Chapter 10
Practice Exercises
10.1
⎛ 14.7 psi ⎞
psi = 730 mm Hg ⎜
⎟ = 14.1 psi
⎝ 760 mm Hg ⎠
⎛ 29.921 in. Hg ⎞
in. Hg = 730 mm Hg ⎜
⎟ = 28.7 in. Hg
⎝ 760 mm Hg ⎠
10.2
⎛ 1 bar ⎞ ⎛ 1 atm ⎞⎛ 101,325 Pascal ⎞
Pascals = 888 mbar ⎜
⎟⎜
⎟⎜
⎟ = 88,800 Pascal
1 atm
⎝ 1000 mbar ⎠ ⎝ 1.013 bar ⎠⎝
⎠
⎛ 1 bar ⎞ ⎛ 1 atm ⎞⎛ 760 torr ⎞
torr = 888 mbar ⎜
⎟⎜
⎟⎜
⎟ = 666 torr
⎝ 1000 mbar ⎠ ⎝ 1.013 bar ⎠⎝ 1 atm ⎠
10.3
⎛ 10 mm Hg ⎞
mm Hg = 25 cm Hg ⎜
⎟ = 250 mm Hg
⎝ 1 cm Hg ⎠
⎛ 760 mm Hg ⎞
mm Hg = 770 torr ⎜
⎟ = 770 mm Hg
⎝ 760 torr ⎠
The maximum pressure = 770 mm Hg + [(250 mm Hg) × 2] = 1270 mm Hg
The minimum pressure = 770 mm Hg – [(250 mm Hg) × 2] = 270 mmHg
10.4
The pressure of the gas in the manometer is the pressure of the atmosphere less the pressure of the mercury,
10.7 cm Hg.
Using the pressure in the atmosphere from the previous example:
⎛ 10 mm Hg ⎞
mm Hg = 10.7 cm Hg ⎜
⎟ = 107 mm Hg
⎝ 1 cm Hg ⎠
770 mm Hg – 107 mm Hg = 663 mm Hg
10.5
10.6
P1V1 P2 V2
=
T1
T2
V2 = 3V1 and T2 = 2T1
P1V1 P2 3V1
=
T1
2T1
P2 = 2/3 P1
The pressure must change by 2/3.
Since volume is to decrease, pressure must increase, and we multiply the starting pressure by a volume
ratio that is larger than one. Also, since P1V1 = P2V2, we can solve for P2:
P2 =
10.7
P1V1
=
V2
( 740 torr )(880 mL )
(870 mL )
= 750 torr
In general the combined gas law equation is:
P2
PVT
= 1 1 2 =
T1V2
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
( 745 torr ) ( 950 m3 ) ( 333.2 K )
(1150 m ) ( 298.2 K )
3
207
= 688 torr
Chapter 10
10.8
10.9
10.10
When gases are held at the same temperature and pressure, and dispensed in this fashion during chemical
reactions, then they react in a ratio of volumes that is equal to the ratio of the coefficients (moles) in the
balanced chemical equation for the given reaction. We can, therefore, directly use the stoichiometry of the
balanced chemical equation to determine the combining ratio of the gas volumes:
⎛ 2 volume O2 ⎞
L O2 = (4.50 L CH4) ⎜
⎟ = 9.00 L O2
⎝ 1 volume CH 4 ⎠
⎛ 2 volume O2 ⎞
L O2 = (6.75 L CH4) ⎜
⎟ = 13.50 L O2
⎝ 1 volume CH 4 ⎠
13.50 L O2
× 100%
21% O2 =
x L air
⎛ 100% ⎞
L air = (13.50 L O2) ⎜
⎟ = 64.3 L air
⎝ 21% ⎠
Starting with the combined gas law:
P1V1
PV
= 2 2
T1
T2
Rearrange the equation to find a new volume (V2)
PVT
V2 = 1 1 2
T1P2
Calculate the new volume for the butane (C4H10) using the temperature and pressure of the oxygen (O2)
( 760 torr )( 75.0 mL )( 308 K )
V2 =
= 76.1 mL C4H10
( 318 K )( 725 torr )
Now calculate the number of mL of O2 require to react with 76.1 mL C4H10
⎛ 13 volume O 2 ⎞
mL O2 = 76.1 mL C4H10 ⎜
⎟ = 495 mL O2
⎝ 2 volume C4 H10 ⎠
10.11
First determine the number of moles of CO2 in the tank:
PV
n=
RT
⎛ 1 atm ⎞
P = 2000 psig ⎜
⎟ = 140 atm
⎝ 14.696 psig ⎠
⎛ ( 30.48 cm )3 ⎞ ⎛ 1 mL ⎞
⎛ 1L ⎞
⎟⎜
3⎜
V = 6.0 ft ⎜
3
3 ⎟ ⎜ 1000 mL ⎟ = 170 L
⎟
⎝
⎠
⎝ (1 ft )
⎠ ⎝ 1 cm ⎠
L ⋅ atm
mol ⋅ K
T = 22 °C + 273 = 295 K
R = 0.0821
mol CO2 in the tank =
(140 atm )(170 L )
L ⋅ atm 295 K
)
( 0.0821 mol
⋅ K )(
= 980 mol CO2
Then find the total number of grams of CO2 in the tank, MW CO2 = 44.01 g/mol
⎛ 44.01 g CO 2 ⎞
g CO2 in the tank = 980 mol CO2 ⎜
⎟ = 43,000 g CO2
⎝ 1 mol CO2 ⎠
Amount of solid CO2 = 43,000 g CO2 × 0.35 = 15,000 g solid CO2
208
Chapter 10
10.12
n=
PV
=
RT
( 57.8 atm )(12.0 L )
L atm 298 K
)
( 0.0821 mol
K )(
= 28.3 moles gas
28.3 mol Ar (39.95 g Ar/mol) = 1,130 g Ar
10.13
Find the number of moles of air
(1.0000 atm )( 0.54423 L ) = 0.024281 mol air
PV
=
n=
RT
0.082057 L atm ( 273.15 K )
(
mol K
)
⎛ 28.8 g air ⎞
Mass of the air = (0.024281 mol air) ⎜
⎟ = 0.699 g air
⎝ 1 mol air ⎠
The mass of the flask = 735.6898 g – 0.699 g air = 734.991 g
Mass of the organic compound = 735.6220 g – 734.991 g = 0.631 g
The number of moles of the organic compound equals the number of moles of air:
0.631 g organic compound
= 26.0 g/mol
MW =
0.024281 mole organic compound
10.14
Since PV = nRT, then n = PV/RT
⎛ 1 atm ⎞
685 torr ) ⎜
(
⎟ ( 0.300 L )
PV
⎝ 760 torr ⎠
n =
=
= 0.0110 moles gas
RT
0.0821 L atm ( 300.2 K )
(
mol K
)
1.45 g
= 132 g mol−1
0.0110 mol
The gas must be xenon.
molar mass =
10.15
⎛ 28.8 g air ⎞ ⎛ 1 mol air ⎞
Density of air = 1 mol air ⎜
⎟⎜
⎟ = 1.29 g/L
⎝ 1 mol air ⎠ ⎝ 22.4 L ⎠
⎛ 222.0 g Rn ⎞ ⎛ 1 mol Rn ⎞
Density of radon at STP = 1 mol Rn ⎜
⎟⎜
⎟ = 9.91 g/L
⎝ 1 mol Rn ⎠ ⎝ 22.4 L ⎠
Since radon is almost eight times denser than air, the sensor should be in the lowest point in the house: the
basement.
10.16
d = m/V
Taking 1.00 mol SO2:
m = 64.1 g
nRT
V=
=
P
density =
(1.00 mol ) ( 0.0821
L atm
mol K
) ( 253.15 K )
1 atm
⎛
⎞
⎜ 96.5 kPa 101.325 kPa ⎟
⎝
⎠
64.1 g
= 2.94 g/L
21.8 L
209
= 21.8 L = 21,800 mL
Chapter 10
10.17
In general PV = nRT, where n = mass × formula mass. Thus
mass
RT
formula mass
We can rearrange this equation to get;
(mass/V)RT dRT
=
formula mass
P
P
PV =
(5.60 g L ) ( 0.0821
formula mass =
−1
L atm
mol K
) ( 296.2 K )
L atm
mol K
) ( 313.2 K )
= 138 g mol–1
⎛ 1 atm ⎞
( 750 torr ) ⎜
⎟
⎝ 760 torr ⎠
The empirical mass is 69 g mol–1. The ratio of the molecular mass to the empirical mass is
138 g mol-1
=2
69 g mol-1
Therefore, the molecular formula is 2 times the empirical formula, i.e., P2F4.
