Gases: Their Properties and Behavior

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Chapter 9

• Gases Their Properties and Behavior

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Three States of Matter

Solids
Liquids
Gases
3
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, 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)

4
Compressibility of Gases

• Airbags fill with N2 gas in an accident.
• Gas is generated by the decomposition of sodium
  azide, NaN3.
• 2 NaN3 2 Na 3 N2

Composition of Air Nitrogen Oxygen Argon Carbob
dioxide
5
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
6
Factors Affecting Gas Pressure

• Temperature
• Raising the temperature of a gas increases the
  pressure
• The faster moving particles collide with the
  walls of the container more frequently
• Temperature and pressure is also a linear
  relationship
• In contrast, decreasing the temperature of a gas
  decreases the pressure

7
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

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Atmospheric Pressure

• - pressure created from the mass of the
  atmosphere pressing down on the earths surface
• Standard atmospheric pressure at sea level 760
  mmHg

9
Problem

• Convert these pressure values.
• 120 mmHg to atm
• 100 kPa to mmHg
• 270 torr to atm

10
Properties of Gases

• Volume (V)
• mL
• L
• cm3
• Amount of gas (n) moles
• Temperature (T) - Kelvins

11
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

12
The Gas Laws

• Ideal Gas A gas whose behavior follows the gas
  laws exactly.
• The physical properties of a gas can be defined
  by four variables
• P pressure
• T temperature
• V volume
• n number of moles

13
The Gas Laws

• The Pressure-Volume Relationship Boyles 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

PV k
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The Gas Laws
Boyles Law
(constant n and T)
PV k
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Sample Problem UsingBoyles Law
A balloon contains 30.0 L of helium gas at
103kPa. What is the volume of the helium when
the balloon rises to an altitude where the
pressure is only 25.0 kPa? (assume the
temperature remains constant) What do you
think will happen to the volume at a higher
temperature knowing what you know already about
gases?
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Sample Problem UsingBoyles Law
P1 103 kPa P2 25.0 kPa V1 30.0 L V2
? L P1V1 P2V2 or P1V1 / P2 V2 V2
(30.0 L) (103 kPa)
25.0 KPa V2 1.24 x 102 L (3 sig figs)
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Sample Problem UsingBoyles Law
Nitrous oxide (N2O) is used as an anesthetic. The
pressure on 2.50 L of N2O changes from 105 KPa to
40.5 KPa. If the temperature does not change,
what will the new volume be? P1 105 kPa
P2 40.5 kPa V1 2.50 L V2 ? L P1V1
P2V2 or P1V1 / P2 V2 V2 (2.50 L)
(105 kPa)
40.5 KPa V2 6.48 L (3 sig figs)
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Sample Problem UsingBoyles Law
A gas with a volume of 4.00 L at a pressure of
205 KPa is allowed to expand to a volume of 12.0
L. What is the pressure in the container if the
temperature remains constant? P1 205 kPa
P2 ? kPa V1 4.00 L V2 12.0 L P1V1
P2V2 or P1V1 / V2 P2 P2 (4.00 L)
(205 kPa)
12.0 L P2 68.3 KPa (3 sig figs)
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Sample Problem UsingBoyles Law
The volume of a gas at 99.6 KPa and 24ºC is
4.23L. What volume will it occupy at 93.3 KPa and
24ºC? P1 99.6 kPa P2 93.3 kPa T1 24ºC V1
4.23 L V2 ? L T2 24ºC P1V1 P2V2 or
P1V1 / P2 V2 V2 (4.23 L) (99.6 kPa)
93.3
kPa V2 4.52 L (3 sig figs)
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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

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Problems

• A sample of carbon dioxide gas at 125C and 248
  torr occupies a volume of 275 L. What will the
  gas pressure be if the volume is increased to 321
  L at 125C?
• A)212 torr
• B)289 torr
• C)356 torr
• D)441 torr
• E)359 torr

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The Gas Laws

• The Temperature-Volume Relationship
• Charles 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

