Download 12 The Gaseous State of Matter Chapter Outline Properties of Gases

Slide 1 ___________________________________ 12 The Gaseous State of Matter
___________________________________ ___________________________________ Air in a hot air balloon
expands upon heating.
Some air escapes from
the top, lowering the
air density, making
the balloon buoyant.
___________________________________ ___________________________________ ___________________________________ Foundations of College Chemistry, 14th Ed. Morris Hein and Susan Arena
Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Chapter Outline
2 ___________________________________ 12.1 Properties of Gases
A. Measuring the Pressure of a Gas
B. Pressure Dependence: Number of Molecules and Temperature
12.2 Boyle’s Law
12.3 Charles’ Law
12.4 Avogadro’s Law
A. Mole-Mass-Volume Calculations
12.5 Combined Gas Laws
12.6 Ideal Gas Law
A. Kinetic-Molecular Theory
B. Real Gases
12.7 Dalton’s Law of Partial Pressures
12.8 Density of Gases
12.9 Gas Stoichiometry
___________________________________ ___________________________________ ___________________________________ ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Properties of Gases
3 ___________________________________ Gases:
i) Have indefinite volume
Expand to fill a container
___________________________________ ii) Have indefinite shape
Assume the shape of a container
iii) Have low densities
Example
dair = 1.2 g/L at 25 °C
dwater = 1.0 g/mL at 25 °C
___________________________________ ___________________________________ Volume occupied by
1 mol of H2O:
as a liquid (18 mL)
as a gas (22.4 L)
___________________________________ ___________________________________ iv) Have high velocities and kinetic energies
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 4 ___________________________________ Measuring Pressure
Pressure: Force per unit area
___________________________________ force
Pressure = area
___________________________________ Pressure depends on:
1) The number of gas molecules
2) Gas temperature
3) Volume occupied by the gas
___________________________________ Pressure results from
gas molecule collisions
with the container walls.
___________________________________ SI unit of pressure is the pascal (Pa) = 1 newton/meter2
___________________________________ Unit Conversions:
1 atm = 760 mm Hg = 760 torr
= 101.3 kPa = 1.013 bar = 14.69 psi
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 5 ___________________________________ ___________________________________ Practicing Pressure Conversions
___________________________________ Convert 740. mm Hg to a) atm and b) kPa.
___________________________________ a) Use the conversion factor: 1 atm = 760 mm Hg
740. mm Hg
×
___________________________________ 1 atm
= 0.974 atm
760 mm Hg
___________________________________ b) Use the conversion factor: 101.3 kPa = 760 mm Hg
740. mm Hg ×
___________________________________ 101.3 kPa = 98.63 kPa
760 mm Hg
___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 6 ___________________________________ Atmospheric Pressure
___________________________________ Definition: total pressure exerted by gases in the atmosphere
___________________________________ Due to the mass of the atmospheric gases pressing
downward on the Earth’s surface.
___________________________________ Major Components of Dry Air
___________________________________ ___________________________________ ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Measuring Pressure
7 ___________________________________ Measuring Pressure
___________________________________ Use a Barometer
1) Invert a long tube of Hg
over an open dish of Hg.
___________________________________ 2) Hg will be supported
(pushed up) by the pressure
of the atmosphere.
___________________________________ ___________________________________ 3) Height of Hg column can be
used to measure pressure.
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Pressure Dependence 8 ___________________________________ 1) On the Number of Molecules
Pressure (P ) is directly proportional to the number
of gas molecules present (n ) at constant
temperature (T ) and volume (V ).
___________________________________ ___________________________________ Increasing n creates more frequent collisions with the
container walls, increasing the pressure
___________________________________ V = 22.4 L
T = 25.0 °C
0.5 mol H2
P = 0.5 atm
1 mol H2
P = 1 atm
___________________________________ 2 mol H2
P = 2 atm
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 9 ___________________________________ ___________________________________ Pressure Dependence ___________________________________ 2) On Temperature
Pressure is directly proportional to temperature when
moles (n ) and volume (V ) are held constant.