10.18
formula mass
(mass/V)RT dRT
=
P
P
(5.55 g L ) ( 0.0821
formula mass =
−1
(1.25 atm )
= 114 g mol–1
9 C and 6 H
8 C and 18 H
7 C and 30 H
6 C and 42 H
5 C and 54 H
4 C and 66 H
3 C and 78 H
2 C and 90 H
1 C and 102 H
The most probable compound is C8H18 also known as octane.
10.19
CS2(g) + 3O2(g) J 2SO2(g) + CO2(g)
⎛ 1 mol CS2 ⎞
mol of CS2 = 10.0 g CS2 ⎜
⎟ = 0.131 mol CS2
⎝ 76.15 g CS2 ⎠
⎛ 1 mol CO2 ⎞
mol CO2 = 0.131 mol CS2 ⎜
⎟ = 0.131 mol CO2
1
mol
CS
2
⎝
⎠
⎛ 2 mol SO2 ⎞
mol SO2 = 0.131 mol CS2 ⎜
⎟ = 0.262 mol SO2
⎝ 1 mol CS2 ⎠
L CO2 =
L SO2 =
L⋅atm 301 K
( 0.131 mol CO2 ) ( 0.0821 mol
)
⋅K ) (
⎛
⎛ 1 atm ⎞ ⎞
⎜ 880 torr ⎜
⎟⎟
⎝ 760 torr ⎠ ⎠
⎝
L⋅atm 301 K
( 0.262 mol SO2 ) ( 0.0821 mol
)
⋅K ) (
⎛
⎛ 1 atm ⎞ ⎞
⎜ 880 torr ⎜
⎟⎟
⎝ 760 torr ⎠ ⎠
⎝
The total number of liters is = 8.40 L.
210
= 2.80 L CO2
= 5.60 L SO2
Chapter 10
10.20
CaCO3(s) J CaO(s) + CO2(s)
mol CO2 =
PV
=
RT
( 738 torr ) ⎛⎜
1 atm ⎞
⎟ ( 0.250 L )
⎝ 760 torr ⎠
L atm 296 K
)
( 0.0821 mol
K )(
= 0.00999 mol CO2
⎛ 1 mol CaCO3 ⎞
mol CaCO3 = 0.00999 mol CO2 ⎜
⎟ = 0.00999 mol CaCO3
⎝ 1 mol CO 2 ⎠
100.09 g CaCO3 ⎞
g CaCO3 = 0.00999 mol CaCO3 ⎛⎜
⎟ = 1.00 g CaCO3
⎝ 1 mol CaCO3 ⎠
10.21
⎛ 1 mol Ar ⎞
mol Ar = 10.0 g Ar ⎜
⎟ = 0.250 mol Ar
⎝ 39.95 g Ar ⎠
PAr =
( 0.250 mol Ar ) ( 0.0821
1.00 L
L⋅atm
mol⋅K
) ( 293 K ) = 6.01 atm
⎛ 1 mol N 2 ⎞
mol N2 = 10 g N2 ⎜
⎟ = 0.357 mol N2
⎝ 28.02 g N 2 ⎠
P N2 =
( 0.357 mol N 2 ) ( 0.0821
L⋅atm
mol⋅K
1.00 L
) ( 293 K ) = 8.59 atm
⎛ 1 mol O 2 ⎞
mol O2 = 10 O2 ⎜
⎟ = 0.313 mol O2
⎝ 32.00 g O 2 ⎠
P O2 =
( 0.313 mol O2 ) ( 0.0821
L⋅atm
mol⋅K
) ( 293 K )
= 7.53 atm
1.00 L
Ptotal = PAr + PN2 + PO2 = 6.01 atm + 8.59 atm + 7.53 atm = 22.13 atm
10.22
We can determine the pressure due to the oxygen since Ptotal = PN2 + PO2.
PO2 = Ptotal – PN2 = 237.0 atm – 115.0 atm = 122.0 atm. We can now use the ideal gas law to determine the
number of moles of O2:
PV
(122.0 atm)(17.00 L)
=
= 84.8 mol O2
L atm ⎞
RT
⎛
0.0821
(298
K)
⎜
mol K ⎟⎠
⎝
⎛ 32.0 g O2 ⎞
g O2 = (84.8 mol O2) ⎜
⎟ = 2713 g O2
⎝ 1 mol O2 ⎠
n=
10.23
The total pressure is the pressure of the methane and the pressure of the water. We can determine the
pressure of the methane by subtracting the pressure of the water from the total pressure.
The pressure of the water is determined by the temperature of the sample. At 30 °C, the partial pressure of
water is 31.82 torr.
PCH4 = Ttotal – Pwater = 775 torr – 31.82 torr = 743.18 torr
The pressure in the flask is 743.18 torr.
⎛ 1 atm ⎞
(743.18 torr) ⎜
⎟ (2.50 L)
760 torr ⎠
PV
⎝
mol CH4 =
= 0.0983 mol CH4
=
L atm ⎞
RT
⎛
⎜ 0.0821 mol K ⎟ (303 K)
⎝
⎠
211
Chapter 10
10.24
First we find the partial pressure of nitrogen, using the vapor pressure of water at 15 °C:
PN2 = Ptotal – Pwater = 745 torr – 12.79 torr = 732 torr.
To calculate the volume of the nitrogen we can use the combined gas law
P1V1
PV
= 2 2
T1
T2
For this problem,
V2 =
P1V1T2
(732 torr)(0.310 L)(273 K)
=
= 283 mL
P2 T1
(760 torr)(288 K)
10.25
Since the stoichiometric ratio of the SO2 and SO3 are the same, the pressure in the flask after the reaction
when the only substance in the flask is SO3 will be the same as the pressure in flask when there is just SO2,
0.750 atm. The pressure will be 1.125 atm when the O2 is just added.
10.26
Find the number of moles of both the H2 and NO then find the mol fractions.
⎛ 1 mol H 2 ⎞
mol H2 = (2.15 g H2) ⎜
⎟ = 1.07 mol H2
⎝ 2.016 g H 2 ⎠
⎛ 1 mol NO ⎞
mol NO = (34.0 g NO) ⎜
⎟ = 1.13 mol NO
⎝ 30.01 g NO ⎠
1.07 mol H 2
χ H2 =
= 0.486
1.13 mol NO + 1.07 mol H 2
χNO =
1.13 mol NO
= 0.514
1.13 mol NO + 1.07 mol H 2
PH2 = (Ptotal)(χH2) = (2.05 atm)(0.486) = 0.996 atm
PNO = (Ptotal)(χNO) = (2.05 atm)(0.514) = 1.05 atm
10.27
The mole fraction is defined in Equation 10.5:
PO2
116 torr
XO2 =
=
= 0.153 or 15.3%
Ptotal
760 torr
10.28
effusion rate (Br − 81)
=
effusion rate (Br − 79)
10.29
Use Equation 10.7;
effusion rate (HX)
=
effusion rate (HCl)
M Br −79
=
M Br −81
78.9
= 0.988
80.9
M HCl
M HX
⎛ effusion rate (HX) ⎞
M HX = M HCl × ⎜
⎟
⎝ effusion rate (HCl) ⎠
2
= 36.46 g mol−1 × (1.88) 2 = 128.9 g mol−1
The unknown gas must be HI.
212
Chapter 10
Review Questions
10.1
The reason it hurts more to be jabbed by a point of a pencil rather than the eraser, even though the force is
the same, is because the area of the point is smaller than the area of the eraser, and therefore, the pressure is
higher.
10.2
Since the density of water is approximately 13 times smaller than that of mercury, a barometer constructed
with water as the moveable liquid would have to be some 13 times longer than one constructed using
mercury. Also, the vapor pressure of water is large enough that the closed end of the barometer may fill
with sufficient water vapor so as to affect atmospheric pressure readings. In fact, the measurement of
atmospheric pressure at normal temperatures would be about 18 torr too low, due to the presence of water
vapor in the closed end of the barometer.
10.3
(a)
(b)
(c)
(d)
(e)
(f)
1 atm
101.325 kPa
and
101.325 kPa
1 atm
1 mm Hg
1 torr
and
1 torr
1 mm Hg
760 torr
1 atm
and
1 atm
760 torr
101,325 Pa
760 torr
and
760 torr
101,325 Pa
101,325 Pa
1.013 bar
and
1.013 bar
101,325 Pa
1 bar
0.9868 atm
and
0.9868 atm
1 bar
10.4
A closed–end manometer reads pressure without the need to correct for atmospheric pressure.
10.5
(a)
(b)
(c)
(d)
Temperature–Volume Law: The volume of a given mass of a gas is directly proportional to the
Kelvin temperature, provided the pressure is held constant:
V ∝ T or V1/T1 = V2/T2, at constant P. This is Charles' Law.
Temperature–Pressure Law: The pressure of a gas is directly proportional to the Kelvin
temperature, provided the volume is held constant:
P ∝ T or P1/T1 = P2/T2, at constant V. This is Gay-Lussac’s Law.