V a T
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The Gas Laws
Charles Law
V a T
(constant n and P)
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Sample Problem UsingCharless Law
A balloon inflated in a room at 24ºC has a volume
of 4.00 L. The balloon is then heated to a
temperature of 58ºC. What is the new volume if
the pressure remains constant? T1 24ºC or 297
K V1 4.00 L T2 58ºC or 331 K V2 ? L
When using gas laws always express the
temperatures in kelvins! T1 24ºC 273 297
K T2 58ºC 273 331 K
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Sample Problem UsingCharless Law
A balloon inflated in a room at 24ºC has a volume
of 4.00 L. The balloon is then heated to a
temperature of 58ºC. What is the new volume if
the pressure remains constant? T1 24ºC or 297
K V1 4.00 L T2 58ºC or 331 K V2 ? L
V1 V2 or V1T2 V2
T1 T2
T1 V2 (4.00 L) (331 K) 4.46 L 297 K
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Sample Problem UsingCharless Law
If a sample of gas occupies 6.80 L at 325ºC, what
will its volume be at 25ºC if the pressure does
not change? T1 325ºC or 598 K V1 6.80 L T2
25ºC or 298 K V2 ? L V1 V2 or
V1T2 V2 T1
T2 T1 V2 (6.80 L) (298 K)
3.39 L 598 K
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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

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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 123C and 1.35 atm. What would be its
  volume at 468C and 1.35 atm?
• A)5.38 L
• B)10.9 L
• C)19.0 L
• D)38.3 L
• E)77.9 L

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The Gas Laws

• The Amount-Volume Relationship Avogadros 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

V a n
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The Gas Laws
Avogadros Law
V a n
(constant T and P)
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This is where we get the fact that 22.4 L 1 mole

• Only at STP
• 0ºC
• 1 atm
• This way we compare gases at the same
  temperature and pressure.

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Summary
Boyles Law Charles Law Avogadros Law
constant T n constant P n constant P T
V 1/P V T V n

PinitialVinitial PfinalVfinal
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The Ideal Gas Law

• Boyles, Charless and Avogadros 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

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Sample Problem Using Ideal Gas Law
When the temperature of a rigid hollow sphere
containing 685 L of helium gas is held at 621 K,
the pressure of the gas is 1.89 x 103 kPa. How
many moles of helium does the sphere contain? P
1.89 x 103 kPa V 685 L T 621 K PV
nRT or PV / RT n n (1.89 x 103 kPa) (685
L) mol K (8.31L kPa) (621K) n 251 mol He
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Sample Problem Using Ideal Gas Law
A childs lungs can hold 2.20 L. How many grams
of air do her lungs hold at a pressure of 102 kPa
and a body temperature of 37ºC? Use a molar mass
of 29 g for air. P 102 kPa V 2.20 L T
310 K PV nRT or PV / RT n n (102
kPa) (2.20 L) mol K (8.31L kPa) (310K) n
0.087 mol air 0.087 mol air x 29g air / mol
air 2.5 g air
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Problems

• A sample of nitrogen gas is confined to a 14.0 L
  container at 375 torr and 37.0C. 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

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Stoichiometric Relationships with Gases

• Various questions can be asked that relate gas
  laws to stoichiometry.

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Problems

• A 250.0-mL sample of ammonia, NH3(g), exerts a
  pressure of 833 torr at 42.4C. What mass of
  ammonia is in the container?
• A)0.0787 g
• B)0.180 g
• C)8.04 g
• D)17.0 g
• E)59.8 g

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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

41
Problems

• What is the density of carbon dioxide gas at
  -25.2C 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

42
Problems

• A flask with a volume of 3.16 L contains 9.33
  grams of an unknown gas at 32.0C and 1.00 atm.
  What is the molar mass of the gas?
• A)7.76 g/mol
• B)66.1 g/mol
• C)74.0 g/mol
• D)81.4 g/mol
• E)144 g/mol

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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 20.0C, is the gas
  likely to be methane, CH4, nitrogen, N2, oxygen,
  O2, neon, Ne, or argon, Ar?
• A)CH4
• B)N2
• C)Ne
• D)Ar
• E)O2

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