T = 0 °C
T = 100 °C
2.24 atm
3.06 atm
___________________________________ ___________________________________ Increasing T causes:
a) more frequent and
b) higher energy collisions
___________________________________ ___________________________________ 0.1 mol of gas
in a 1L container
___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Boyle’s Law
10 The volume of a fixed quantity of gas is inversely
proportional to the pressure exerted by the gas at
constant mass and temperature.
___________________________________ PV = constant (k ) or P  1
V
___________________________________ P=k ×1
V
___________________________________ Most common form:
___________________________________ P1V1 = P2V2
___________________________________ Graph showing inverse PV
relationship
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Boyle’s Law Problems
11 ___________________________________ What volume will 3.5 L of a gas occupy if the pressure is
changed from 730. mm Hg to 600. mm Hg?
___________________________________ P1V1 = P2V2
Knowns
___________________________________ V1 = 3.5 L P1 = 730. mm Hg P2 = 600. mm
Hg
___________________________________ P1V1
V2 =
P2
Solve For V2
Calculate V2 = 3.5 L ×
___________________________________ 730. mm Hg
= 4.3 L
600. mm Hg
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Boyle’s Law Problems
12 ___________________________________ A sample of Ne gas occupies 250. mL at 880. torr.
Calculate the PNe if the volume is increased to 1.0 L,
assuming constant temperature. (Note: Convert mL to L.)
___________________________________ P1V1 = P2V2
Knowns
___________________________________ V1 = 0.250 L V2 = 1.0 L P1 = 880. mm Hg
Solving For P2
P2 =
___________________________________ P1V1
V2
___________________________________ 0.250 L
= 220 mm Hg
Calculate P2 = 880. torr ×
1.0 L
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide 13 ___________________________________ Boyle’s Law Problems
A sample of gaseous nitrogen in a 65.0 L automobile air
bag has a pressure of 745 mm Hg.
If the sample is transferred to a 25.0 L bag at the same
temperature, what is the pressure in the bag?
___________________________________ a) 2.18 mm Hg
___________________________________ ___________________________________ b) 1940 mm Hg
___________________________________ c) 287 mm Hg
d) 0.458 mm Hg
___________________________________ P1V1
65.0 L
P2 =
= 745 torr ×
= 1940 mm Hg
25.0 L
V2
___________________________________ Sense check: As volume decreases, pressure should increase!
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 14 ___________________________________ Temperature in Gas Law Problems
Kelvin Temperature Scale
___________________________________ Derived from the relationship between temperature
and volume of a gas.
___________________________________ As a gas is cooled by 1 ºC increments,
the gas volume decreases in increments of 1/273.
___________________________________ All gases are expected to have zero volume if cooled to −273 ºC.
___________________________________ V ‐T relationship of methane
(CH4) with extrapolation (‐‐‐‐‐) to absolute zero.
___________________________________ ___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 15 ___________________________________ Temperature in Gas Law Problems
___________________________________ This temperature (−273 ºC) is referred to as absolute zero.
Absolute zero is the temperature (0 K) when the
volume of an ideal gas becomes zero.
___________________________________ All gas law problems use the Kelvin temperature scale!
___________________________________ Celsius temperature
___________________________________ TK = T°C + 273
___________________________________ ___________________________________ Kelvin temperature
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Slide ___________________________________ Charles’ Law
16 ___________________________________ The volume of a fixed quantity of gas is directly
proportional to the absolute temperature of the gas
at constant pressure.
___________________________________ V = k T or V T
___________________________________ V
=k
T
___________________________________ Most common form:
___________________________________ V1 V2
=
T1 T2
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Charles’ Law Problems
17 ___________________________________ 3.0 L of H2 gas at −15 ºC is allowed to warm to 27 ºC at
constant pressure. What is the gas volume at 27 ºC?
___________________________________ V1 V2
=
T1 T2
V1 = 3.0 L
T1 = −15 ºC = 258 K
V1T2
Solving For V2
V2 =
T1
___________________________________ Knowns
Calculate
V2 =
___________________________________ V1T2
300. K
= 3.5 L
= 3.0 L ×
258 K
T1
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ T2 = 27 ºC = 300. K
___________________________________ ___________________________________ Charles’ Law Problems
18 ___________________________________ A gas has a volume of 3.00 L at 10.0 ºC.
What is the temperature of the gas if it
expands to 6.00 L, assuming constant pressure?
