Solutions_Manual_to_Zumdahl_Chemistry_

Solutions_Manual_to_Zumdahl_Chemistry_CHAPTER 1 CHEMICAL FOUNDATIONS Questions 19. A law summarizes what happens, e.g., law of conservation of mass in a chemical reaction or the ideal gas law, PV = nRT. A theory (mod ...

Solutions_Manual_to_Zumdahl_Chemistry_CHAPTER 1 CHEMICAL FOUNDATIONS Questions 19. A law summarizes what happens, e.g., law of conservation of mass in a chemical reaction or the ideal gas law, PV = nRT. A theory (model) is an attempt to explain why something happens. Dalton’s atomic theory explains why mass is conserved in a chemical reaction. The kinetic molecular theory explains why pressure and volume are inversely related at constant temperature and moles of gas present, as well as explaining the other mathematical relationships summarized in PV = nRT. 20. A dynamic process is one that is active as opposed to static. In terms of the scientific method, scientists are always performing experiments to prove or disprove a hypothesis or a law or a theory. Scientists do not stop asking questions just because a given theory seems to account satisfactorily for some aspect of natural behavior. The key to the scientific method is to continually ask questions and perform experiments. Science is an active process, not a static one. 21. The fundamental steps are (1) making observations; (2) formulating hypotheses; (3) performing experiments to test the hypotheses. The key to the scientific method is performing experiments to test hypotheses. If after the test of time the hypotheses seem to account satisfactorily for some aspect of natural behavior, then the set of tested hypotheses turns into a theory (model). However, scientists continue to perform experiments to refine or replace existing theories. 22. A random error has equal probability of being too high or too low. This type of error occurs when estimating the value of the last digit of a measurement. A systematic error is one that always occurs in the same direction, either too high or too low. For example, this type of error would occur if the balance you were using weighed all objects 0.20 g too high, that is, if the balance wasn’t calibrated correctly. A random error is an indeterminate error, whereas a systematic error is a determinate error. 23. A qualitative observation expresses what makes something what it is; it does not involve a number; e.g., the air we breathe is a mixture of gases, ice is less dense than water, rotten milk stinks. The SI units are mass in kilograms, length in meters, and volume in the derived units of m3. The assumed uncertainty in a number is ±1 in the last significant figure of the number. The precision of an instrument is related to the number of significant figures associated with an2 CHAPTER 1 CHEMICAL FOUNDATIONS experimental reading on that instrument. Different instruments for measuring mass, length, or volume have varying degrees of precision. Some instruments only give a few significant figures for a measurement, whereas others will give more significant figures. 24. Precision: reproducibility; accuracy: the agreement of a measurement with the true value. a. Imprecise and inaccurate data: 12.32 cm, 9.63 cm, 11.98 cm, 13.34 cm b. Precise but inaccurate data: 8.76 cm, 8.79 cm, 8.72 cm, 8.75 cm c. Precise and accurate data: 10.60 cm, 10.65 cm, 10.63 cm, 10.64 cm Data can be imprecise if the measuring device is imprecise as well as if the user of the measuring device has poor skills. Data can be inaccurate due to a systematic error in the measuring device or with the user. For example, a balance may read all masses as weighing 0.2500 g too high or the user of a graduated cylinder may read all measurements 0.05 mL too low. A set of measurements that are imprecise implies that all the numbers are not close to each other. If the numbers aren’t reproducible, then all the numbers can’t be very close to the true value. Some say that if the average of imprecise data gives the true value, then the data are accurate; a better description is that the data takers are extremely lucky. 25. Significant figures are the digits we associate with a number. They contain all of the certain digits and the first uncertain digit (the first estimated digit). What follows is one thousand indicated to varying numbers of significant figures: 1000 or 1 × 103 (1 S.F.); 1.0 × 103 (2 S.F.); 1.00 × 103 (3 S.F.); 1000. or 1.000 × 103 (4 S.F.). To perform the calculation, the addition/subtraction significant figure rule is applied to 1.5 − 1.0. The result of this is the one-significant-figure answer of 0.5. Next, the multiplication/division rule is applied to 0.5/0.50. A one-significant-figure number divided by a two-significant-figure number yields an answer with one significant figure (answer = 1). 26. From Figure 1.9 of the text, a change in temperature of 180°F is equal to a change in temperature of 100°C and 100 K. A degree unit on the Fahrenheit scale is not a large as a degree unit on the Celsius or Kelvin scales. Therefore, a 20° change in the Celsius or Kelvin temperature would correspond to a larger temperature change than a 20° change in the Fahrenheit scale. The 20° temperature change on the Celsius and Kelvin scales are equal to each other. 27. Straight line equation: y = mx + b, where m is the slope of the line and b is the y-intercept. For the TF vs. TC plot: TF = (9/5)TC + 32 y = m x + b The slope of the plot is 1.8 (= 9/5) and the y-intercept is 32°F. For the TC vs. TK plot: TC = TK − 273 y = m x + b The slope of the plot is 1, and the y-intercept is −273°C.CHAPTER 1 CHEMICAL FOUNDATIONS 3 28. When performing a multiple step calculation, always carry at least one extra significant figure in intermediate answers. If you round-off at each step, each intermediate answer gets further away from the actual value of the final answer. So to avoid round-off error, carry extra significant figures through intermediate answers, then round-off to the proper number of significant figures when the calculation is complete. In this solutions manual, we rounded off intermediate answers to the show the proper number significant figures at each step; our answers to multistep calculations will more than likely differ from yours because we are introducing round-off error into our calculations. 29. The gas phase density is much smaller than the density of a solid or a liquid. The molecules in a solid and a liquid are very close together. In the gas phase, the molecules are very far apart from one another. In fact, the molecules are so far apart that a gas is considered to be mostly empty space. Because gases are mostly empty space, their density is very small. 30. a. coffee; saltwater; the air we breathe (N2 + O2 + others); brass (Cu + Zn) b. book; human being; tree; desk c. sodium chloride (NaCl); water (H2O); glucose (C6H12O6); carbon dioxide (CO2) d. nitrogen (N2); oxygen (O2); copper (Cu); zinc (Zn) e. boiling water; freezing water; melting a popsicle; dry ice subliming f. Electrolysis of molten sodium chloride to produce sodium and chlorine gas; the explosive reaction between oxygen and hydrogen to produce water; photosynthesis, which converts H2O and CO2 into C6H12O6 and O2; the combustion of gasoline in our car to produce CO2 and H2O Exercises Significant Figures and Unit Conversions 31. a. exact b. inexact c. exact d. inexact (π has an infinite number of decimal places.) 32. a. one significant figure (S.F.). The implied uncertainty is ±1000 pages. More significant figures should be added if a more precise number is known. b. two S.F. c. four S.F. d. two S.F. e. infinite number of S.F. (exact number) f. one S.F. 33. a. 6.07 × 10−15 ; 3 S.F. b. 0.003840; 4 S.F. c. 17.00; 4 S.F. d. 8 × 108; 1 S.F. e. 463.8052; 7 S.F. f. 300; 1 S.F. g. 301; 3 S.F. h. 300.;