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4 Chapter 1 Matter, Measurement, and Problem Solving Because these equations do not directly express K in terms of °F, you must combine the equations and then solve the equation for °F. Substituting for °C: K = °F 1.8 - 32 + 273.15; rearrange K 273.15 = °F 1.8 32 rearrange 1.8(K 273.15) = (°F 32); finally, °F = 1.8(K - 273.15) + 32. Now substitute K into the equation and compute the answer. °F = 1.8(77 - 273.15) + 32 = 1.8(-196) + 32 = -353 + 32 = 321 °F Alternatively, you could first convert to K to °C, using the formula K = and then convert °C to °F. So, 77 K = 273.15 + °C. Rearranging to solve for °C we get °C = 77K 273.15 = -196.15 °C. Then substitute °F 32 °F 32 the temperature in °C in the formula °C = 1.8 - getting -196.15 = 1.8 Multiplying both sides by 1.8, we get -196.15 °C 1.8 = °F 32 and -353.07 °C = °F - 32. Adding 32 to both sides of the equation we get °F = -321.07 °F or -321 °F, with the proper number of significant figures. °F - - 32 (c) To convert from °F to °C, first find the equation that relates these two quantities. °C = 1.8 Now substitute °F into the equation and compute the answer. °C = 109 1.8 32 = -141 1.8 = -78.3 °C (d) To convert from °F to K, first find the equations that relate these two quantities. K = °C + 273.15 and °C = °F 32 1.8 Because these equations do not directly express K in terms of °F, you must combine the equations and then °F 32 solve the equation for K. Substituting for °C: K = 1.8 + 273.15. Now substitute °F into the equation and compute the answer. K = (98.6 1.8 32) 273.15 = 66.6 1.8 273.15 = 37.0 + 273.15 = 310.2 K Alternatively, you could first convert to °F to °C, using the formula °C = °F 1.8 32 , and then convert °C to K, using K = 273.15 + °C. So, °C = 98.6 °F 1.8 32 = 66.6 1.8 = 37.0 Then K = 273.15 + = 310.2 °F - 32 1.53 To convert from °F to °C, first find the equation that relates these two quantities: °C = 1.8 Now substitute °F into the equation and compute the answer. Note: The number of digits reported in this answer follows significant figure conventions, covered in Section 1.6. °C = -80. °F 1.8 = -112 1.8 = 62.2 °C Begin by finding the equation that relates the quantity that is given (°C) and the quantity you are trying to find (K). K = °C + 273.15. Because this equation gives the temperature in K directly, simply substitute the correct value for the temperature in °C and compute the answer. K = + 273.15 = 210.9 K 1.55 Use Table 2 to determine the appropriate prefix multiplier and substitute the meaning into the expressions. (a) 10⁻⁹ is equivalent to "nano," so 1.2 X 10⁻⁹ m = 1.2 nanometers = 1.2 nm. (b) 10⁻¹⁵ is equivalent to "femto," so 22 X 10⁻¹⁵ S = 22 femtoseconds = 22 fs. (c) is equivalent to "giga," 1.5 X g = 1.5 gigagrams = 1.5 Gg. (d) 10⁶ is equivalent to "mega," so 3.5 X 10⁶ L = 3.5 megaliters = 3.5 ML. 1.57 Use Table 2 to determine the appropriate prefix multiplier and substitute the meaning into the expressions. (a) 10⁻⁹ is equivalent to "nano," so 4.5 ns = 4.5 nanoseconds = 4.5 X 10⁻⁹ S. (b) 10⁻¹⁵ is equivalent to "femto," SO 18 fs = 18 femtoseconds = 18 X 10⁻¹⁵ S = 1.8 X 10⁻¹⁴ S. Remember that in scientific notation, the first number should be smaller than 10. (c) 10⁻¹² is equivalent to "pico," 128 pm = 128 X 10⁻¹² m = 1.28 X 10⁻¹⁰ m. Remember that in scientific notation, the first number should be smaller than 10. (d) 10⁻⁶ is equivalent to "micro," so 35 µm = 35 micrometers = 35 X 10⁻⁶ m = 3.5 X 10⁻⁵ m. Remember that in scientific notation, the first number should be smaller than 10. Copyright © 2017 Pearson Education, Inc.