Transcript Chapter 9 Gases: Their Properties and Behavior

Chapter 9
Gases: Their Properties and
Behavior
Gases and Gas Pressure
Gas
% by Vol Gas
% by Vol
Nitrogen
78.084
Krypton
0.0001
Oxygen
20.948
Carbon monoxide
0.00001
Argon
0.934
Xenon
0.000008
Carbon dioxide
0.033
Ozone
0.000002
Neon
0.00182
Ammonia
0.000001
Hydrogen
0.0010
Nitrogen dioxide
0.0000001
Helium
0.00052
Sulfur dioxide
0.00000002
Methane
0.0002
Properties of Gases
• Gases mix completely with one another to form
homogenous mixtures
• Gases can be compressed (keyboard cleaner)
• Gases exert pressure on what ever is around
them (balloon, film canister)
• Gases expand into whatever volume is available
(coke bottle and balloon)
• Gases are described in terms of their
temperature and pressure, the volume occupied
and the amount of gas present (gas properties)
Properties of Gases
• Pressure (P)
Pressure = force / area
Force = mass x acceleration
• Units of Pressure
–
–
–
–
Atmosphere (atm)
Torr
Pascals (Pa)
mmHg
• Pressure conversions
– 1 atm = 1.01325 x 105 Pa
– 1 atm = 760 torr
– 1 atm = 760 mmHg
Problem
• Convert these pressure values.
– 120 mmHg to atm
– 100 kPa to mmHg
– 270 torr to atm
Properties of Gases
• Volume (V)
– mL
–L
– cm3
• Amount of gas (n) – moles
• Temperature (T) - Kelvins
Kinetic Molecular Theory
• A gas is composed of
molecules whose size
is much smaller than
the distance between
them
• Gas molecules move
randomly at various
speeds and in every
possible direction
Kinetic Molecular Theory
• Except when gas molecules collide, forces of
attraction and repulsion between them are
negligible
• When collisions between molecules occur, they
are elastic
• The average kinetic energy of gas molecules is
proportional to the absolute temperature (liquid
N2 ballons, can, solar bag)
Ek = ½ (mass)(speed)2
Distribution of molecular speeds at three temperatures.
Relationship between molar mass and
molecular speed.
Problem
• Place these gases in order of increasing
average molecular speed at 25oC: Kr, CH4,
N2, and CH2Cl2
The Gas Laws
• Gas properties
– Gases are described in terms of their
temperature and pressure, the volume
occupied and the amount of gas present (gas
properties)
• Gas Laws can be derived using
– Kinetic Molecular Theory
The Gas Laws
• The Pressure-Volume Relationship:
Boyle’s Law
– The volume (V) of an ideal gas varies
inversely with the applied pressure (P) when
temperature (T) and the amount (n, moles)
are constant
– PiVi = PfVf
Problems
• A sample of nitrogen gas at 298 K and 745 torr
has a volume of 37.42 L. What volume will it
occupy if the pressure is increased to 894 torr at
constant temperature?
–
–
–
–
–
A)22.3 L
B)31.2 L
C)44.9 L
D)112 L
E)380 L
Problems
• A sample of carbon dioxide gas at 125°C and
248 torr occupies a volume of 275 L. What will
the gas pressure be if the volume is increased to
321 L at 125°C?
–
–
–
–
–
A)212 torr
B)289 torr
C)356 torr
D)441 torr
E)359 torr
The Gas Laws
• The Temperature-Volume Relationship –
Charles’s Law
– The volume (V) of an ideal gas varies directly
with absolute temperature (T) when pressure
(P) and amount (n) are constant.
– Vi / Ti = Vf / Tf
Problems
• A sample container of carbon monoxide
occupies a volume of 435 mL at a pressure of
785 torr and a temperature of 298 K. What
would its temperature be if the volume were
changed to 265 mL at a pressure of 785 torr?
–
–
–
–
–
A)182 K
B)298 K
C)387 K
D)489 K
E)538 K
Problems
• A 0.850-mole sample of nitrous oxide, a gas
used as an anesthetic by dentists, has a volume
of 20.46 L at 123°C and 1.35 atm. What would
be its volume at 468°C and 1.35 atm?
–
–
–
–
–
A)5.38 L
B)10.9 L
C)19.0 L
D)38.3 L
E)77.9 L
The Combined Gas Law
• Combined Gas Law – used when a
specific amount of gas is exposed to two
different conditions
– P1V1 / T1 = P2V2 / T2
Problems
• A sample of propane, a component of LP
gas, has a volume of 35.3 L at 315 K and
922 torr. What is its volume at STP?
– A)25.2 L
– B)30.6 L
– C)33.6 L
– D)37.1 L
– E)49.2 L
Problems
• Calculate the pressure of a helium sample at 207.3°C and 768 mL if it exerts a pressure of
175 kPa at 25.0°C and 925 mL.
–
–
–
–
–
A)32.1 kPa
B)46.6 kPa
C)657 kPa
D)953 kPa
E)340 kPa
Problems
• A carbon dioxide sample weighing 44.0g
occupies 32.68 L at 65°C and 645 torr.