Pressure–Volume Law: The volume of a given mass of a gas is inversely proportional to the
pressure, provided the temperature is held constant:
V ∝ 1/P or P1V1 = P2V2, at constant T. This is Boyle's Law.
Combined Gas Law: The pressure and volume of a gas are directly proportional to the Kelvin
temperature, provided the number of particles is held constant.
PV ∝ T or P1V1/T1 = P2V2/T2, at constant n.
R = 0.0821 L atm mol–1 K–1
10.6
PV = nRT;
10.7
Mole fraction is the ratio of the number of moles of one component of a mixture to the total number of
moles of all components.
10.8
An ideal gas obeys the gas laws over all pressures and temperatures. A real gas behaves most like an ideal
gas at low pressures and high temperatures.
10.9
(a)
(b)
(c)
(d)
number of moles and temperature
number of moles and pressure
number of moles and volume
number of moles
213
Chapter 10
10.10
Ptotal = Pa + Pb + Pc + ···
10.11
Middle drawing
Left drawing:
A: 0.500 atm
Middle drawing: A: 0.600 atm
Right drawing A: 0.667 atm
B: 0.500 atm
B: 0.400 atm
B: 0.333 atm
10.12
Diffusion is the spontaneous intermingling of one substance with another while effusion is the movement
of a gas through a very tiny opening into a region of lower pressure.
dB
MB
effusion rate (A)
=
=
effusion rate (B)
dA
MA
10.13
A gas consists of hard, super small or volumeless particles in random motion, and the particles neither
attract nor repel one another.
10.14
The minimum temperature corresponds to zero kinetic energy, which is accomplished only when velocity is
zero. In other words, the molecules have ceased all movement.
10.15
(a)
(b)
As the pressure of a gas increases, the rate of effusion should increase since the molecules will hit
the walls of the container more frequently and with greater force. If the molecules hit more
frequently, they are more likely to go through the small openings in the walls of the container.
As the temperature of the gas increases, the rate of effusion will increase since temperature is
proportional to kinetic energy which is dependent on the velocity of the particles. The faster the
particles move, the more likely they are to hit the walls and pass through the small openings.
10.16
The increase in temperature requires an increase in kinetic energy. This can happen only if the gas
velocities increase. Higher velocities cause the gas particles to strike the walls of the container with more
force, and this in turn causes the container to expand if a constant pressure is to be maintained.
10.17
The temperature and pressure will decrease.
10.18
The increase in temperature causes an increase in the force with which the gas particles strike the container
walls. If the container cannot expand, an increase in pressure must result.
10.19
The answer (c) NH3 will have the largest ν rms since it has the lowest molecular mass.
10.20
It is not true that the gas particles occupy no volume themselves, apart from the volume between the gas
particles. Also, it is not true that the gas particles exert no force on one another. In other words, real
molecules occupy space and attract or repel one another. Because of short-range interactions, it is also not
true that particles travel always in straight paths.
10.21
(b) has a larger value of the van der Waals constant b, since it is a larger molecule.
10.22
A small value for the constant a suggests that the gas molecules have weak forces of attraction among
themselves.
10.23
The helium atoms are moving faster than the argon atoms because they have less mass and the rate of
effusion is inversely proportional to mass.
10.24
Under the same conditions of T and V, the pressure of a real gas is less than the pressure of an ideal gas
because real gases do not have perfectly elastic collisions and may clump together and stick to the walls of
the container, thus decreasing the number of collisions the gas makes. The volume of a real gas is greater
than the volume of an ideal gas because the atoms and molecules take up space.
214
Chapter 10
Review Problems
10.25
10.26
10.27
10.28
(a)
⎛ 760 torr ⎞
torr = (0.329 atm) ⎜
⎟ = 250 torr
⎝ 1 atm ⎠
(b)
⎛ 760 torr ⎞
torr = (0.460 atm) ⎜
⎟ = 350 torr
⎝ 1 atm ⎠
(a)
⎛ 1 atm ⎞
atm = (595 torr) ⎜
⎟ = 0.783 atm
⎝ 760 torr ⎠
(b)
⎛ 1 atm ⎞
atm = (160 torr) ⎜
⎟ = 0.211 atm
⎝ 760 torr ⎠
(c)
⎛ 1 atm ⎞
= 3.95 × 10–4 atm
atm = (0.300 torr) ⎜
⎟
⎝ 760 torr ⎠
(a)
⎛ 760 torr ⎞
torr = (1.26 atm) ⎜
⎟ = 958 torr
⎝ 1 atm ⎠
(b)
⎛ 1 atm ⎞
atm = (740 torr) ⎜
⎟ = 0.974 atm
⎝ 760 torr ⎠
(c)
⎛ 760 torr ⎞
mm Hg = 738 torr ⎜
⎟ = 738 mm Hg
⎝ 760 mm Hg ⎠
(d)
⎛
⎞
760 torr
torr = (1.45 × 103 Pa) ⎜
⎟ = 10.9 torr
5
⎝ 1.01325 × 10 Pa ⎠
(a)
⎛ 760 torr ⎞
torr = (0.625 atm) ⎜
⎟ = 475 torr
⎝ 1 atm ⎠
(b)
⎛ 1 atm ⎞
atm = (825 torr) ⎜
⎟ = 1.09 atm
⎝ 760 torr ⎠
(c)
⎛ 760 torr ⎞
torr = 62 mm Hg ⎜
⎟ = 62 torr
⎝ 760 mm Hg ⎠
(d)
⎛ 1.013 bar ⎞
bar = 1.22 kPa ⎜
⎟ = 0.0122 bar
⎝ 101.32 kPa ⎠
10.29
In a closed-end manometer the difference in height of the mercury levels in the two arms corresponds to the
pressure of the gas. Therefore, the pressure of the gas is 125 mm Hg.
⎛ 760 torr ⎞
125 mm Hg ⎜
⎟ = 125 torr
⎝ 760 mm Hg ⎠
10.30
The closed-end manometer data indicates that the pressure inside the flask is 236 mm Hg. The open-end
manometer data indicate that Patm = 512 mm Hg + 236 mm Hg = 748 mm Hg.