___________________________________ V1 V2
=
T1 T2
___________________________________ V1 = 3.00 L
V2 = 6.00 L
T1 = 10.0 ºC = 283 K
T1V2
Solving For T2 T2 =
V1
T1V2
6.00 L
= 566 K
Calculate T2 =
= 283 K ×
3.00 L
V1
Knowns
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ ___________________________________ ___________________________________ Slide ___________________________________ Charles’ Law Problems
19 ___________________________________ At 321 K, a gas occupies 635 mL of volume.
If the temperature is decreased to 216 K,
what is the new gas volume?
___________________________________ ___________________________________ a) 916 mL
b) 109 mL
V2 =
c) 943 mL
V1T2
216 K
= 427 mL
= 635 mL ×
321 K
T1
___________________________________ d) 427 mL
___________________________________ Sense Check: As temperature decreases, volume decreases!
___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Avogadro’s Law
20 ___________________________________ Equal volumes of different gases at constant T and P
contain the same number of molecules.
___________________________________ ___________________________________ ___________________________________ ___________________________________ 1 volume unit
4 molecules
1 volume unit
4 molecules
2 volume units
8 molecules
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Slide ___________________________________ ___________________________________ Avogadro’s Law
21 ___________________________________ Given the following gas phase reaction:
N2 + 3 H 2
2 NH3
___________________________________ If 12.0 L of H2 gas are present, what volume of N2 gas is
required for complete reaction? T and P are held constant.
___________________________________ By Avogadro’s Law, we can use the reaction stoichiometry
to predict the N2 gas needed.
Knowns
___________________________________ VH2 = 12.0 L
___________________________________ Solving For VN2
Calculate
12.0 L H2 × 1 L N2 = 4.00 L N2 required
3 L H2
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide ___________________________________ Avogadro’s Law
22 ___________________________________ Given the following gas phase reaction:
2 H2 + O 2
2 H2 O
___________________________________ At constant T and P, how many liters of O2 are required
to make 45.6 L of H2O?
___________________________________ a) 11.4 L
b) 45.6 L
c) 22.8 L
___________________________________ 45.6 L H2O ×
d) 91.2 L
1 L O2 = 22.8 L O2 required
2 L H 2O
___________________________________ ___________________________________ Sense Check: Less moles of O2 equal less L of O2!
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 23 ___________________________________ Mole/Mass/Volume Relationships
___________________________________ Molar Volume: volume 1 mol of gas occupies at STP
molar volume = 22.4 L/mol at STP
___________________________________ Molar volume can be used as a conversion factor if the
mass and volume occupied by a gas are known.
___________________________________ Example:
___________________________________ 1.0 L of O2 at STP has a mass of 1.429 g. Show
that the molar mass of O2 is 32.0 g/mol.
___________________________________ 22.4 L O2 = 32.0 g/mol O2
1.429 g O2
×
1.0 L O2
1 mol O2
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 24 ___________________________________ ___________________________________ Mole/Mass/Volume Relationships
___________________________________ If 3.00 L of a gas measured at STP has a mass of 5.35 g,
calculate the molar mass.
___________________________________ a) 39.9 g/mol
b) 79.6 g/mol
c) 12.6 g/mol
___________________________________ 22.4 L O2 = 39.9 g/mol
5.35 g gas
×
1 mol gas
3.00 L gas
___________________________________ d) 25.0 g/mol
___________________________________ Unit Check: Molar mass has units of g/mol,
so use dimensional analysis when setting up the problem!
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide ___________________________________ Combined Gas Laws
25 A combination of Boyle’s and Charles’ Laws.
___________________________________ Used in problems involving changes in P, T, and V
with a constant amount of gas.
___________________________________ P1V1
P V
= 2 2
T1
T2
___________________________________ The volume of a fixed quantity of gas depends on the
temperature and pressure.
It is not possible to state the volume of gas without
stating the temperature and pressure.
___________________________________ ___________________________________ Standard Temperature and Pressure (STP):
___________________________________ 0.00 °C (273.15 K) and 1 atm (760 torr)
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 26 ___________________________________ Combined Gas Law Problems
A sample of gas occupies 125 mL at STP.
What is the volume of the gas at 65 ºC and 320. torr?
