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Understanding Dimensional Analysis, Temperature Conversions, and Density Calculations

This chapter delves into the principles of dimensional analysis, showcasing how equivalence statements like 1 inch = 2.54 cm can transform into conversion factors for unit conversions. Practical examples illustrate how to convert centimeters to inches and miles to kilometers. Important temperature conversions among Fahrenheit, Celsius, and Kelvin are covered, including their absolute scales and relative values. The chapter concludes with density calculations, defining it as mass per unit volume and providing examples to demonstrate specific gravity and volume determination.

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Understanding Dimensional Analysis, Temperature Conversions, and Density Calculations

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  1. Chapter 5, Part 3 Measurements and Calculations

  2. 5.6 Dimensional Analysis 1 in. = 2.54 cm is an equivalence statement and can be turned into a conversion factor:1 in./2.54 cm or 2.54 cm/1 in. Any equivalence statement can be used in this manner.

  3. Example: 62 cm = ? In. 62 cm x 1 in./2.54 cm = 24 in. (note sig figs) Example: 26.2 mi. = ? Km. 26.2 mi. X 1760 yd/1 mi. X 1 m/1.094 yd x 1 km/103 m = 42.1 km Embedded problem: (convert the speed of light from 3.00 x 108 meters per second to miles per hour.)

  4. 5.7 Temperature Conversions Fahrenheit Celsius Kelvin b.p. water 212 100 373 f.p. water 32 0 273 Absolute zero -460 -273 0 (note: no degree symbol “o” is used in the Kelvin scale. It is an absolute scale.) Conversions: Celsius to Kelvin: add 273 to Celsius

  5. Figure 5.6: The three major temperature scales.

  6. Figure 5.7: Converting 70 degrees Celsius to Kelvin units.

  7. Figure 5.8: Comparison of the Celsius and Fahrenheit scales.

  8. Example: 70.oC = ? K 70.oC + 273 = 343 K Example: 77 K = ? oC 77 K - 273 = -196oC Problem: Which temperature is colder, 172 K or -75 oC? (172 K)(Why?)

  9. 5.8 Density- amount of matter present in a given volume of a substance. Density = mass/volume Mass = density x volume Volume = Mass/Density Specific gravity- ratio of the density of a given liquid to the density of water @ 4oC (has no unit)

  10. Example: 23.50 mL of a certain liquid has a mass of 35.062 g. Calculate density. D = M/V = 35.062 g/23.50 mL = 1.492 g/mL Problem: 35.8 mL of a cleaner has a mass of 28.1 g. Which of the four substances in the table on p. 144 is the major component? D = M/V = 28.1 g/35.8 mL = 0.785 g/mL Therefore, isopropyl alcohol. Example: V = M/D = 225 g/13.6 g/mL = 16.5 mL

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