215
Chapter 10
10.31
765 torr – 720 torr = 45 torr
⎛ 760 mm Hg ⎞
45 torr ⎜
⎟ = 45 mm Hg
⎝ 760 torr ⎠
⎛ 1 cm ⎞
cm Hg = (45 mm Hg) ⎜
⎟ = 4.5 cm Hg
⎝ 10 mm ⎠
gas
4.5 cm
10.32
820 torr – 750 torr = 70 torr
⎛ 760 mm Hg ⎞
70 torr ⎜
⎟ = 70 mm Hg
⎝ 760 torr ⎠
⎛ 1 cm ⎞
cm Hg = (70 mm Hg) ⎜
⎟ = 7.0 cm Hg
⎝ 10 mm ⎠
gas
7.0 cm
10.33
⎛ 760 torr ⎞
65 mm Hg ⎜
⎟ = 65 torr
⎝ 760 mm Hg ⎠
748 torr + 65 torr = 813 torr
10.34
⎛ 760 torr ⎞
82 mm Hg ⎜
⎟ = 82 torr
⎝ 760 mm Hg ⎠
752 torr – 82 torr = 670 torr
216
Chapter 10
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
PVT
(740 torr)(2.58 L)(348.2 K)
= 796 torr
P2 = 1 1 2 =
T1V2
(297.2 K)(2.81 L)
10.35
In general the combined gas law equation is:
10.36
In general the combined gas law equation is:
10.37
Use Boyle’s Law to solve for the second volume:
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
P1V1T2
(0.985 atm)(648 mL)(336.2 K)
=
= 1.08 atm
P2 =
T1V2
(289.2 K)(689 mL)
V2 =
10.38
P1V1
=
P2
( 255 mL )( 725 torr )
365 torr
= 507 mL
P1V1 = P2V2
PV
V2 = 1 1 since the pump has a fixed diameter, the length of the tube is proportional to its volume
P2
P1A1 = P2A2
A2 =
P1A1
1 atm(75.0 cm)
=
= 13.6 cm
P2
5.50 atm
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
PVT
(373 torr)(9.45 L)(293.2 K)
= 219.8 K = − 53.4 D C
T2 = 2 2 1 =
P1V1
(761 torr)(6.18 L)
10.39
In general the combined gas law equation is:
10.40
In general the combined gas law equation is:
10.41
Use Charles’s Law to solve the second volume:
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
PVT
(2.00 atm)(220 mL)(298.2 K)
= 191 K = − 82.2 D C
T2 = 2 2 1 =
P1V1
(1.51 atm)(455 mL)
VT
3.86 L (353 K)
= 4.28 L
V2 = 1 2 =
T1
318 K
10.42
Use Charles’s Law to solve for the second volume:
VT
2.50 L (258 K)
= 2.19 L
V2 = 1 2 =
T1
295 K
10.43
Compare pressure change to temperature to solve for temperature change:
(1700 torr )( 558 K )
PT
= 1116 K = 1120 K
1116 K – 273 K = 843 °C
T2 = 2 1 =
P1
850 torr
217
Chapter 10
PT
= 1 2 =
T1
( 45 lb in ) (316 K)
−2
= 50.2 lb in −2
10.44
P2
10.45
In general the combined gas law equation is
V2 =
10.46
10.48
10.49
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
P1V1T2
(745 torr)(2.68 L)(648.2 K)
=
= 5.73 L
T1P2
(297.2 K)(760 torr)
In general the combined gas law equation is:
V2 =
10.47
283 K
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
P1V1T2
(741 torr)(280 mL)(306.2 K)
=
= 287 mL
T1P2
(291.2 K)(760 torr)
⎛
⎛ 1 mol ⎞ ⎞ ⎛
L atm ⎞
( 300 K )
⎜⎜ 10.0 g ⎜
⎟ ⎟⎟ ⎜ 0.0821
32.0
g
mol
K ⎟⎠
nRT
⎝
⎠⎠⎝
⎛ 760 torr ⎞
⎝
P =
=
= 3.08 atm ⎜
⎟ = 2340 torr
V
2.50
L
(
)
⎝ 1 atm ⎠
⎛
⎛ 1 mol ⎞ ⎞ ⎛
L atm ⎞
( 381 K )
⎜ 12.0 g ⎜
⎟ ⎟⎟ ⎜ 0.0821
⎜
18.0
g
mol
K ⎟⎠
nRT
⎝
⎠⎠⎝
⎝
P =
=
= 5.80 atm
V
( 3.60 L )
In general PV = nRT, where n = mass ÷ formula mass. Thus
mass
PV =
RT
(formula mass)
and we arrive at the formula for the density (mass divided by volume) of a gas:
P × (formula mass)
d=
RT
(
)
)
1 atm (32.0 g/mol)
(742 torr) 760
torr
d=
L atm (297.2 K)
0.0821 mol
K
(
d = 1.28 g/L for O2
10.50
In general PV = nRT, where n = mass ÷ formula mass. Thus
mass
PV =
RT
(formula mass)
and we arrive at the formula for the density (mass divided by volume) of a gas:
d=
P × (formula mass)
RT
(
)
1 atm (39.95 g/mol)
(748.0 torr) 760
torr
d=
L
atm
0.0821 mol K (293.80 K)
(
)
d = 1.63 g/L for Ar
218
Chapter 10
PV
=
RT
( 624 torr ) ⎛⎜
atm ⎞
⎟ ( 0.0265 L )
⎝ 760 torr ⎠
=
L atm ⎞
⎛
⎜ 0.0821 mol K ⎟ ( 293 K )
⎝
⎠
(9.04 × 10
−4
)
⎛ 44.0 g ⎞
mol ⎜
⎟ = 0.0398 g
⎝ 1 mol ⎠
10.51
n =
10.52
PV
n =
=
RT
10.53
L atm ⎞ ⎛ 1000 mL ⎞ ⎛ 760 torr ⎞
mL torr
⎛
R = ⎜ 0.0821
= 6.24 × 104
⎟
⎜
⎟
⎜
⎟
mol K ⎠ ⎝ 1 L ⎠ ⎝ 1 atm ⎠
mol K
⎝
10.54
If PV = nRT, then R = PV/nT.
(( 750 torr ) (
1 atm
760 torr
)) ( 0.250 L )
L atm ⎞
⎛
⎜ 0.0821 mol K ⎟ ( 300 K )
⎝
⎠
(
)
⎛ 16.0 g ⎞
= 1.00 × 10−2 mol ⎜
⎟ = 0.160 g
⎝ 1 mol ⎠
Let P = 1 atm = 101,325 Pa, T = 273 K, and n = 1.
Next, express the volume of the standard mole using the units m3, instead of L, remembering that 22.4 L =
22,400 cm3:
3
⎛ 1m ⎞
3
m3 = 22, 400 cm3 × ⎜
⎟ = 0.0224 m
100
cm
⎝
⎠
⎛ (101,325 Pa ) 0.0224 m3 ⎞
⎟ = 8.31 m3 Pa mol−1 K −1
R = ⎜⎜
⎟
1
mole
273
K
(
)(
)
⎜
⎟
⎝
⎠
(
)
10.55
dRT
mass RT
=
=
molecular mass =
P
PV
10.56
Note: 0.08747 mg/mL = 0.08747 g/L
dRT
=
molecular mass =
P
(1.13 g/L ) ⎛⎜ 0.0821
L atm ⎞
( 295 K )
mol K ⎟⎠
⎝
= 27.6 g/mol
1 atm
(755 torr) 760
torr
(
( 0.08747 g/L ) ⎛⎜ 0.0821
L atm ⎞
( 290.2 K )
mol K ⎟⎠
= 2.08 g/mol
⎛ 1 atm ⎞
(760 torr) ⎜
⎟
⎝ 760 torr ⎠
⎝
This gas is most likely H2.
10.57
(a)
(b)
(c)
(d)
)
⎛ 30.1 g C2 H 6 ⎞ ⎛ 1 mol ⎞
density C2H6 = ⎜
= 1.34 g L–1
⎟⎜
⎟
⎝ 1 mol C2 H 6 ⎠ ⎝ 22.4 L ⎠
⎛ 28.0 g N 2 ⎞ ⎛ 1 mol ⎞
–1
density N2 = ⎜
⎟⎜
⎟ = 1.25 g L
1
mol
N
22.4
L
⎝
⎠
2
⎝
⎠
⎛ 70.9 g Cl2 ⎞ ⎛ 1 mol ⎞
–1
density Cl2 = ⎜
⎟⎜
⎟ = 3.17 g L
1
mol
Cl
22.4
L
⎝
⎠
2 ⎠
⎝
⎛ 39.9 g Ar ⎞ ⎛ 1 mol ⎞
–1
density Ar = ⎜
⎟⎜
⎟ = 1.78 g L
⎝ 1 mol Ar ⎠ ⎝ 22.4 L ⎠
219
Chapter 10
10.58
(a)
(b)
(c)
(d)
10.59
⎛ 20.2 g Ne ⎞ ⎛ 1 mol ⎞
–1
density Ne = ⎜
⎟⎜
⎟ = 0.902 g L
⎝ 1 mol Ne ⎠ ⎝ 22.4 L ⎠
⎛ 32.0 g O 2 ⎞ ⎛ 1 mol ⎞
–1
density O2 = ⎜
⎟⎜
⎟ = 1.43 g L
1
mol
O
22.4
L
⎝
⎠
2 ⎠
⎝
⎛ 16.0 g CH 4 ⎞ ⎛ 1 mol ⎞
–1
density CH4 = ⎜
⎟⎜
⎟ = 0.714 g L
1
mol
CH
22.4
L
⎠
4 ⎠⎝
⎝
⎛ 88.0 g CF4 ⎞ ⎛ 1 mol ⎞
–1
density CF4 = ⎜
⎟⎜
⎟ = 3.93 g L
1
mol
CF
22.4
L
⎠
4 ⎠⎝
⎝
First determine the number of moles from the ideal gas law:
n=
(
)
(
mol K
Now calculate the molecular mass:
mass
molecular mass =
=
# of moles
10.60
(a)
(
1 atm
1L
(10.0 torr) 760
255 mL ) 1000
PV
torr (
mL
=
L
atm
RT
0.0821
(298.2 K)
)
(
= 1.37 × 10−4 mol
1g
(12.1 mg ) ( 1000
mg )
1.37 × 10−4 mol
dRT
(mass)RT
=
P
PV
formula mass =
)
)
(
= 88.2 g/mol
L atm (298.2 K)
(6.3 × 10−3 g) 0.0821 mol
K
formula mass =
1 atm (385 mL)
1L
(11 torr) 760
torr
1000 mL
(
)
)
–1
formula mass = 28 g mol
(b)
The formula weights of the boron hydrides are:
BH3, 13.8
B2H6, 27.7
B4H10, 53.3
And we conclude that the sample must have been B2H6.
