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Measurements & Calculations

Measurements & Calculations. Chapter 2. Nature of Measurement. Measurement - quantitative observation consisting of two parts: Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63    Joule seconds. Scientific Notation.

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Measurements & Calculations

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  1. Measurements & Calculations • Chapter 2

  2. Nature of Measurement • Measurement - quantitative observation consisting of two parts: • Part 1 - number • Part 2 - scale (unit) • Examples: • 20grams • 6.63 Joule seconds

  3. Scientific Notation • Also called exponential notation and powers of ten notation. Scientific notation has two advantages: • the number of significant digits can easily be indicated • fewer zeros are needed to write a very large or very small number.

  4. Scientific Notation • LIP -- Left is positive. • 238,000 = • 1,500,000 = • RIN -- Right is negative. • 0.00043 = • 0.089 = 2.38 x 105 1.5 x 106 4.3 x 10-4 8.9 x 10-2

  5. International System(le Système International) • Based on metric system and units derived from metric system.

  6. The Fundamental SI Units

  7. Table 2.2: The Commonly used Prefixes in the Metric System

  8. Table 2.3: The Metric System for Measuring Length

  9. Figure 2.1: Comparison of English and metric units for length on a ruler

  10. One liter is defined as a cubic decimeter and 1 mL is one cubic centimeter.

  11. Figure 2.3: A 100-ml Graduated Cylinder

  12. Common types of laboratory equipment used to measure liquid volume.

  13. Mass & Weight • Mass is a measure of the resistance of an object to a change in its state of motion -- a constant--measured in kilograms. • Weight is the measure of the pull of gravity on an object and varies with the object’s location--measured in newtons.

  14. Figure 2.4: An electronic analytical balance used in chemistry labs

  15. Uncertainty in Measurement • A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

  16. Measurement of volume using a buret. The volume is read at the bottom of the meniscus.

  17. Figure 2.5: Measuring a Pin

  18. Precision and Accuracy • Accuracyrefers to the agreement of a particular value with the true value. • Precisionrefers to the degree of agreement among several elements of the same quantity.

  19. Types of Error • Random Error (Indeterminate Error) - measurement has an equal probability of being high or low. • Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique.

  20. a) is neither precise nor accurate, b) is precise but not accurate (small random, large systematic errors) c) both precise and accurate (small random, no systematic errors.

  21. Accuracy • Trial Graduated Cylinder Buret • 1 25 mL 26.54 mL • 2 25 mL 26.51 mL • 3 25 mL 26.60 mL • 4 25 mL 26.49 mL • 5 25 mL 26.57 mL • Average 25 mL 26.54 mL • Which is more accurate? • Graduated cylinder produces systematic error --value is too low. Buret

  22. Rules for Counting Significant Figures - Overview • 1. Nonzero integers • 2. Zeros • - leading zeros • - captive zeros • - trailing zeros • 3. Exact numbers

  23. Rules for Counting Significant Figures - Details • Nonzero integers always count as significant figures. • 3456 has • 4 sig figs.

  24. Rules for Counting Significant Figures - Details • Zeros • -Leading zeros do not count as significant figures. • 0.0486 has • 3 sig figs.

  25. Rules for Counting Significant Figures - Details • Zeros • -Captive zeros always count as significant figures. • 16.07 has • 4 sig figs.

  26. Rules for Counting Significant Figures - Details • Zeros • - Trailing zerosare significant only if the number contains a decimal point. • 9.300 has • 4 sig figs.

  27. Rules for Counting Significant Figures - Details • Exact numbershave an infinite number of significant figures. Can come from counting or definition. • 15 atoms • 1 inch = 2.54cm, exactly

  28. Rules for Rounding • 1. In a series of calculations, carry the extra digits through to the final result, then round. • 2. If the digit to be removed • a. is less than five, the preceding digit stays the same. • b. is equal to or greater than five, the preceding digit is increased by 1.

  29. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:# sig figs in the result equals the number in the least precise measurement used in the calculation. • 6.38  2.0 = • 12.76 13 (2 sig figs)

  30. Rules for Significant Figures in Mathematical Operations • Addition and Subtraction:# sig figs in the result equals the number of decimal places in the least precise measurement. • 6.8 + 11.934 = • 22.4896 22.5 (3 sig figs)

  31. Dimensional Analysis • Also called unit cancellation is a method of solving problems by using unit factors to change from one unit to another. • Unit factor(conversion or equivalence factor) -- the unit that you have goes on bottom, and the unit that you want goes on top.

  32. Dimensional Analysis Proper use of “unit factors” leads to proper units in your answer.

  33. Dimensional Analysis • What is the dimension of a 25.5 in bicycle frame in centimeters? • (25.5 in)(2.54 cm/1 in) = 64.8 cm • Units must be cancelled and the answer must have correct sig figs, be underlined, and include proper units!!

  34. Dimensional Analysis • The length of the marathon race is approximately 26.2 miles. What is this distance in kilometers? • (26.2 mi)(1760 yd/1 mi)(1 m/1.094 yd) • (1 km/1000m) = 42.1 km • Look to see if your answer is reasonable!! • Had your answer been 0.0000421 km, would it have been reasonable?

  35. Temperature • Celsius scale =C • Kelvin scale = K • Fahrenheit scale =F

  36. Three major temperature scales.

  37. Figure 2.6: Thermometers based on the three temperature scales in (a) ice water and (b) boiling water

  38. Figure 2.8: Converting 70°C to units measured on the Kelvin scale

  39. Figure 2.9: Comparison of the Celsius and Fahrenheit scales

  40. Temperature

  41. Temperature Calculations • Convert - 40.0 oC to Kelvin. • K = C + 273.15 • K = -40.0 + 273.15 • K = 233.2 K

  42. Temperature Calculations • Convert 375 K to Celsius. • K = C + 273.15 • C = K - 273.15 • C = 375 - 273.15 • C = 102 oC

  43. Temperature Calculations • Convert - 40.0 oC to Fahrenheit. 100 F - 3200 = -7200 100 F = -4000 F = - 40.0 oF

  44. Temperature Calculations • Convert 76.0 oF to Celsius. 180 C = 4400 C = 24.4 oC

  45. Density • Densityis the mass of substance per unit • volume of the substance:

  46. Volume of an Irregular Object • How can the volume of an irregular object such as a rock be determined using common laboratory equipment? • Water displacement

  47. Density Calculations • A medallion has a mass of 55.64 g. When placed in a graduated cylinder containing 75.2 mL of water, the water level rises to 77.8 mL. Is the medallion platinum? Yes, same density as Pt. D = 21 g/mL

  48. Density Calculations • If an object has a density of 0.7850 g/cm3 and a mass of 19.625 g, what is its volume? V = 25.00 cm3

  49. Density • When mass is graphed against volume, what does the slope of the line represent? • Slope =  y/ x = m/V •  density = slope

  50. Figure 2.11: A hydrometer being used to determine the density of the antifreeze solution in a car’s radiator

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