___________________________________ P1V1
P V
= 2 2
T1
T2
___________________________________ Knowns V1 = 0.125 L P1 = 760 torr
P2 = 320 torr
Solving For V2
___________________________________ T1 = 273 K
T2 = 65 ºC = 338 K
___________________________________ P1V1T2
V2 =
T1P2
___________________________________ Calculate
V2 = V1 × P1 ×T2 = 0.125 L × 760. torr × 338 K = 0.368 L
320. torr 273 K
P2 T 1
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 27 ___________________________________ ___________________________________ Combined Gas Law Problems
What is the volume at STP for a gas that occupies
1.62 L at 616 torr and 42 °C?
___________________________________ P1V1
P V
= 2 2
T1
T2
___________________________________ Knowns V1 = 1.62 L
Solving For V2
___________________________________ P1 = 616 torr T1 = 42 °C = 315 K
P2 = 760. torr T2 = 273 K
___________________________________ P1V1T2
V2 =
T1P2
___________________________________ Calculate
V2 = V1 ×P1 × T2= 1.62 L × 616 torr × 273 K = 1.14 L
760. torr
315 K
P2 T 1
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide 28 ___________________________________ Combined Gas Law Problems
___________________________________ A balloon is filled with 266 L of He gas, measured at 38 °C
and 0.995 atm. What will its volume be when the
temperature is lowered to −76 ° C and the pressure
is 0.561 atm?
___________________________________ ___________________________________ a) 299 L
b) 95.0 L
___________________________________ c) 745 L
d) 237 L
___________________________________ V2 = V1 × P1 × = 266 L × 0.995 atm × 197 K = 299 L
T2 P2 T1
0.561 atm
311 K
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Ideal Gas Law
29 ___________________________________ A single equation relating all properties of a gas.
PV = nRT
___________________________________ where R is the universal gas constant
___________________________________ ___________________________________ Constant n and T
Constant n and P
V 1/P
Boyle’s Law
V T
Charles’ Law
V n
Avogadro’s Law
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Constant P and T
___________________________________ ___________________________________ Ideal Gas Constant
30 ___________________________________ R is derived from conditions at STP. Calculate R.
PV = nRT
___________________________________ Knowns P = 1.00 atm V = 22.4 L T = 273 K n = 1.00 mol
Solving For R
R =
___________________________________ PV
nT
___________________________________ Calculate
___________________________________ R = P × V = 1.00 atm × 22.4 L = 0.0821 L . atm
mol . K
1.00 mol × 273 K
n×
T
___________________________________ Units are critical in ideal gas problems!
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Ideal Gas Law Practice
31 ___________________________________ How many moles of He are contained in a 0.900 L
container at 30. ºC and 0.800 atm?
___________________________________ PV = nRT
Knowns P = 0.800 atm V = 0.900 L T = 30. ºC = 303 K
Solving For n
___________________________________ PV
RT
n =
___________________________________ Calculate
n = P × V=
R×
T
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ = 0.0289 mol
0.800 atm × 0.900 L
0.0821 L . atm × 303 K
mol . K
___________________________________ ___________________________________ Ideal Gas Law Practice
32 ___________________________________ What volume will be occupied by 0.393 mol of N2
at 0.971 atm and 24 °C?
___________________________________ PV = nRT
Knowns P = 0.971 atm n = 0.393 mol T = 24 ºC = 297 K
Solving For V
V =
___________________________________ nRT
P
___________________________________ Calculate
___________________________________ V = nRT = 0.393 mol × 0.0821 L . atm × 297 K = 9.87 L
P
mol . K
___________________________________ 0.971 atm
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 33 ___________________________________ Ideal Gas Law Practice
___________________________________ The ideal gas law can also be written in terms of
molar mass of a gas.
___________________________________ PV = nRT
n =
___________________________________ mass in grams (g)
___________________________________ molar mass ( )
___________________________________ PV = gRT

© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide ___________________________________ Ideal Gas Law Practice
34 ___________________________________ A 0.210 g gas sample has a pressure of 432 torr
in a 333 mL container at 23 ºC.
What is the molar mass of the gas?
