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 an
1
,2 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 multi-
plication/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= mx + 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.; 3 S.F.
, 4 CHAPTER 1 CHEMICAL FOUNDATIONS
34. a. 100; 1 S.F. b. 1.0 × 102; 2 S.F. c. 1.00 × 103; 3 S.F.
d. 100.; 3 S.F. e. 0.0048; 2 S.F. f. 0.00480; 3 S.F.
g. 4.80 × 10 −3 ; 3 S.F. h. 4.800 × 10 −3 ; 4 S.F.
35. When rounding, the last significant figure stays the same if the number after this significant
figure is less than 5 and increases by one if the number is greater than or equal to 5.
a. 3.42 × 10 −4 b. 1.034 × 104 c. 1.7992 × 101 d. 3.37 × 105
36. a. 4 × 105 b. 3.9 × 105 c. 3.86 × 105 d. 3.8550 × 105
37. Volume measurements are estimated to one place past the markings on the glassware. The
first graduated cylinder is labeled to 0.2 mL volume increments, so we estimate volumes to
the hundredths place. Realistically, the uncertainty in this graduated cylinder is ±0.05 mL.
The second cylinder, with 0.02 mL volume increments, will have an uncertainty of ±0.005
mL. The approximate volume in the first graduated cylinder is 2.85 mL, and the volume in
the other graduated cylinder is approximately 0.280 mL. The total volume would be:
2.85 mL
+0.280 mL
3.13 mL
We should report the total volume to the hundredths place because the volume from the first
graduated cylinder is only read to the hundredths (read to two decimal places). The first
graduated cylinder is the least precise volume measurement because the uncertainty of this
instrument is in the hundredths place, while the uncertainty of the second graduated cylinder
is to the thousandths place. It is always the lease precise measurement that limits the
precision of a calculation.
38. a. Volumes are always estimated to one position past the marked volume increments. The
estimated volume of the first beaker is 32.7 mL, the estimated volume of the middle
beaker is 33 mL, and the estimated volume in the last beaker is 32.73 mL.
b. Yes, all volumes could be identical to each other because the more precise volume
readings can be rounded to the other volume readings. But because the volumes are in
three different measuring devices, each with its own unique uncertainty, we cannot say
with certainty that all three beakers contain the same amount of water.
c. 32.7 mL
33 mL
32.73 mL
98.43 mL = 98 mL
The volume in the middle beaker can only be estimated to the ones place, which dictates that
the sum of the volume should be reported to the ones place. As is always the case, the least
precise measurement determines the precision of a calculation.
39. For addition and/or subtraction, the result has the same number of decimal places as the
number in the calculation with the fewest decimal places. When the result is rounded to the
correct number of significant figures, the last significant figure stays the same if the number
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 an
1
,2 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 multi-
plication/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= mx + 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.; 3 S.F.
, 4 CHAPTER 1 CHEMICAL FOUNDATIONS
34. a. 100; 1 S.F. b. 1.0 × 102; 2 S.F. c. 1.00 × 103; 3 S.F.
d. 100.; 3 S.F. e. 0.0048; 2 S.F. f. 0.00480; 3 S.F.
g. 4.80 × 10 −3 ; 3 S.F. h. 4.800 × 10 −3 ; 4 S.F.
35. When rounding, the last significant figure stays the same if the number after this significant
figure is less than 5 and increases by one if the number is greater than or equal to 5.
a. 3.42 × 10 −4 b. 1.034 × 104 c. 1.7992 × 101 d. 3.37 × 105
36. a. 4 × 105 b. 3.9 × 105 c. 3.86 × 105 d. 3.8550 × 105
37. Volume measurements are estimated to one place past the markings on the glassware. The
first graduated cylinder is labeled to 0.2 mL volume increments, so we estimate volumes to
the hundredths place. Realistically, the uncertainty in this graduated cylinder is ±0.05 mL.
The second cylinder, with 0.02 mL volume increments, will have an uncertainty of ±0.005
mL. The approximate volume in the first graduated cylinder is 2.85 mL, and the volume in
the other graduated cylinder is approximately 0.280 mL. The total volume would be:
2.85 mL
+0.280 mL
3.13 mL
We should report the total volume to the hundredths place because the volume from the first
graduated cylinder is only read to the hundredths (read to two decimal places). The first
graduated cylinder is the least precise volume measurement because the uncertainty of this
instrument is in the hundredths place, while the uncertainty of the second graduated cylinder
is to the thousandths place. It is always the lease precise measurement that limits the
precision of a calculation.
38. a. Volumes are always estimated to one position past the marked volume increments. The
estimated volume of the first beaker is 32.7 mL, the estimated volume of the middle
beaker is 33 mL, and the estimated volume in the last beaker is 32.73 mL.
b. Yes, all volumes could be identical to each other because the more precise volume
readings can be rounded to the other volume readings. But because the volumes are in
three different measuring devices, each with its own unique uncertainty, we cannot say
with certainty that all three beakers contain the same amount of water.
c. 32.7 mL
33 mL
32.73 mL
98.43 mL = 98 mL
The volume in the middle beaker can only be estimated to the ones place, which dictates that
the sum of the volume should be reported to the ones place. As is always the case, the least
precise measurement determines the precision of a calculation.
39. For addition and/or subtraction, the result has the same number of decimal places as the
number in the calculation with the fewest decimal places. When the result is rounded to the
correct number of significant figures, the last significant figure stays the same if the number