10.61
⎛
⎛ 1 mol ⎞ ⎞ ⎛
L atm ⎞
( 293.2 K )
⎜ 0.136 g ⎜
⎟ ⎟⎟ ⎜ 0.0821
⎜
32.0
g
mol
K ⎟⎠
nRT
⎝
⎠⎠⎝
⎝
V =
=
= 0.104 L
P
⎛
⎛ 1 atm ⎞ ⎞
⎜ 748 torr ⎜
⎟⎟
⎝ 760 torr ⎠ ⎠
⎝
10.62
⎛
⎛ 1 mol ⎞ ⎞ ⎛
L atm ⎞
( 295.2 K )
⎜⎜ 1.67 g ⎜
⎟ ⎟⎟ ⎜ 0.0821
mol K ⎟⎠
nRT
⎝ 28.0 g ⎠ ⎠ ⎝
⎝
V =
=
= 1.45 L
P
⎛
⎛ 1 atm ⎞ ⎞
⎜ 756 torr ⎜
⎟⎟
⎝ 760 torr ⎠ ⎠
⎝
10.63
2CO + O2 J 2CO2
moles CO =
( 683 torr ) ⎛⎜
1 atm ⎞
⎟ ( 0.300 L )
⎝ 760 torr ⎠
L atm ⎞
⎛
⎜ 0.0821 mol K ⎟ ( 298 K )
⎝
⎠
= 1.10 × 10−2 moles
220
Chapter 10
( 715 torr ) ⎛⎜
1 atm ⎞
⎟ ( 0.150 L )
⎝ 760 torr ⎠
moles O2 =
4.32 × 10−3 moles
L atm ⎞
⎛
⎜ 0.0821 mol K ⎟ ( 398 K )
⎝
⎠
∴ O2 is the limiting reactant
⎛ 2 mol CO 2 ⎞
−3
moles CO2 = (4.32 × 10−3 moles O2 ) ⎜
⎟ = 8.64 × 10 moles CO 2
⎝ 1 mol O 2 ⎠
V =
10.64
(8.64 × 10
moles NH3 =
)
L atm ⎞
⎛
mol ⎜ 0.0821
( 300 K )
mol
K ⎟⎠
⎝
2.17 × 10−1 L = 217 mL
⎛ 1 atm ⎞
( 745 torr ) ⎜
⎟
⎝ 760 torr ⎠
−3
( 750 torr ) ⎛⎜
1 atm ⎞
( 0.300 L )
760
torr ⎟⎠
⎝
= 1.20 × 10−2 moles
L atm ⎞
⎛
⎜ 0.0821 mol K ⎟ ( 301 K )
⎝
⎠
( 780 torr ) ⎛⎜
1 atm ⎞
⎟ ( 0.220 L )
⎝ 760 torr ⎠
= 8.51 × 10−3 moles
moles O2 =
L atm ⎞
⎛
⎜ 0.0821 mol K ⎟ ( 323 K )
⎝
⎠
Assume NH3 is the limiting reagent.
⎛ 2 mol N 2 ⎞
−3
moles N 2 = (1.20 × 10−2 moles NH3 ) ⎜
⎟ = 6.00 × 10 moles N 2
4
moles
NH
3⎠
⎝
Assume O2 is the limiting reagent:
⎛ 2 mol N 2 ⎞
−3
moles N 2 = (8.51 × 10−3 moles O2 ) ⎜
⎟ = 5.68 × 10 mol N 2 ∴ O2 is limiting reactant
3
mol
O
2 ⎠
⎝
L atm ⎞
1000 mL ⎞
⎛
5.68 × 10−3 mol ⎜ 0.0821
( 373 K ) ⎛⎜
mol K ⎟⎠
1 L ⎟⎠
⎝
⎝
= 179 mL
mL N 2 =
1 atm ⎞
( 740 torr ) ⎛⎜
⎟
⎝ 760 torr ⎠
(
)
10.65
The balanced equation is
2C4H10 + 13O2 J 8CO2 + 10H2O
⎛ 13 mL O 2 ⎞
3
mL O 2 = (175 mL C4 H10 ) ⎜
⎟ = 1.14 × 10 mL O2
⎝ 2 mL C4 H10 ⎠
10.66
The balanced equation is
2C6H14 + 19O2 J 12CO2 + 14H2O
⎛ 19 mL O 2 ⎞
3
mL O 2 = (855 mL CO2 ) ⎜
⎟ = 1.35 × 10 mL O2
12
mL
CO
2⎠
⎝
10.67
⎛ 1 mol C3 H 6 ⎞
mol C3H6 = (18.0 g C3H6) ⎜
⎟ = 0.428 mol C3H6
⎝ 42.08 g C3 H 6 ⎠
⎛ 1 mol H 2 ⎞
mol H2 = (0.428 mol C3H6) ⎜
⎟ = 0.428 mol H2
⎝ 1 mol C3 H 6 ⎠
221
Chapter 10
V=
10.68
10.69
(
)
L atm (297.2 K)
(0.428 mol H 2 ) 0.0821 mol
nRT
K
= 10.7 L H2
=
1
atm
P
(740 torr)
( 760 torr )
⎛ 1 mole HNO3 ⎞
mol HNO3 = (12.0 g HNO3) ⎜
⎟ = 0.190 mol HNO3
⎝ 63.01 g HNO3 ⎠
⎛ 3 moles NO2 ⎞
mol NO2 = (0.190 mol HNO3) ⎜
⎟ = 0.286 mol NO2
⎝ 2 moles HNO3 ⎠
L atm ⎞
( 0.286 moles NO2 ) ⎛⎜ 0.0821
( 298 K )
nRT
mol
K ⎟⎠
⎝
=
V=
= 7.07 L or 7.07 × 103 mL
P
⎛ 1 atm ⎞
( 752 torr ) ⎜
⎟
⎝ 760 torr ⎠
CH4 + 2O2 J CO2 + 2H2O
n CH 4
PV
=
=
RT
(
( 725 torr ) ⎛⎜
)
1 atm ⎞
−3
⎟ 16.8 × 10 L
760
torr
⎝
⎠
= 6.34 × 10–4 mol CH4
L atm ⎞
⎛
⎜ 0.0821 mol K ⎟ ( 308 K )
⎝
⎠
⎛ 2 mol O 2 ⎞
–3
mol O2 = (6.34 × 10–4 mol CH4) ⎜
⎟ = 1.27 × 10 mol O2
1
mol
CH
4⎠
⎝
L atm ⎞
⎛
1.27 × 10−3 moles ⎜ 0.0821
( 300 K )
nRT
mol K ⎟⎠
⎝
=
= 3.63 × 10−2 L = 36.3 mL O 2
VO2 =
P
⎛ 1 atm ⎞
( 654 torr ) ⎜
⎟
⎝ 760 torr ⎠
(
10.70
n NH3 =
PV
=
RT
)
(825 torr ) ⎛⎜
(
)
1 atm ⎞
−3
⎟ 33.6 × 10 L
⎝ 760 torr ⎠
= 1.11 × 10–3 mol NH3
L
atm
⎛
⎞
⎜ 0.0821 mol K ⎟ ( 400 K )
⎝
⎠
⎛ 6 mol H 2 O ⎞
–3
mol H2O = 1.11 mol NH3 ⎜
⎟ = 1.67 × 10 mol H2O
4
mol
NH
3⎠
⎝
L atm ⎞
⎛
−3
1.67 × 10 moles ⎜ 0.0821
( 591 K )
nRT
mol
K ⎟⎠
⎝
=
= 8.36 × 10−2 L = 83.6 mL
VH 2O =
P
⎛ 1 atm ⎞
( 735 torr ) ⎜
⎟
⎝ 760 torr ⎠
(
10.71
)
Assume all gases behave ideally and recall that 1 mole of an ideal gas at 0 °C and 1 atm occupies a volume
of 22.4 L. So,
⎛ 760 torr ⎞
PN2 = 0.30 atm ⎜
⎟ = 228 torr
⎝ 1 atm ⎠
⎛ 760 torr ⎞
PO2 = 0.20 atm ⎜
⎟ = 152 torr
⎝ 1 atm ⎠
222
Chapter 10
⎛ 760 torr ⎞
PHe = 0.40 atm ⎜
⎟ = 304 torr
⎝ 1 atm ⎠
⎛ 760 torr ⎞
PCO2 = 0.10 atm ⎜
⎟ = 76 torr
⎝ 1 atm ⎠
10.72
PCO2 = 840 torr – 320 torr = 520 torr
⎛ 520 torr ⎞
n CO 2 = (0.200 mol) ⎜
⎟ = 0.124 moles
⎝ 840 torr ⎠
10.73
PTot = PN2 + PO2 + PHe
PTot = 200 torr + 150 torr + 300 torr = 650 torr
10.74
PTot = PN2 + PO2 + PCO2
PCO2 = PTot – PN2 –PO2
PCO2 = 740 torr – 120 torr – 400 torr = 220 torr
10.75
Ptotal = (PCO + PH2O)
PH2O = 17.54 torr at 20 °C, from Table 10.2.
PCO = 754 – 17.54 torr = 736 torr
The temperature stays constant so, P1V1 = P2V2, and
PV
(736 torr)(268 mL)
V2 = 1 1 =
= 260 mL
P2
(760 torr)
10.76
Ptotal = PH2 + PH2O
PH2O = 23.76 torr at 25 °C, from Table 10.2.