___________________________________ PV = gRT

Knowns
___________________________________ P = 432 torr = 0.568 atm V = 0.333 L
T =296 K mass = 0.210 g
___________________________________ Solving For 
___________________________________ Calculate
 = gRT = 0.210 g × 0.0821 L atm/mol K × 296 K= 27.0 g/mol
PV
Slide 35 0.568 atm × 0.333
L
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ ___________________________________ Ideal Gas Law Practice
___________________________________ Calculate the molar mass () of an unknown gas
if 0.768 g occupies a volume of 754 mL at 30. ºC
and 342 torr.
___________________________________ a) 35.4 g/mol
___________________________________ b) 21.9 g/mol
___________________________________ c) 87.3 g/mol
d) 55.0 g/mol
___________________________________  = gRT = 0.768 g × 0.0821 L atm/mol K × 303 K= 56.3 g/mol
PV
0.450 atm × 0.754
L
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 36 ___________________________________ ___________________________________ Kinetic Molecular Theory
___________________________________ A general theory developed to explain the behavior
and theory of gases, based on the motion of particles.
___________________________________ Assumptions of Kinetic Molecular Theory (KMT):
1) Gases consist of tiny particles.
___________________________________ 2) The distance between particles is large when compared
to particle size. The volume occupied by a gas is
mostly empty space.
3) Gas particles have no attraction for one another.
___________________________________ ___________________________________ 4) Gas particles move linearly in all directions, frequently
colliding with the container walls or other particles.
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide 37 ___________________________________ Kinetic Molecular Theory
___________________________________ Assumptions of KMT (continued):
5) Collisions are perfectly elastic.
No energy is lost during collisions.
___________________________________ 6) The average kinetic energy for particles is the same for
all gases (regardless of molar mass) at the same
temperature.
KE = 1/2mv 2
___________________________________ ___________________________________ where m is the mass and v is the velocity of the particle
The average kinetic energy is directly proportional to
temperature (in K).
___________________________________ Gases which behave under these assumptions are
know as ideal gases.
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Real Gases
38 ___________________________________ Real gases typically behave like ideal gases over
a fairly wide range of temperatures and pressures.
___________________________________ Conditions where real gases deviate from ideal gases:
___________________________________ 1) At high pressure (small volumes)
___________________________________ Distance between particles is small and the particles
do not behave independently.
___________________________________ 2) At low temperature
Particles experience intermolecular interactions.
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 39 ___________________________________ ___________________________________ Dalton’s Law of Partial Pressures
The total pressure of a mixture is the sum of the partial
pressures of the different gases in the mixture.
___________________________________ Ptotal = P1 + P2 + P3…
___________________________________ Each gas behaves independently in the mixture.
___________________________________ Application of Dalton’s Law
Gases collected over H2O contain
both the gas and H2O vapor.
___________________________________ Vapor pressure of H2O is constant
at a given T.
___________________________________ Pbottle is equalized so that Pbottle = Patm thus
Collecting a gas over water
___________________________________ Patm = Pgas + PH2O
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Partial Pressures Problems
40 ___________________________________ A sample of O2 gas is collected over water at 22 ºC and
662 torr. What is the partial pressure of O2 gas? The
vapor pressure of water is 19.8 torr at 22 ºC.
___________________________________ ___________________________________ Knowns
Patm = 662 torr
Solving For PO2
Calculate
PH2O = 19.8 torr
___________________________________ PO2 = Patm – PH2O
___________________________________ PO2 = 662 torr – 19.8 torr = 642 torr
___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Partial Pressures Problems
41 ___________________________________ A 250. mL sample of O2 was collected over water at
23 ºC and 760 torr. What volume will the O2 occupy at
23 ºC when PO2 is 760. torr?
The vapor pressure of water at 23 ºC is 21.2 torr.
Knowns VO2 + H2O = 250 mL
PH2O= 21.2 torr
Solving For VO2
___________________________________ ___________________________________ Patm = PO2 + PH2O = 760. torr
___________________________________ 1) Solve for PO2 using Dalton’s Law
2) Solve for VO2 using Boyle’s Law
___________________________________ Calculate
___________________________________ PO2 = Ptotal – PH2O= 760 torr – 21.2 torr = 739 torr
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ Partial Pressures Problems
42 ___________________________________ (continued)
A 250. mL sample of O2 was collected over water at
23 ºC and 760 torr. What volume will the O2 occupy at
23 ºC when PO2 is 760 torr?
