Properties of Gases

1
Properties of Gases

• Gases expand to fill any container.
• random motion, no attraction
• Gases are fluids (like liquids).
• particles flow easily
• Gases have very low densities.
• lots of empty space particles spaced far apart
• Gases are easily compressible.
• empty space reduced to smaller volume

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Kinetic Molecular Theory
Postulates of the Kinetic Molecular Theory of
Gases

• Gases consist of tiny particles (atoms or
  molecules)
• These particles are so small, compared with the
  distances between
• them, that the volume (size) of the individual
  particles can be assumed
• to be negligible (zero). Gases have low
  densities.
• 3. The particles are in constant random
  straight-line motion, colliding with the walls of
  the container. These collisions with the walls
  cause the pressure exerted by the gas.
• 4. The particles are assumed not to attract
  or to repel each other.
• 5. The average kinetic energy of the gas
  particles is directly proportional
• to the Kelvin temperature of the gas

3
Collisions of Gas ParticlesPressure collisions
on container walls
4
Changing the Size of the Container

• In a smaller container - particles have less room
  to move.
• Particles hit the sides of the container more
  often.
• This causes an increase in pressure.
• As volume decreases pressure increases.

5
Pressure Force/Area

• KEY UNITS AT SEA LEVEL (alsoknown as standard
  pressure)
• 101.325 kPa (kilopascal)
• 1 atm
• 760 mm Hg
• 760 torr
• 14.7 psi

Sea level
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6
Pressure and Balloons
B
When balloon is being filled PA gt PB
A
When balloon is filled and tied PA PB
When balloon deflates PA lt PB
A pressure exerted BY balloon
B pressure exerted ON balloon
7
Balloon Riddle
When the balloons are untied, will the large
balloon (A) inflate the small balloon (B) will
they end up the same size or will the small
balloon inflate the large balloon? Why?
8
Barometers
Mount Everest
Sea level On top of Mount Everest
Sea level
9
Temperature

• Always use temperature in Kelvin when working
  with gases. Std temperature 273 K

ºF
-459
32
212
ºC
-273
0
100
K
0
273
373
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STP
STP
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11
Boyles Law

• As the pressure on a gas increases

• As the pressure on a gas increases -
• the volume decreases
• Pressure and volume are inversely related

1 atm
2 atm
4 Liters
2 Liters
12
Boyles Law Illustrated
Zumdahl, Zumdahl, DeCoste, World of Chemistry
2002, page 404
13
Boyles Law
Volume (mL) Pressure (torr) P.V (mL.torr)
10.0 20.0 30.0 40.0 760.0 379.6 253.2 191.0 7.60 x 103 7.59 x 103 7.60 x 103 7.64 x 103

• The pressure and volume of a gas are inversely
  related
• at constant mass temp

PV k
P1 x V1 P2 x V2
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Boyles Law example
A quantity of gas under a pressure of 106.6 kPa
has a volume of 380 cm3. What is the volume of
the gas at standard pressure, if the temperature
is held constant?
P1 x V1 P2 x V2
(106.6 kPa) x (380 cm3) (101.3 kPa) x (V2)
V2 400 cm3
15
Charless Law
Timberlake, Chemistry 7th Edition, page 259
16
300 K

• If you start with 1 liter of gas at 1 atm
  pressure and 300 K
• and heat it to 600 K one of 2 things happens

17
600 K
300 K

• Either the volume will increase to 2 liters at 1
  atm

18
600 K
300 K

• Or the pressure will increase to 2 atm.

19
Charles Law
Volume (mL) Temperature (K) V / T (mL / K)
40.0 44.0 47.7 51.3 273.2 298.2 323.2 348.2 0.146 0.148 0.148 0.147

• The volume and absolute temperature (K) of a
  gas are directly related
• at constant mass pressure

V1 / T1 V2 / T2
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Gay-Lussacs Law
Temperature (K) Pressure (torr) P/T (torr/K)
248 691.6 2.79
273 760.0 2.78
298 828.4 2.78
373 1,041.2 2.79

• The pressure and absolute temperature (K) of a
  gas are directly related
• at constant mass volume