PH2 = Ptotal – PH2O = 742 – 23.76 = 718 torr
The temperature stays constant so, P1V1 = P2V2, and
PV
(718 torr)(288 mL)
V2 = 1 1 =
= 272 mL
P2
(760 torr)
10.77
From Table 10.2, the vapor pressure of water at 20 °C is 17.54 torr. Thus only (742 – 17.54) = 724 torr is due to
"dry" methane. In other words, the fraction of the wet methane sample that is pure methane is 724/742 = 0.976.
The question can now be phrased: What volume of wet methane, when multiplied by 0.976, equals 244 mL?
Volume "wet" methane × 0.976 = 244 mL
Volume "wet" methane = 244 mL/0.976 = 250 mL
In other words, one must collect 250 total mL of "wet methane" gas in order to have collected the
equivalent of 244 mL of pure methane.
10.78
First convert the needed amount of oxygen at 760 torr to the volume that would correspond to the
laboratory conditions of 746 torr: P1V1 = P2V2 or V2 = P1V1/P2
V2 = 275 mL × 760 torr/746 torr = 280 mL of dry oxygen gas
The wet sample of oxygen gas will also be collected at atmospheric pressure, 746 torr. The vapor pressure
of water at 15 °C is equal to 12.8 torr (from Table 10.2), and the wet sample will have the following partial
pressure of oxygen, once it is collected:
PO2 = Ptotal – PH2O = 746 – 12.8 = 733 torr of oxygen in the wet sample. Thus the wet sample of oxygen is
composed of the following % oxygen:
% oxygen in the wet sample = 733/746 × 100 = 98.3 %
223
Chapter 10
The question now becomes what amount of a wet sample of oxygen will contain the equivalent of 280 mL
of pure oxygen, if the wet sample is only 98.3 % oxygen (and 1.7 % water). 0.983 × Vwet = 280 mL, hence
Vwet = 285 mL. This means that 285 mL of a wet sample of oxygen must be collected in order to obtain as
much oxygen as would be present in 280 mL of a pure sample of oxygen.
10.79
The relative rates are inversely proportional to the square roots of their molecular masses:
rate( 235 UF6 )
rate( 238 UF6 )
=
molar mass ( 238 UF6 )
molar mass ( 235 UF6 )
=
352 g mol−1
349 g mol−1
= 1.0043
Meaning that the rate of effusion of the 235UF6 is only 1.0043 times faster than the 238UF6 isotope.
10.80
Use equation 10.7
effusion rate x
=
effusion rate C3H8
M C3 H 8
Mx
⎛ effusion rate C3 H8 ⎞
M x = M C3 H 8 ⎜
⎟
⎝ effusion rate x ⎠
⎛ 1 ⎞
= 44.1 g/mol ⎜
⎟
⎝ 1.65 ⎠
10.81
2
2
= 16.2 g/mol
Effusion rates for gases are inversely proportional to the square root of the gas density, and the gas with the
lower density ought to effuse more rapidly. Nitrogen in this problem has the higher effusion rate because it
has the lower density:
rate(N 2 )
1.96 g L−1
=
= 1.25
rate(CO 2 )
1.25 g L−1
10.82
Ethylene, C2H4, the lightest of these three, diffuses the most rapidly, and Cl2, the heaviest, will diffuse the
slowest.
Cl2 < SO2 < C2H6
Additional Exercises
10.83
10.84
⎛ 2000 lb ⎞
5
Total weight = (45.6 tons + 8.3 tons) ⎜
⎟ = 1.08 × 10 lbs
1
ton
⎝
⎠
Total pressure = 85 psi + 14.7 psi = 99.7 psi/tire
1.08 × 105 lbs
number of tires =
= 10.8 tires
(99.7 lbs in −2 /tire)(100 in 2 )
The minimum number of tires is 12 since tires are mounted in multiples of 2.
We found that 1 atm = 33.9 ft of water. This is equivalent to 33.9 ft × 12 in./ft = 407 in. of water, which in
this problem is equal to the height of a water column that is uniformly 1.00 in.2 in diameter. Next, we
convert the given density of water from the units g/mL to the units lb/in.3:
lb
3
in.
⎛ 1.00 g ⎞ ⎛ 1 lb ⎞ ⎛ 1 mL ⎞ ⎛ 2.54 cm ⎞
= ⎜
⎟⎜
⎟⎜
⎟⎜
⎟
⎝ 1.00 mL ⎠ ⎝ 454 g ⎠ ⎝ 1 cm3 ⎠ ⎝ 1 in. ⎠
3
224
= 0.0361
lb
in.3
Chapter 10
The area of the total column of water is now calculated: 1.00 in.2 × 407 in. = 407 in.3, along with the mass
of the total column of water: 407 in.3 × 0.0361 lb/in.3 = 14.7 lb. Finally, we can determine the pressure
(force/unit area) that corresponds to one atm: 1 atm = 14.7 lb ÷ 1.00 in.2 = 14.7 lb/in.2
10.85
⎛ 6.0 in × 3.2 in ⎞
2
Total footprint = (4 tires) ⎜
⎟ = 76.8 in
tire
⎝
⎠
3500 lb
Total pressure =
= 45.6 lb/in 2
2
76.8 in
Gauge pressure = 45.6 lb/in 2 - 14.7 lb/in 2 = 30.9 lb/in 2
10.86
First calculate the initial volume (V1) and the final volume (V2) of the cylinder, using the given geometrical
data, noting that the radius is half the diameter (10.7/2 = 5.35 cm):
V1 = π × (5.35 cm)2 × 13.4 cm = 1.20 × 103 cm3
V2 = π × (5.35 cm)2 × (13.4 cm – 12.7 cm) = 62.9 cm3
In general the combined gas law equation is:
T2 =
10.87
P1V1
PV
= 2 2 , and in particular, for this problem, we have:
T1
T2
P2 V2 T1
(34.0 atm)(62.9 cm3 )(364 K)
=
= 649 K = 376 D C
3
3
P1V1
(1.00 atm)(1.20 × 10 cm )
First convert the temperature data to the Kelvin scale: 273 + 5/9(60.0 – 32.0) = 289 K and 273 + 5/9(104 –
32) = 313 K. Next, calculate the final pressure at the gauge, taking into account the temperature change
only:
P2 =
P1T2
(64.7 lb in.−2 )(313 K)
=
= 70.1 lb in.−2
T1
(289 K)
This represents the actual pressure inside the tire. The pressure gauge measures only the difference
between the pressure inside the tire and the pressure outside the tire (atmospheric pressure). Hence the
gauge reading is equal to the internal pressure of the tire less atmospheric pressure: (70.1 – 14.7) lb/in2 =
55.4 lb/in2
10.88
Assume a 1 sq in. cylinder of water
(
⎛ 12 in. ⎞
2
V = (12,468 ft) ⎜
⎟ 1 in.
⎝ 1 ft ⎠
)
3
⎛ 2.54 cm ⎞ ⎛ 1 mL ⎞
6
= (149616 in.3 ) ⎜
⎟ = 2.4518 × 10 mL
⎟ ⎜
⎝ 1 in. ⎠ ⎝ 1 cm3 ⎠
⎛ 1 lb ⎞
⎛ 1.025 g ⎞
3
Mass = (2.4518 × 106 mL) ⎜
= (2.51306 × 106 g) ⎜
⎟ = 5.54026 × 10 lb
⎟
⎝ 1 mL ⎠
⎝ 453.6 g ⎠
10.89
⎛ 1 atm ⎞
Pressure = (5.54026 × 103 lb in −2 ) ⎜
⎟ = 376.89 atm
⎝ 14.7 lb in −2 ⎠
To calculate the pressure at 100 ft assume a cylinder of water 100 ft long and 1 in2.
3
2.54 cm ⎞ ⎛ 1 mL ⎞ ⎛ 1.025 g ⎞ ⎛ 1 lb ⎞
⎛ 12 in ⎞
mass = (100 ft) ⎜
(1 in )2 ⎛⎜
⎟ = 44.4 lb
⎟⎜
⎟
⎟ ⎜
⎟⎜
⎝ 1 ft ⎠
⎝ 1 in ⎠ ⎝ 1 cm3 ⎠ ⎝ 1 mL ⎠ ⎝ 453.6 g ⎠
⎛ 1 atm
⎞
= 3.02 atm
P = (44.4 lb in −2 ) ⎜
−2 ⎟
⎝ 14.7 lb in ⎠
Since the pressure decreases by a factor of 3, the volume must increase by a factor of 3. Divers exhale
to decrease the amount of gas in their lungs, so it does not expand to a volume larger than the divers
lungs.
