We write scientific notation as6.022  1023 • Calculators handle scientific notation by only inputting the exponent, using an EXP or EE key • You should enter the mantissa as you would for a regular number, then press EXP or EE, then enter the exponent Malone and Dolter - Basic Concepts of Chemistry 8e

  24. Scientific Notation and Significant Digits The nice thing about scientific notation is that the coefficient must be written with the correct number of significant digits All zeroes must be significant (no zeroes just to hold the place) Malone and Dolter - Basic Concepts of Chemistry 8e

  25. Decimal Notation 1,253 3,500,000 0.0000029 500 500. 299790000 Scientific Notation 1.253 × 103 (4 sf) 3.5 × 106 (2 sf) 2.9 × 106 (2 sf) 5 × 102 (1 sf) 5.00 × 102 (3 sf) 2.9979 × 108 (5 sf) Scientific Notation and Significant Digits - Examples Malone and Dolter - Basic Concepts of Chemistry 8e

  26. Setting a Goal - Part BThe Measurements Used In Chemistry • You will learn how to manipulate the units of measurement for the purposes of problem solving Malone and Dolter - Basic Concepts of Chemistry 8e

  27. Objective for Section 1-4 • To list several fundamental and derived units of measurement in the metric (SI) system Malone and Dolter - Basic Concepts of Chemistry 8e

  28. 1-4 Measurement of Mass, Length and Volume • In the United States, a fairly awkward system of measurement is used for most things - the English system (see Table 1-1) • Scientists use the metric and SI systems of units for the measurement of physical quantities Malone and Dolter - Basic Concepts of Chemistry 8e

  29. English/Non-SI and SI Units Non-SI: “fluid Ounces” SI: mL Malone and Dolter - Basic Concepts of Chemistry 8e

  30. 1-4 Measurement of Mass, Length and Volume……Continued • The SI system using standard units (see Table 1-2) is based on very precisely known properties of matter and light • New units can be derived from the fundamental ones (see Table 1-3) Malone and Dolter - Basic Concepts of Chemistry 8e

  31. Fundamental SI Units Malone and Dolter - Basic Concepts of Chemistry 8e

  32. SI Prefixes Malone and Dolter - Basic Concepts of Chemistry 8e

  33. Fundamental SI units • Mass - the quantity of matter that a sample contains • Note that weight is a measure of the attraction of gravity for a sample and it varies depending on the distance of the mass to a planet or moon • Scientists often speak imprecisely of the “weight” of an amount of substance. They really mean mass. Malone and Dolter - Basic Concepts of Chemistry 8e

  34. Fundamental SI units are used to generate new units • Volume - space a given quantity of matter occupies • Volume - expressed in terms of length - m3 • m3 - an inconveniently large volume, so we use liter (L; one cubic decimeter) • We often use a mL (1 cubic centimeter) for more manageable amounts of matter Malone and Dolter - Basic Concepts of Chemistry 8e

  35. Objective for Section 1-5 • To interconvert measurements by the factor-label method Malone and Dolter - Basic Concepts of Chemistry 8e

  36. 1-5 Conversion of Units by the Factor-Label Method • The standard method to convert between two different units is the factor-label or dimensional analysis method • Dimensional analysis converts a measurement in one unit to another by the use of a conversion factor • Conversion factors are developed from relationships between units Malone and Dolter - Basic Concepts of Chemistry 8e

  37. Conversion Factors • Unit factors - factors that relate a quantity in a certain unit to 1 of another unite.g.103 m = 1 km • The conversion factor is created by dividing both sides by the same quantity • 103 m = 1 = 1 km103 m 103m Malone and Dolter - Basic Concepts of Chemistry 8e

  38. Dimensional Analysis • Multiplying a quantity in one unit by an appropriate conversion factor converts the number into the new unit • Note that conversion factors are exact relationships • Exact relationships have unlimited precision, so they can be ignored for the purposes of deciding the number of significant digits in a calculation Malone and Dolter - Basic Concepts of Chemistry 8e

  39. Convert 25mLto mL Convert 1.54Åto pm 25mL × 10-6 L/1mL × 1 mL/10-3 L = 2.5 × 10-2 mL or 0.025 mL 1.54Å×10-10 m/1 Å× 1 pm/10-12 m = 1.54 × 102 = 154 pm Dimensional Analysis - Examples Malone and Dolter - Basic Concepts of Chemistry 8e

  40. Sample Conversion • Convert 10.0 km to miles Unit map: Relationship: 1.609 km = 1.000 mi Conversion factor Solution: Malone and Dolter - Basic Concepts of Chemistry 8e

  41. Objective for Section 1-6 • To Identify several key points on the Celsius and Kelvin temperature scales Malone and Dolter - Basic Concepts of Chemistry 8e

  42. 1-6 Measurement of Temperature • Temperature - measure of the intensity of the heat of a substance • Thermometer - device to measure temperature • Kelvin - K - SI unit of temperature • Celsius - °C - commonly used unit • Fahrenheit - °F - only used in USA Malone and Dolter - Basic Concepts of Chemistry 8e

  43. Relationships Between Temperature Scales Malone and Dolter - Basic Concepts of Chemistry 8e

  44. The Kelvin Scale • The idea of negative temperatures is a problem for any mathematical treatment of temperature dependent properties • It was found that a practical minimum temperature did exist (absolute zero) which has a value of -273.15°C • This is defined as 0 K (no degree sign) • The Kelvin degree is the same size as the Celsius degree (K = °C + 273.15) Malone and Dolter - Basic Concepts of Chemistry 8e

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