The vapor pressure of water at 23 ºC is 21.2 torr.
___________________________________ ___________________________________ Calculate Solve for VO2 with Boyle’s Law
P1V1 = P2V2
V2 =
___________________________________ P1V1
V2 =
P2
___________________________________ P1V1
739 mm Hg
= 0.250 L ×
= 0.243 L O2
760 mm Hg
P2
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide ___________________________________ Gas Density
43 ___________________________________ Density of a liquid or solid is expressed in g/mL, but
gas density is very low, so the standard units are g/L.
density (d ) =
___________________________________ g
mass
=
L
volume
___________________________________ The density of a gas at STP can also be related to the
compound’s molar mass.
g
1 mol
dstp = molar mass
×
22.4 L
mol
(
)
)(
___________________________________ g
=
L
___________________________________ Note: gas densities must be cited at a specific
temperature as volume changes as a function of
temperature (Charles’ Law).
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Gas Density Practice
44 ___________________________________ Calculate the density of Cl2 at STP.
(
d = molar mass
___________________________________ g
g
1 mol
×
=
22.4 L
L
mol
)(
)
___________________________________ molar mass Cl2 = 70.9 g/mol
d =
70.9 g Cl2
1 mol Cl2
___________________________________ × 1 mol Cl2 = 3.17 g/L
22.4 L Cl2
___________________________________ Sense Check: Gas densities are expected to be low.
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 45 ___________________________________ ___________________________________ Gas Stoichiometry
___________________________________ ___________________________________ ___________________________________ ___________________________________ At STP: the molar volume can be used as a conversion
factor to convert between moles and volume.
___________________________________ Non STP Conditions: use the ideal gas law to convert
between moles and volume.
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide 46 ___________________________________ Gas Stoichiometry Practice at STP ___________________________________ For the following reaction:
Calculate the number of moles of phosphorus needed to
react with 4.0 L of H2 gas at 273 K and 1.0 atm.
P4 (s) + 6 H2 (g)
___________________________________ 4 PH3 (g)
___________________________________ Knowns V =4.0 L T = 273 K P = 1.0 atm
Solution Map
L H2
mol H2
___________________________________ mol P4
___________________________________ Calculate
1 mol H2
× 1 mol P4
mol P4 = 4.0 L H2 ×
22.4 L H2
6 mol H2
= 0.0030 mol P4
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 47 ___________________________________ ___________________________________ Gas Stoichiometry Volume Practice
___________________________________ Calculate the volume of N2 necessary to react with
9.0 L of H2 gas at 450 K and 5.00 atm.
N2 (g) + 3 H2 (g)
___________________________________ 2 NH3 (g)
___________________________________ a) 9.0 L
b) 3.0 L
c) 27.0 L
9.0 L H2 ×
1 L N2
3 L H2
___________________________________ = 3.0 L N2
d) 1.0 L
___________________________________ At constant T and P, the volume ratio can be used
in place of the mole ratio!
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ ___________________________________ Gas Stoichiometry Practice
With the Ideal Gas Law
48 ___________________________________ Given the following reaction:
2 NaN3 (s)
2 Na (s) + 3 N2 (g)
___________________________________ If an air bag should be filled with a pressure of 1.09 atm
at 22 ºC, what amount of solid NaN3 is needed to fill
a bag with a volume of 45.5 L?
___________________________________ Knowns P = 1.09 atm V = 45. 5L T = 295K
___________________________________ Solving for n of N2 then find the mass of NaN3 needed.
___________________________________ Calculate
= 2.05 mol N2
n = PV =
1.09 atm × 45.5 L
RT
0.0821 L atm/mol K × 295 K
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide ___________________________________ Gas Stoichiometry Practice
With the Ideal Gas Law
49 ___________________________________ (continued)
Given the following reaction:
2 NaN3 (s)
___________________________________ 2 Na (s) + 3 N2 (g)
___________________________________ If an air bag should be filled with a pressure of 1.09 atm
at 22.0 ºC, what amount of solid NaN3 is needed to fill
a bag with a volume of 45.5 L?
