QUICK QUIZ 1.1
For lead and aluminum, the ratio of their atomic masses is
about 8 and the ratio of their densities is about 4. This implies
that a given volume of lead will contain about (a) twice the
number of atoms as the same volume of aluminum, (b) half the
number of atoms as the same volume of aluminum, (c) one fourth
the number of atoms as the same volume of aluminum or, (d) one
eighth the number of atoms as the same volume of aluminum?
QUICK QUIZ 1.1 ANSWER
(b). If lead and aluminum had the same number of atoms for
the same given volume then their atomic mass ratio would
equal their density ratio. The lesser amount (4 compared to 8)
for the density ratio implies that a given volume of lead
contains about half the number of atoms as the same volume of
aluminum. Mathematically, one can look at the equation
.
relating the ratios,
.
atom s
m ass
m ass
lead
aluminum
volum e 
volum e X
atom ~ ( 4 ) X ( 1 )  1 .
atom s
m ass
m ass
1
8
2
aluminum
aluminum
lead
volum e
volum e
atom
lead
Verify that the units cancel in numerators and denominators to
yield the correct units on the left side of the equation.
QUICK QUIZ 1.2
The dimensions of two quantities must be
identical if you are either (a) adding or multiplying,
(b) adding or dividing, (c) subtracting or multiplying,
(d) subtracting or dividing, (e) adding or subtracting,
or (f) multiplying or dividing the two quantities?
QUICK QUIZ 1.2 ANSWER
(e). Only quantities of the same dimensions may be added or
subtracted. For example, you may add inches (length
dimension) to feet (length dimension) but could not add seconds
(time dimension) to kilograms (mass dimension). Different
dimensions may be multiplied or divided, for example it is
permissible to divide feet by seconds to obtain dimensions of
length/time.
QUICK QUIZ 1.3
In France, a liter of gasoline costs 1.3 Euros. An American
student is at a gas station in France and wants to know how many
gallons of gasoline she can buy with the 41 Euros that she has in her
pocket. Knowing that one liter is close to a quart and that there are 4
quarts in a gallon she reasons that she can buy (a) about 2 gallons, (b)
about 5 gallons, (c) about 8 gallons, (d) about 12 gallons of gasoline?
QUICK QUIZ 1.3 ANSWER
(c). Converting units we have:
41Euros X
1liter
1 quart 1 gallon 30
X
X
~
~ 8 gallons.
1.3 Euros 1liter
4 quarts 4
QUICK QUIZ 1.4
(end of section 1.6)
In an experiment to determine the identity of an
unknown sample, you measure the density of your
sample to be 0.315 grams/cm3. In a chemistry and
physics handbook, you find a chart listing the
densities of various materials from gases to solids.
Your sample is closest in density to the material in the
chart with a density of (a) 10.2 grams/cm3, (b) 2.01
grams/cm3, (c) 0.002 grams/cm3, or (d) 0.315 X 10-3
grams/cm3?
QUICK QUIZ 1.4 ANSWER
(b). When comparing numbers representing physical data, it is best
to compare the ratios or multiplicative factors of the two numbers
rather than the difference of the two numbers. In terms of
difference, material (c) is the closest to the unknown sample with a
difference of only 0.315 - 0.002 = .313 g/cm3. However, in terms of
ratios, material (b) is about 6 times denser than the unknown sample
while material (c) is about 160 times less dense than the unknown.
In fact, from these densities, material (c) must be a gas while
material (b) is a solid and the unknown could be a solid such as
Styrofoam. Another way to obtain a rough comparison between
values is to look at the order of magnitude of each number. Order of
magnitude values are 101, 100, 10-3, and 10-4 for materials (a), (b),
(c), and (d), respectively and 10-1 for the unknown sample.
Therefore, 10-1 (the unknown) is closest to 100 (material (b).
QUICK QUIZ 1.5
(end of section 1.7)
Unlike meter sticks that measure to a precision of + 0.1 cm, Vernier calipers
are devices that can measure to a precision of + 0.01 cm. In a lab experiment,
your partner measures the thickness of your textbook with a meter stick and
obtains a value of 4.3 cm. You then measure the thickness of the textbook
using the Vernier caliper. Assuming that neither instrument is broken and that
the measurements were made correctly, the value you would obtain using the
Vernier caliper could be (a) 4.30 cm, (b) 4.31 cm, (c) 4.24 cm, (d) 4.43 cm, (e)
4.30 or 4.31 cm, (f) 4.30, 4.31, or 4.24 cm, (g) 4.30, 4.31, 4.24, or 4.43 cm?
QUICK QUIZ 1.5 ANSWER
(f). The precision of the meter stick implies that the value of
4.3 cm can vary by + 0.1 cm and therefore from a range of
4.2 to 4.4 cm. Any value within this range could be obtained
by a measurement with the Vernier caliper and only the value
4.43 cm is outside of this range.