225
Chapter 10
10.90
From the data we know that the pressure in flask 1 is greater than atmospheric pressure, and greater than
the pressure in flask 2. The pressure in flask 1 can be determined from the manometer data. The pressure in
flask 1 is:
⎛ 760 mm Hg ⎞ ⎛ 1 cm ⎞
P = (0.827 atm) ⎜
⎟ ⎜ 10 mm ⎟ + 12.26 cm = 75.11 cm Hg
⎝ 1 atm
⎠⎝
⎠
The pressure in flask 2 is lower than flask 1
⎛ 0.826 g mL−1 ⎞
P = 75.11 cm Hg – (16.24 cm oil) ⎜
⎟ = 74.12 cm Hg = 741.2 torr
⎜ 13.6 g mL−1 ⎟
⎝
⎠
10.91
Ptotal = 740 torr = PH2 + Pwater
The vapor pressure of water at 25 °C is available in Table 10.2: 23.76 torr. Hence:
PH2 = (740 – 24) torr = 716 torr
Next, we calculate the number of moles of hydrogen gas that this represents:
n=
(
)
1 atm
0.335 L )
( 716 torr ) 760
PV
torr (
=
=
L atm 298.2 K
RT
0.0821 mol
(
)
K
(
)
0.0129 mol H 2
The balanced chemical equation is: Zn(s) + 2HCl(aq) J H2(g) + ZnCl2(aq)
and the quantities of the reagents that are needed are:
⎛ 1 mol Zn ⎞ ⎛ 65.39 g Zn ⎞
g Zn = (0.0129 mol H 2 ) ⎜
⎟⎜
⎟ = 0.844 g Zn
⎝ 1 mol H 2 ⎠ ⎝ 1 mol Zn ⎠
⎛ 2 mol HCl ⎞ ⎛ 1000 mL HCl ⎞
mL HCl = (0.0129 mol H 2 ) ⎜
⎟⎜
⎟ =
⎝ 1 mol H 2 ⎠ ⎝ 6.00 mol HCl ⎠
10.92
4.30 mL HCl
Using the ideal gas law, determine the number of moles of H2 and O2 gas initially present:
For hydrogen:
n=
(
for oxygen:
n=
(
)
(
)
1 atm
1L
400 mL ) 1000
(1250 torr ) 760
PV
torr (
mL
=
= 2.52 × 10−2 mol H 2
RT
0.0821 L atm ( 318 K )
mol K
(
)
)
(
)
1 atm
1L
300 mL ) 1000
( 740 torr ) 760
PV
torr (
mL
=
= 1.19 × 10−2 mol O 2
RT
0.0821 L atm ( 298 K )
(
mol K
)
This problem is an example of a limiting reactant problem in that we know the amounts of H2 and O2
initially present. Since 1 mol of O2 reacts completely with 2 mol of H2, we can see, by inspection, that
there is excess H2 present. Using the amounts calculated above, we can make 2.38 × 10–2 mol of H2O
and have an excess of 1.4 × 10–3 mol of H2. Thus, the total amount of gas present after complete
reaction is 2.52 × 10–2 mol. Using this value for n, we can calculate the final pressure in the reaction
vessel:
(
)(
L atm
2.52 × 10−2 mol 0.0821 mol
nRT
K
P=
=
1
L
V
( 500 mL ) 1000 mL
(
)
) ( 393 K ) = 1.63 atm = 1.24 × 103 torr
226
Chapter 10
10.93
This is a limiting reactant problem. First we need to calculate the moles of dry CO2 that can be produced
from the given quantities of CaCO3 and HCl:
⎛ 1 mol CaCO3 ⎞
mol CaCO3 = (12.3 g CaCO3 ) ⎜
⎟ = 0.123 mol CaCO3
⎝ 100.09 g CaCO3 ⎠
⎛ 0.250 mol HCl ⎞
mol HCl = (185 mL HCl) ⎜
⎟ = 0.0463 mol HCl
⎝ 1000 mL HCl ⎠
Thus, HCl is limiting and we use this to determine the moles of CO2 that can be produced:
⎛ 1 mol CO 2 ⎞
mol CO2 = (0.0463 mol HCl) ⎜
⎟ = 0.0231 mol CO 2
⎝ 2 mol HCl ⎠
Next we realize that CO2 is collected over water at a total pressure of 745 torr. Thus, the pressure of “dry”
CO2 is calculated as follows: Ptotal = 745 torr = PCO2 + Pwater. The vapor pressure of water at 20°C is
available in Table 10.2, 17.54 torr. Hence, PCO2 = 745 torr – 18 torr = 727 torr. Finally, the volume of this
“dry” CO2 is calculated using the ideal gas equation:
(
( 0.0231 mol ) 0.0821
nRT
V=
=
P
( 727 torr )
10.94
(
L atm
mol K
1 atm
760 torr
) ( 293.2 K ) = 0.582 L CO = 582 mL
2
)
Cl2 + SO32– + H2O J 2Cl– + SO42– + 2H+
moles Cl2 =
⎛ 0.200 moles Na 2SO3 ⎞ ⎛ 1 mole SO32−
⎟⎜
⎝ 1000 mL Na 2SO3 ⎠ ⎜⎝ 1 mole Na 2SO3
( 50.0 mL Na 2SO3 ) ⎜
⎞⎛ 1 mole Cl
2
⎟⎜
⎟⎜ 1 mole SO 2−
3
⎠⎝
= 1.00 × 10−2 moles Cl2
VCl2 =
10.95
(1.00 × 10
)
L atm ⎞
⎛
moles ⎜ 0.0821
( 298 K )
mol K ⎟⎠
⎝
= 0.253 L = 253 mL
1 atm ⎞
( 734 torr ) ⎛⎜
⎟
⎝ 760 torr ⎠
−2
The temperatures must first be converted to Kelvin:
5
5
× ( D F − 32) =
× ( − 50 − 32) = − 46 D C = 227 K
9
9
5
5
D
C=
× ( D F − 32) =
× (120 − 32) = 49 D C = 322 K
9
9
Next, the pressure calculation is done using the following equation:
PT
(35 lb in.−2 )(322 K)
P2 = 1 2 =
= 50 lb in.−2
T1
(227 K)
D
10.96
C=
(a)
(b)
Zn(s) + 2HCl(aq) J H2(g) + ZnCl2(aq)
Calculate the number of moles of hydrogen:
n=
(
)
1 atm
12.0 L )
( 760 torr ) 760
PV
torr (
=
= 0.499 mol H 2
L
atm
RT
0.0821 mol K ( 293.2 K )
(
)
and the number of moles of zinc:
⎛ 1 mol Zn ⎞
mol Zn = ( 0.499 mol H 2 ) ⎜
⎟ = 0.499 mol Zn
⎝ 1 mol H 2 ⎠
227
⎞
⎟
⎟
⎠
Chapter 10
The number of grams of zinc needed is, therefore:
⎛ 65.39 g Zn ⎞
g Zn = (0.499 mol Zn) ⎜
⎟ = 32.6 g Zn
⎝ 1 mol Zn ⎠
(c)
⎛ 2 mol HCl ⎞
mol HCl = (0.499 mol Zn) ⎜
⎟ = 0.998 mol HCl
⎝ 1 mol Zn ⎠
⎛ 1000 mL HCl ⎞
mL HCl = (0.998 mol HCl) ⎜
⎟ = 125 mL HCl
⎝ 8.00 mol HCl ⎠
10.97
(a)
First determine the % by mass S and O in the sample:
% S = 1.448 g/3.620 g × 100 = 40.00 % S
% O = 2.172 g/3.620 g × 100 = 60.00 % O
(b)
Next, determine the number of moles of S and O in a sample of the material weighing 100 g
exactly, in order to make the conversion from % by mass to grams straightforward: In 100 g of
the material, there are 40.00 g S and 60.00 g O:
40.00 g S ÷ 32.07 g/mol = 1.247 mol S
60.00 g O ÷ 16.00 g/mol = 3.750 mol O
Dividing each of these mole amounts by the smaller of the two gives the relative mole amounts of
S and O in the material: for S, 1.247 mol ÷ 1.247 mol = 1.000 relative moles, for O, 3.750 mol ÷
1.247 mol= 3.007 relative moles, and the empirical formula is, therefore, SO3.
(c)
We determine the formula mass of the material by use of the ideal gas law:
n=
(
)
1 atm
1.120 L )
( 750 torr ) 760
PV
torr (
=
=
L
atm
RT
0.0821 mol K ( 298.2 K )
(
)
0.0451 mol
The formula mass is given by the mass in grams (given in the problem) divided by the moles
determined here: formula mass = 3.620 g ÷ 0.0451 mol = 80.2 g mol–1. Since this is equal to the
formula mass of the empirical unit determined in step (b) above, namely SO3, then the molecular
formula is also SO3.
