Answer Key
Chapter 13: Standard Review Worksheet
1. While the barometer is used to measure atmospheric pressure, a device called a mercury
manometer is used to measure the pressure of samples of gas in the laboratory. A
manometer consists basically of a U-shaped tube filled with mercury, with one arm of the
U open to the atmosphere. If the pressure of the gas sample equals atmospheric pressure,
then the mercury levels will be the same in both sides of the U. If the pressure of the gas is
not the same as the atmospheric pressure, then the difference in height of the mercury
levels can be sued to determine by how many mm Hg the pressure of the gas sample differs
from atmospheric pressure.
2. The expression P _ V = constant is Boyle’s law. In order for the product (P _ V) to remain
constant, if one of these terms increases, the other must decrease. A second formulation of
Boyle’s law is one more commonly used in solving problems:
P 1 _ V 1 = P2 _ V 2
With this second formulation, we can determine pressure–volume information about a
given sample under two sets of conditions. These two mathematical formulas are just two
different ways of saying the same thing: If the pressure on a sample of gas is increased, the
volume of the sample of gas will decrease. A graph of Boyle’s law data is given in Figure
13.5. This sort of graph (xy = k) is known to mathematicians as a hyperbola.
3. The qualification is necessary because the volume of a gas sample depends on all its
properties. The properties of a gas are all interrelated (as shown by the ideal gas law, PV =
nRT). If we want to use one of the derivative gas laws (Boyle’s, Charles’s, or Avogadro’s
gas laws), which isolate how the volume of a gas sample varies with just one of its
properties, then we must keep all the other properties constant while that one property is
studied.
4. Charles’s law is a direct proportionality when the temperature is expressed in Kelvins (if
you increase T, this increases V), whereas Boyle’s law is an inverse proportionality (if you
increase P, this decreases V).
5. Charles’s law holds true only if the amount of gas remains the same (for example, the
volume of a gas sample would increase if there were more gas present) and also if the
pressure remains the same (a change in pressure also changes the volume of a gas sample).
6. Avogadro’s law is a direct proportionality: The greater the number of gas molecules in a
sample, the larger the sample’s volume will be.
7. Comparing the volumes of two samples of the same gas to determine the relative amount of
gas present in the samples requires that the two samples of gas are at the same pressure and
temperature. The volume of a sample of gas would vary with either temperature (according
to Charles’s law) or pressure (according to Boyle’s law) or both. Avogadro’s law holds true
for comparing gas samples that are under the same conditions of pressure and temperature.
8. Boyle’s law states that the volume of a gas is inversely proportional to its pressure (at
constant temperature for a fixed amount of gas):
V = (constant)/P
Charles’s law indicates that the volume of a gas sample is related to its temperature (at
constant pressure for a fixed amount of gas):
V = (constant) _ T
Avogadro’s law states that the volume of a gas sample is proportional to the number of
moles of gas (at constant pressure and temperature):
V = (constant) _ n
We can combine all these relationships (and constants) to show how the volume of a gas is
proportional to all its properties simultaneously:
V = (constant) _ Tn
P
This can be arranged to the familiar form of the ideal gas law: PV = nRT.
9. Use P1V1 = P2V2.
(3.2 atm)(25.0 L) = P2 (45.0 L)
1.78 atm = P2
10. Use
V1
T1
=
V2
.
T2
21.5 L
V2
=
[(45+ 273) K] [(-37+ 273) K]
16.0 L = V2
11. Since both samples are hydrogen, the number of moles is directly related to mass; thus use
V1
Mass1
=
V2
mass2
21.6 L
V2
=
32.8 g 12.3 g
8.10 L = V2
12. Use
PV
11
T1
=
PV
22
T2
.
(3.14 atm) (2.97
= ()P2 (1.04 L)
[(38+ 273)K]
[(118+ 273) K]
11.3 atm = P2
13. Use PV = nRT, n =
P = 475 mm Hg _
PV
RT
.
1 atm
=
760 mm H
0.625 atm
(0.625 atm) (1.25 L)
= 0.0379
L atm
(0.08206 ) [(22+
273)K]
mol K
0.0379 mol O2 _ 32.00 g 2O = 1.21 g O2
1 mol O
2
n=
mol O2
14. The total pressure in a mixture of gases is the sum of the individual partial pressures of the
gases present in a mixture.
15. When a gas is collected by displacement of water from a container, the gas becomes
saturated with water vapor. The collected gas is actually a mixture of the desired gas and
water vapor. To determine the partial pressure of the desired gas in the mixture, it is
necessary to subtract the pressure of water vapor from the total pressure of the sample:
Pgas = Ptotal – Pwater vapor
Dalton’s law of partial pressures states that the total pressure in a mixture of gases is the
sum of the partial pressures of the components of the mixture. Since the saturation pressure
of water vapor is a function only of temperature, such water vapor pressures are
conveniently tabulated (see Table 13.2 in the text).
16. 12.5 g O2 _
1 mol O
2
=
32.00 g 2O
0.391 mol O2
25.0 g N2 _
1 mol N2
=
28.02 g 2N
0.892 mol N2
PO 2 =
L atm
(0.391 mol) (0.08206 )[(28273)K]
+
mol K
(25.0 L)
PN 2 =
K atm
(0.892 mol) (0.08206 )[(28273)K]
+
mol K
(25.0 L)
= 0.386 atm
= 0.881 atm
Ptotal = 1.267 atm
17. PH 2 O = 31.8 torr _
1 atm
=
760 tor
0.0418 atm
PO 2 = 1.10 atm – 0.0418 atm = 1.06 atm
V=
K atm
(0.80 mol) (0.08206 )[(30273)K]
+
mol K
(1.06 atm)
V = 18.8 L
18. The main postulates of the kinetic-molecular theory for gases are as follows: (a) Gases
consist of tiny particles (atoms or molecules), and the size of these particles themselves is
negligible compared with the bulk volume of a gas sample; (b) the particles in a gas are in
constant random motion, colliding with the walls of the container; (c) the particles in a gas
sample do not exert any attractive or repulsive forces on one another; and (d) the average
kinetic energy of the particles in a sample of gas is directly related to the absolute
temperature of the gas sample. The pressure exerted by a gas is a result of the molecules
colliding with (and pushing on) the walls of the container. The pressure increases with
temperature because at a higher temperature the molecules are moving faster and hit the
walls of the container with greater force. A gas fills whatever volume is available to it
because the molecules in a gas are in constant random motion. If the motion of the
molecules is random, they eventually will move out into whatever volume is available until
the distribution of molecules is uniform. At constant pressure, the volume of a gas sample
increases as the temperature is increased because with each collision having greater force,
the container must expand so that the molecules hit the walls less frequently to maintain the
same pressure.
19. The balanced equation is Zn + 2HCl
10.0 g Zn _
1 mol Zn
_ 1 mol H2
65.38 g Zn 1 mol Zn
0.200 mol HCl _
1 mol H2
2 mol HCl
ZnCl2 + H2.
= 0.153 mol H2
= 0.100 mol H2
Thus 0.100 mol H2 is produced because HCl is limiting.
V=
K atm
(0.100 mol) (0.08206 )[(22273)K]
+
mol K
1 atm
(755 atm
)
760 mm Hg
V = 2.44 L
20. Gases do not behave most ideally at STP. Standard temperature and pressure (0°C, 1 atm)
is chosen as standard because it is easy to produce these conditions in the lab, not because
gases behave most ideally at these conditions. Many students believe this to be the case,
however.