Calculate
___________________________________ Use the reaction stoichiometry!
2.05 mol N2 × 2 mol
3 mol
NaN
3 N2
___________________________________ × 64.99 g NaN3 = 88.8 g NaN3
1 mol NaN3
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 50 ___________________________________ ___________________________________ Gas Stoichiometry Practice
What volume of O2 at 760. torr and 25 ºC is needed to
react fully with 3.2 g of C2H6 (propane)?
2 C2H6 (g) + 7 O2 (g)
___________________________________ 4 CO2 (g) + 6 H2O (l)
___________________________________ m = 3.2 g T = 298 K P = 1.00 atm
Knowns
Solution Map
m C2H6
Calculate
___________________________________ mol C2H6
mol O2
volume O2
___________________________________ 1 mol C2H6
7 mol O2
= 0.37 mol O2
×
3.2 g C2H6 ×
30.08 g C2H6 2 mol C2H6
V = nRT
P
=
1.00 atm
___________________________________ = 9.1 L
© 2014 John Wiley & Sons, Inc. All rights reserved.
Slide ___________________________________ 0.37 mol × 0.0821 L . atm × 298 K
mol . K
___________________________________ Gas Stoichiometry Practice
51 ___________________________________ What volume of H2 at 739 torr and 21 ºC is liberated
by 42.7 g of Zn when it reacts with HCl?
Zn (s) + 2 HCl (g)
a) 7.6 L
b) 16.2 L
c) 3.2 L
d) 1.8 L
m Zn
___________________________________ ZnCl2 (s) + H2 (g)
mol Zn
mol H2
___________________________________ volume H2
42.7 g Zn × 1 mol Zn × 1 mol H2 = 0.653 mol H2
65.38 g Zn 1 mol Zn
___________________________________ ___________________________________ V = nRT = 0.653 mol × 0.0821 L atm/mol K × 294 K= 16.2 L H
2
P
0.972 atm
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide 52 ___________________________________ Chemistry in Action
___________________________________ What the Nose Knows
Dogs use smell to detect many drugs, explosives, etc.
based on trace amounts of chemical compounds in the air.
___________________________________ Sensing low concentrations of chemicals is useful!
___________________________________ Better Coffee
Better Science
Artificial noses could sniff
out cancer or explosives!
___________________________________ For more information, see: http://www.scs.illinois.edu/suslick/smell_seeing.html
___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 53 ___________________________________ ___________________________________ Learning Objectives
___________________________________ 12.1 Properties of Gases
1) Explain atmospheric pressure and how it is measured.
2) Be able to convert between the various units of pressure.
___________________________________ 12.2 Boyle’s Law
___________________________________ 3) Use Boyle’s Law to calculate changes in pressure or
volume of a gas at constant temperature.
___________________________________ 12.3 Charles’ Law
___________________________________ 4) Use Charles’ Law to calculate changes in temperature or
volume of a gas at constant pressure.
___________________________________ © 2014 John Wiley & Sons, Inc. All rights reserved.
Slide 54 ___________________________________ Learning Objectives
___________________________________ 12.4 Avogadro’s Law
5) Solve problems using the relationships between moles,
mass, and volume of gases.
___________________________________ ___________________________________ 12.5 Combined Gas Law
6) Use the combined gas law to calculate changes in
pressure, volume, or temperature of a gas sample.
___________________________________ 12.6 Ideal Gas Law
___________________________________ 7) Use the ideal gas law to solve problems involving
pressure, volume, temperature, and moles of a gas.
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________ Slide 55 ___________________________________ Learning Objectives
___________________________________ 12.7 Dalton’s Law of Partial Pressures
___________________________________ 8) Use Dalton’s Law of Partial Pressures to calculate the
total pressure for a mixture of gases or the pressure of
a single gas in a mixture of gases.
___________________________________ 12.8 Density of Gases
9) Calculate the density of a gas. (Pay attention to units!)
___________________________________ 12.9 Gas Stoichiometry
___________________________________ 10) Solve stoichiometry problems involving gases.
(Pay attention to the states of matter and use gas laws
only for gases!)
© 2014 John Wiley & Sons, Inc. All rights reserved.
___________________________________