Download Chemistry 1000 (Fall 2007)

Chemistry 1000 (Fall 2013)
Problem Set #0: Math Review, Units and Significant Figures
Solutions
Answers to Questions in Silberberg (only those w/out answers at the back of the book)
1.22 From the glossary at the back of the text:
Mass is “the quantity of matter than an object contains”.
Weight is “the force exerted by a gravitational field on an object”.
As long as we are comparing samples experiencing the same gravitational field strength,
an object’s weight is directly proportional to its mass. When the gravitational field
strength changes, an object’s weight changes but its mass remains constant.
Since gravity is weaker on the moon than on earth, your weight will be lower on the
moon – even though your mass is the same in both locations.
1.24
Heat is a form of energy. Temperature is not.
Heat is an extensive property. Temperature is an intensive property.
From the glossary at the back of the text:
Heat is “the energy transferred between objects because of a difference in their
temperatures”.
To grasp the difference between the two concepts, imagine two cups of tea (or coffee).
One is a “large” and one is a “small”. Both begin at 100 C (same temperature). Both
are left to cool to room temperature (again, the same temperature). So, the temperature
change is the same for both drinks since temperature does not depend on the size of the
sample (making it an intensive property).
As the two drinks cool, heat is transferred from each drink to the surrounding air. More
heat is transferred from the “large” drink than from the “small” drink. So, the heat
change is *not* the same for the two drinks. Heat does depend on the size of the sample
(making it an extensive property).
1.25
The conversion from C to K involves adding 273.15. This is different from most other
unit conversions which typically involve multiplying by a given number. When you add
a constant to two different numbers, you change the ratio between them.
e.g. 2 C is twice as large as 1 C, but 275.15 K is not twice as large as 274.15 K.
1.49
An exact number is a number that is counted (rather than measured) or defined (e.g. the
fact that there are 100 cm in 1 m). It has no uncertainty associated with it. As such, it
can be considered to have an infinite number of significant figures and does not affect the
number of significant figures for any calculated value.
1.51
(a)
(b)
(c)
5 sig. fig.
It appears that the actual number of people was counted.
15,000 could correspond to any number between 14,501 and 15,499.
1.71
(a)
(b)
11.775g
g
 0.7850 mL
15.00mL
so the liquid is most likely isopropanol
The lowest density consistent with that level of precision would correspond to the
smallest mass and largest volume.
11.775  0.003g
15.00  0.02mL

11.772g
g
 0.7838 mL
15.02mL
The highest density consistent with that level of precision would correspond to the largest
mass and smallest volume.
11.775  0.003g
15.00  0.02mL

11.778g
g
 0.7862 mL
14.98mL
So, these readings using those instruments suggests a density between 0.7838 g/mL and
0.7862 g/mL. This range includes the density of isopropanol but not the density of
ethanol. It appears that this equipment is precise enough to distinguish between the two
solvents.
1.73
(a)
(b)
(c)
(d)
Exp II and Exp IV appear to give the same average result.
It’s hard to tell, but Exp I and Exp III may also give the same average result.
Exp III and Exp IV both display high precision.
Exp II and Exp IV both display high accuracy.
Exp I and Exp III both show systematic errors (resulting in low accuracy).
Additional Practice Problems
1.
For each of the following sentences, fill in the missing units choosing a unit that makes
the sentence make sense. If the measurement in the sentence could be reported using
more appropriate units, convert it into these units.
For these questions, there will often be more than one reasonable answer. I’ve included the
answers that first came to my mind but, as long as your sentences make sense (and the unit
conversion is done correctly), they’re fine.
(a)
My grandmother is 720 months old.
My grandmother is 60 years old.
sounds better
(b)
My brother is 1 meter tall.
(c)
I live across the street from the university. It’s only a 2.5 minute walk to class.
2.5 meters might be okay too (for a really narrow street!)
(d)
The temperature was only 270 K so I had to wear a sweater.
The temperature was only – 3˚C so I had to wear a sweater.
(e)
The density of water is 1000 g/L.
The density of water is 1 g/mL.
sounds better
or 1000 mg/mL, 1000 kg/kL, etc.
sounds better (or 1 kg/L)
2.
Give an example of an object whose mass is best expressed in:
(a)
μg
hair, dust, etc.
3.
The radius of a hydrogen atom is 0.529 Å. Report the radius of a hydrogen atom:
(a) in m
1010 m
0.529 A 
 5.29 1011 m
1A
(b)
(b) in pm
5.29  10 11 m 
(c) in nm
4.
5.29 10 11 m 
kg
person, dog, car, etc.
1012 pm
 5.29  101 pm  52.9 pm
1m
109 nm
 5.29 10  2 nm  0.0529nm
1m
Convert 100 nm3 into pm3.
note that
1 nm = 1000 pm
therefore
(1 nm)3 = (1000 pm)3
therefore
1 nm3 = 109 pm3
100nm3 
5.
g
(c)
book, candy bar, etc.
109 pm3
 1011 pm3
1nm3
Solve for A in each of the following equations. Report your answer using the correct
number of significant figures. Use scientific notation if necessary.
Note that rounding in answers is only done to show how the significant figures are carrying
through the calculation. All numbers are left in the calculator and the only “real” rounding is
done on the final answer! You don’t need to show this many steps but it does help prevent
mistakes.
(a)
13.4 A = 14.2 × 0.26 × 124
A
**2 sig. fig.**
14.2  0.26 124
 34
13.4
Multiplication and division only, so sig. fig. controlled by value with smallest number of
sig. fig. 0.26 has two sig. fig. so answer has two sig. fig.
(b)
16.37 A = 12.47 + 6.2
**3 sig. fig.**
A
12.47  6.2 18.7

 1.14
16.37
16.37
Sig. fig. in addition step controlled by value with least decimal places. 6.2 has one
decimal place so 18.7 has one decimal place. Sig. fig. in division step controlled by value
with smallest number of sig. fig. 18.7 has three sig. fig. so answer has three sig. fig.
(c)
4 A = 15 A – 3.21
**2 sig. fig.**
15 A  4 A  3.21
11A  3.21
A  0.29
(d)
63.5 A – 18.7 = 86 – 12.5 A
3  (63.5 A  18.7)  86  12.5 A
**1 sig. fig.**
(2 10 2 A)  (6 101 )  86  12.5 A
(2 10 2 A)  12.5  86  (6 101 )
(2 10 2 A)  1.4 10 2
A
(e)
A = (6.37 × 103) + (1.24 × 104)
1.4 10 2
 0.7
2 10 2
A  (0.637 104 )  (1.24 104 )  1.88 104
**3 sig. fig.**
Sig. fig. in addition step controlled by value with least decimal places after exponents are made
the same (both values are “× 104”). 1.24 has two decimal places so 1.88 has two decimal places.