What is its volume at STP?
– A)22.4 L
– B)31.1 L
– C)34.3 L
– D)35.2 L
– E)47.7 L
The Gas Laws
• The Amount-Volume Relationship:
Avogadro’s Law
– The volume (V) of an ideal gas varies directly
with amount (n) when temperature (T) and
pressure (P) are constant
– V1 / n1 = V2 / n2
The Ideal Gas Law
• Boyle’s, Charles’s and Avogadro’s Laws
can be combined to form the Ideal Gas
Law
– PV = nRT
• R – ideal gas constant
– R = 0.0821 atm L / mol K
– R = 62.36 torr L / mol K
– R = 8.314 J / mol K
Problems
• A sample of nitrogen gas is confined to a 14.0 L
container at 375 torr and 37.0°C. How many
moles of nitrogen are in the container?
–
–
–
–
–
A)0.271 mol
B)2.27 mol
C)3.69 mo1
D)206 mol
E)227 mol
Stoichiometric Relationships with
Gases
• Various questions can be asked that relate
gas laws to stoichiometry.
Problems
• A 250.0-mL sample of ammonia, NH3(g), exerts
a pressure of 833 torr at 42.4°C. What mass of
ammonia is in the container?
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–
–
–
–
A)0.0787 g
B)0.180 g
C)8.04 g
D)17.0 g
E)59.8 g
Stoichiometric Relationships with
Gases
•
The ideal gas law can be used to
determine density if the molar mass of
the gas is known or the molar mass if the
mass of gas is known
d = m / V = PM / RT
•
Density increases with molar mass
Problems
• 9What is the density of carbon dioxide gas
at -25.2°C and 98.0 kPa?
– A)0.232 g/L
– B)0.279 g/L
– C)0.994 g/L
– D)1.74 g/L
– E)2.09 g/L
Problems
• A flask with a volume of 3.16 L contains 9.33
grams of an unknown gas at 32.0°C and 1.00
atm. What is the molar mass of the gas?
–
–
–
–
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A)7.76 g/mol
B)66.1 g/mol
C)74.0 g/mol
D)81.4 g/mol
E)144 g/mol
Problems
• Dr. I. M. A. Brightguy adds 0.1727 g of an
unknown gas to a 125-mL flask. If Dr. B finds the
pressure to be 736 torr at 20.0°C, is the gas
likely to be methane, CH4, nitrogen, N2, oxygen,
O2, neon, Ne, or argon, Ar?
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–
–
–
–
A)CH4
B)N2
C)Ne
D)Ar
E)O2
Partial Pressures and Dalton’s Law
• Dalton’s Law of Partial Pressures – the
total pressure exerted by a mixture of
gases is the sum of the partial pressures
of the individual gases in the mixture.
– Since all gases in a mixture occupy the same
volume and are at the same temperature then
the pressure is directly related to the moles of
gas
ntotal = ngas1 + ngas2 …..
Partial Pressures and Dalton’s Law
• Placing ntotal into the ideal gas law
PtotalV = ntotalRT
Ptotal = ntotalRT / V
Ptotal = Pgas1 + Pgas2 + …..,
Partial Pressures and Dalton’s Law
Pgas1 / Ptotal = ngas1 / ntotal
ngas1 / ntotal = Xgas1
• Xgas1 is called the mole fraction
– All mole fractions = 1
Problems
• What is the pressure in a 7.50-L flask if 0.15 mol
of carbon dioxide is added to 0.33 mol of
oxygen? The temperature of the mixture is
48.0°C.
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A)0.252 atm
B)0.592 atm
C)1.69 atm
D)3.96 atm
E)4.80 atm
Problems
• If 0.750 L of argon at 1.50 atm and 177°C and
0.235 L of sulfur dioxide at 95.0 kPa and 63.0°C
are added to a 1.00-L flask and the flask's
temperature is adjusted to 25.0°C, what is the
resulting pressure in the flask?
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A)0.0851 atm
B)0.244 atm
C)0.946 atm
D)1.74 atm
E)1.86 atm
Partial Pressures and Dalton’s Law
• Collecting Gas over water – most common
way of determining the # moles of a gas
sample as long as the gas is not water
soluble.
Problems
• Small quantities of hydrogen can be prepared by
the addition of hydrochloric acid to zinc. A
sample of 195 mL of hydrogen was collected
over water at 25°C and 753 torr. What mass of
hydrogen was collected? (Pwater = 24 torr at
25°C)
–
–
–
–
–
A)0.00765 g
B)0.0154 g
C)0.0159 g
D)0.0164 g
E)0.159 g
Behavior of Ideal Gases
• Ideal Gas Law provides fairly accurate
predictions for the pressure, volumes and
temperatures of most gases except
– At extremely high pressures
– Extremely low temperatures
Optional Homework
• Text – 9.26, 9.28, 9.36, 9.44, 9.46, 9.48,
9.50, 9.52, 9.54, 9.56, 9.62, 9.64, 9.66,
9.74, 9.78, 9.90, 9.96, 9.104, 9.106
• Chapter 9 Homework on the website
Required Homework
• Chapter 9 Assignment