P1 / T1 P2 / T2
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Combined Gas Law
P T
V T
PV T
k
PV
P1V1T2 P2V2T1
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The Combined Gas Law
A quantity of gas has a volume of 400 cm3 at STP.
What volume will it occupy at 35oC and 83.3 kPa?
(101.325 kPa) x (400 cm3) (83.3 kPa) x (V2)
273 K
308 K
P1 101.325 kPa T1 273 K V1 400 cm3 P2
83.3 kPa T2 35oC 273 308 K V2 ? cm3
V2 548.9 cm3
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The Combined Gas Law
When measured at STP, a quantity of gas has a
volume of 500 cm3. What volume will it occupy at
20oC and 93.3 kPa?
(101.325 kPa) x (500 cm3) (93.3 kPa) x (V2)
273 K
293 K
P1 101.325 kPa T1 273 K V1 500 cm3 P2
93.3 kPa T2 20oC 273 293 K V2 ? cm3
V2 582.8 cm3
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Molar Volume (Avogadro)
1 mol of all gases _at_ STP have a volume of 22.4
L Avogadros Law V1/n1 V2/n2
Timberlake, Chemistry 7th Edition, page 268
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Ideal Gas Law
PV nRT
Brings together all gas properties. P
pressure V volume (must be in liters) n
moles R universal gas constant (0.082 or
8.314) T temperature (must be in Kelvin)
Can be derived from experiment and theory.
26
Ideal Gas Law
What is the pressure of 0.18 mol of a gas in a
1.2 L flask at 298 K?
PV nRT
P x (1.2 L) (0.18 mol) x (.082) x (298 K)
P ? atm n 0.18 mol T 298 K V 1.2 L R
.082 (L x atm)/(mol x K)
P 3.7 atm
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Gas Density
D (MM)P/RT
Larger particles are more dense. Gases are more
dense at higher pressures and lower
temperatures D density P pressure MM
molar mass R universal gas constant T
temperature (must be in Kelvin)
Can be derived from experiment and theory.
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Gas Problems
1. The density of an unknown gas is 0.010g/ml.
What is the molar mass of this gas measured at
-11.00C and 3.25 atm? Use proper sig figs. 2.
What is the volume of 3.35 mol of gas which has a
measured temperature of 47.00C and a pressure of
185 kPa? Use proper sig figs.
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Gas Problems
1. The density of an unknown gas is 0.010g/ml.
What is the molar mass of this gas measured at
-11.00C and 3.25 atm? Use proper sig figs.
g/mol (0.010g/ml) x (.082atm L/mol K) x (262
K) x (1/3.25 atm) x (1000ml/1 L)
Molar mass ? g/mol D 0.010 g/ml T 262
K P 3.25 atm R .082 (L atm)/(mol K)
P 66 g/mol
30
Gas Problems
2. What is the volume of 3.35 mol of gas which
has a measured temperature of 47.00C and a
pressure of 185 kPa? Use proper sig figs.
(185 kPa) x (V) (3.35 mol) x (8.314 L kPa/mol
K) x (320 K)
PV nRT V ? L n 3.35 mol T 320 K P
185 kPa R 8.314 (L kPa)/(mol K)
P 48.2 L
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Daltons Law

• The total pressure of a mixture of gases
  equals the sum of the partial pressures of
  the individual gases.

In a gaseous mixture, a gass partial pressure is
the one the gas would exert if it were by itself
in the container. The mole ratio in a mixture of
gases determines each gass partial pressure.
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Gas Mixtures and Daltons Law
33
Gas Collected Over Water
When a H2 gas is collected by water displacement,
the gas in the collection bottle is actually a
mixture of H2 and water vapor.
34
Daltons Law

• Hydrogen gas is collected over water at 22C.
  Find the pressure of the dry gas if the
  atmospheric pressure is 94.4 kPa.

The total pressure in the collection bottle is
equal to atmospheric pressure and is a mixture of
H2 and water vapor.
GIVEN PH2 ? Ptotal 94.4 kPa PH2O 2.6 kPa
WORK Ptotal PH2 PH2O 94.4 kPa PH2 2.6
kPa PH2 91.8 kPa
Look up water-vapor pressure on p.10 for 22C.
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Daltons Law
The total pressure of mixture (3.0 mol He and 4.0
mol Ne) is 97.4 kPa. What is the partial pressure
of each gas.
?
41.7 kPa
PHe
(97.4 kPa)


?
55.7 kPa
PNe
(97.4 kPa)

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Daltons Law
Suppose you are given four containers three
filled with noble gases. The first 1 L container
is filled with argon and exerts a pressure of 2
atm. The second 3 liter container is filled with
krypton and has a pressure of 380 mm Hg. The
third 0.5 L container is filled with xenon and
has a pressure of 607.8 kPa. If all these gases
were transferred into an empty 2 L containerwhat
would be the pressure in the new container?
PKr 380 mm Hg
Ptotal ?
PAr 2 atm
Pxe 607.8 kPa
V 1 liter V 3 liters V 0.5 liter
V 2 liters
37
just add them up
PKr 380 mm Hg
Ptotal ?
PAr 2 atm
Pxe 607.8 kPa
V 1 liter V 3 liters V 0.5 liter
V 2 liters
Daltons Law of Partial Pressures Total
Pressure Sum of the Partial Pressures PT
PAr PKr PXe
P1 x V1 P2 x V2
P1 x V1 P2 x V2
(0.5 atm) (3L) (X atm) (2L)
(6 atm) (0.5 L) (X atm) (2L)
PKr 0.75 atm
Pxe 1.5 atm
PT 1 atm 0.75 atm 1.5 atm
PT 3.25 atm
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Partial Pressure
A gas is collected over water at 649 torr and
26.00C. If its volume when collected is 2.99 L,
what is its volume at STP? Use proper sig figs.
(83.1 x 2.99) / 299 (101.325 x V2) / 273
P1V1/T1 P2V2/T2 PT PG Pw V2 ?
L V1 2.99 L T1 299 K T2 273 K PT 649
torr P1 86.5 kPa 3.4 kPa 83.1 kPa P2
101.325 kPa
V2 2.24 L
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Gas Stoichiometry
Find the volume of hydrogen gas made when 38.2 g
zinc react with excess hydrochloric acid.
Pressure 107.3 kPa temperature 88oC. Zn (s)
2 HCl (aq) ? ZnCl2 (aq) H2 (g)
40
Gas Stoichiometry
Find the volume of hydrogen gas made when 38.2 g
zinc react with excess hydrochloric acid.
Pressure 107.3 kPa temperature 88oC. Zn (s)
2 HCl (aq) ? ZnCl2 (aq) H2 (g) 38.2 g
excess V ? L H2 P 107.3
kPa T 88oC (361 K)
At STP, wed use 22.4 L per mol, but we arent at
STP.