10.98
We first need to determine the pressure inside the apparatus. Since the water level is 8.5 cm higher inside
than outside, the pressure inside the container is lower than the pressure outside. To determine the inside
pressure, we first need to convert 8.5 cm of water to an equivalent dimension for mercury. This is done
using the density of mercury: PHg = 85 mm/13.6 = 6.25 mm (where the density of mercury, 13.6 g/mL, has
been used.) Pinside = Poutside – PHg = 746 torr – 6 torr = 740 torr. In order to determine the PH2, we need to
subtract the vapor pressure of water at 24 °C. This value may be found in Appendix E4 and is equal to 22.4
torr. The PH2 = Pinside – PH2O = 740 torr – 22.4 torr = 717 torr. Now, we can use the ideal gas law in order
to determine the number of moles of H2 present;
n=
(
)
(
)
1 atm
1L
18.45 mL ) 1000
( 717 torr ) 760
PV
torr (
mL
=
= 7.14 × 10−4 mol H 2
L
atm
RT
0.0821
( 297 K )
(
mol K
)
The balanced equation described in this problem is:
Zn(s) +2HCl(aq) J ZnCl2(aq) + H2(g)
228
Chapter 10
By inspection we can see that 1 mole of Zn(s) reacts to form 1mole of H2(g) and we must have reacted
7.14 × 10–4 mol Zn in this reaction.
(
)
⎛ 65.39 g Zn ⎞
−2
g Zn = 7.14 × 10−4 mol Zn ⎜
⎟ = 4.67 × 10 g Zn
⎝ 1 mol Zn ⎠
10.99
(a)
Ptotal = 746.0 torr = PH2O + PN2
PN2 = 746.0 torr – 22.1 torr = 723.9 torr
Now, use the ideal gas equation to determine the moles of N2 that have been collected:
n=
(
)
(
)
1 atm
1L
18.90 mL ) 1000
( 723.9 torr ) 760
PV
torr (
mL
=
=
L
atm
RT
0.0821 mol K ( 296.95 K )
(
)
7.384 × 10−4 mol N 2
Then the mass of nitrogen that has been collected is determined: 7.384 × 10–4 mol N2 × 28.0
g/mol = 2.068 × 10–2 g N2. Next, the % by mass nitrogen in the material is calculated: % N =
(0.02068 g)/(0.2394 g) × 100 = 8.638 % N
(b)
mass of C in the sample:
⎛ 1 mole CO 2 ⎞ ⎛ 1 mol C
g C = (17.57 × 10−3 g CO 2 ) ⎜
⎟⎜
⎝ 44.01 g CO 2 ⎠ ⎝ 1 mol CO 2
⎞ ⎛ 12.01 g C ⎞
⎟⎜
⎟
⎠ ⎝ 1 mol C ⎠
= 4.795 × 10−3 g C
mass of H in the sample:
⎛ 1 mole H 2 O ⎞ ⎛ 2 mol Η ⎞ ⎛ 1.008 g H ⎞
g H = (4.319 × 10−3 g H 2 O) ⎜
⎟⎜
⎟⎜
⎟
⎝ 18.02 g H 2 O ⎠ ⎝ 1 mol H 2 O ⎠ ⎝ 1 mol H ⎠
= 4.832 × 10−4 g H
mass of N in the sample:
⎛ 8.638 g N ⎞
−4
g N = (6.478 × 10−3 g sample) ⎜
⎟ = 5.596 × 10 g N
100
g
sample
⎝
⎠
mass of O in the sample = total mass – (mass C + H + N)
mg O = 6.478 mg sample − ( 4.795 mg C + 0.4832 mg H + 0.5596 mg N )
= 0.640 mg O
Next we convert each of these mass amounts into the corresponding mole values:
for C, 4.795 × 10–3 g ÷ 12.01 g/mol = 3.993 × 10–4 mol C
for H, 4.832 × 10–4 g ÷ 1.008 g/mol = 4.794 × 10–4 mol H
for N, 5.596 × 10–4 g ÷ 14.01 g/mol = 3.994 × 10–5 mol N
for O, 6.40 × 10–4 g ÷ 16.00 g/mol = 4.00 × 10–5 mol O
Last, we convert these mole amounts into relative mole amounts by dividing each by the smallest
of the four:
for C, 3.993 × 10–4 mol/ 3.994 × 10–5 mol = 9.998
for H, 4.794 × 10–4 mol/ 3.994 × 10–5 mol = 12.00
for N, 3.994 × 10–5 mol/ 3.994 × 10–5 mol = 1.000
for O, 4.00 × 10–5 mol/ 3.994 × 10–5 mol = 1.00
The empirical formula is therefore C10H12NO
229
Chapter 10
(c)
10.100 (a)
The formula mass of the empirical unit is 162. Since this is half the value of the known molecular
mass, the molecular formula must be twice the empirical formula, C20H24N2O2.
The equation can be rearranged to give:
0.04489 ×
V(P − PH 2O )
273 + t °C
= %N × W
This means that the left side of the above equation should be obtainable simply from the ideal gas
law, applied to the nitrogen case. If PV = nRT, then for nitrogen: PV = (mass nitrogen)/(28.01
g/mol) × RT, and the mass of nitrogen that is collected is given by: (mass nitrogen) =
PV(28.01)/RT, where R = 82.1 mL atm/K mol × 760 torr/atm = 6.24 × 104 mL torr/K mol. Using
this value for R in the above equation, we have the following result for the mass of nitrogen,
remembering that the pressure of nitrogen is less than the total pressure, by an amount equal to the
vapor pressure of water:
(mass nitrogen) =
28.01 × V × (Ptotal − PH 2O )
( 6.24 × 10
4 mL torr
mol K
)( 273 + C )
D
Finally, it is only necessary to realize that the value
28.01
6.24 × 104
× 100 = 0.04489
is exactly the value given in the problem.
(b)
% N = 0.04489 ×
(18.90 mL)(746 torr − 22.1 torr)
= 8.639 %
( 0.2394 g )( 273.15 + 23.80 )
10.101 2H2 + O2 J 2H2O
⎛ 1 mol H 2 ⎞
mol H2 = (12.7 g H2) ⎜
⎟ = 6.29 mol H2
⎝ 2.02 g H 2 ⎠
⎛ 1 mol O2 ⎞
mol O2 = (87.5 g O2) ⎜
⎟ = 2.73 mol O2
⎝ 32.0 g O 2 ⎠
∴O2 is the limiting reactant
⎛ 2 mol H 2 O ⎞
mol H2O = (2.73 mol O2) ⎜
⎟ = 5.46 mol H2
⎝ 1 mol O2 ⎠
⎛ 2 mol H 2 ⎞
mol H2 needed = (2.73 mol O2) ⎜
⎟ = 5.46 mol H2
⎝ 1 mol O 2 ⎠
Remaining mol H2 = 6.29 mol H2 – 5.46 mol H2 = 0.83 mol H2
L atm ⎞
( 5.46 mol ) ⎛⎜ 0.0821
( 433 K )
mol K ⎟⎠
⎝
= 16.2 atm
PH 2O =
12.0 L
L atm ⎞
( 0.83 mol ) ⎛⎜ 0.0821
( 433 K )
mol K ⎟⎠
⎝
= 2.4 atm
PH 2 =
12.0 L
PTot = 16.2 atm + 2.4 atm = 18.6 atm
230
Chapter 10
10.102 (a)
We begin by converting the dimensions of the room into cm: 40 ft × 30.48 cm/ft = 1.2 × 103 cm,
20 ft × 30.48 cm/ft = 6.1 × 102 cm, 8 ft × 30.48 cm/ft = 2.4 × 102 cm. Next, the volume of the
room is determined: V = (1.2 × 103 cm)(6.1 × 102 cm)(2.4 × 102 cm) = 1.8 × 108 cm3. Since there
are 1000 cm3 in a liter, volume is: V = 1.8 × 105 L
The calculation of the amount of H2S goes as follows:
⎛ 0.15 L H 2S ⎞
L H 2S = 1.8 × 105 L space ⎜
⎟ = 2.7 × 10−5 L H 2S
⎜ 1 × 109 L space ⎟
⎝
⎠
(
(b)
)
Convert volume (in liters) to moles at STP:
(
)
⎛ 1 mol H 2S ⎞
−6
mol H 2S = 2.7 × 10−5 L H 2S ⎜
⎟ = 1.2 × 10 mol H 2S
⎝ 22.4 L H 2S ⎠
Since the stoichiometry is 1:1, we require the same number of moles of Na2S:
(
)
⎛ 1000 mL Na 2S ⎞
mL Na 2S = 1.2 × 10−6 mol Na 2S ⎜
⎟
⎝ 0.100 mol Na 2S ⎠
= 1.2 × 10−2 mL Na 2S
231