Gases

1
Chapter 5

• Gases

2
Elements that exist as gases at 250C and 1
atmosphere
5.1
3
5.1
4
Physical Characteristics of Gases

• Gases assume the volume and shape of their
  containers.
• Gases are the most compressible state of matter.
• Gases will mix evenly and completely when
  confined to the same container.
• Gases have much lower densities than liquids and
  solids.

5.1
5
Pressure
Units of Pressure
1 pascal (Pa) 1 N/m2 1 atm 760 mmHg 760
torr 1 atm 101,325 Pa
5.2
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10 miles
0.2 atm
4 miles
0.5 atm
Sea level
1 atm
5.2
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h pressure difference
5.2
8
As P (h) increases
V decreases
5.3
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Boyles Law
P a 1/V
P x V constant
P1 x V1 P2 x V2
5.3
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Boyles Law P - V Relationship
Pressure is inversely proportional to volume

• Or pressure is directly proportional to 1/V
• P or V
  or PVk
• If n (number of moles) and T are constant
• P1V1 k P2V2 k
• Then P1V1 P2V2

k V
k P
11
A sample of chlorine gas occupies a volume of 946
mL at a pressure of 726 mmHg. What is the
pressure of the gas (in mmHg) if the volume is
reduced at constant temperature to 154 mL?
P1 x V1 P2 x V2
P1 726 mmHg
P2 ?
V1 946 mL
V2 154 mL
P2
4460 mmHg
5.3
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Charles Law - V - T- Relationship

• Volume proportional to T (in K) V kT
• n and P must be constant
• V/T k or

or
Temperatures must be expressed in Kelvin .
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Charles Law Problem

• A sample of carbon monoxide, a poisonous gas,
  occupies 3.20 L at 125 oC. Calculate the
  temperature (oC) at which the gas will occupy
  1.54 L if the pressure remains constant.
• V1 3.20 L T1 125oC 398 K
• V2 1.54 L T2 ?
• T2 192 K oC K - 273.15 192 - 273
• oC -81oC

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Avogadros Law
V a number of moles (n)
V constant x n
Constant same for all gases
V1/n1 V2/n2
5.3
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Ammonia burns in oxygen to form nitric oxide (NO)
and water vapor. How many liters of NO are
obtained from 10 liters of ammonia at the same
temperature and pressure? How many liters of
oxygen are required?
At constant T and P
5.3
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Ideal Gas Equation
Charles law V a T (at constant n and P)
Avogadros law V a n (at constant P and T)
R is the gas constant
PV nRT
5.4
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PV nRT
R 0.082057 L atm / (mol K)
5.4
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Problems for Chapter 5 Pages 163-156 1-5, 8,
13-16, 18, 20, 22, 24-30, 32, 34, 36, 38, 40, 42,
44, 48, 50, 52, 60, 62, 65, 66, 72, 76, 80
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What is the volume (in liters) occupied by 49.8 g
of HCl at STP?
T 0 0C 273.15 K
P 1 atm
PV nRT
V 30.6 L
5.4
21
What is the pressure exerted by 168 g of argon in
a 38.0 L container at 27oC?
22
Argon is an inert gas used in lightbulbs to
retard the vaporization of the filament. A
certain lightbulb containing argon at 1.20 atm
and 18 0C is heated to 85 0C at constant volume.
What is the final pressure of argon in the
lightbulb (in atm)?
n, V and R are constant
PV nRT
constant
1.48 atm
5.4
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Practice Exercise 5.4 A gas initially at 4.0 L,
1.2 atm, and 66oC undergoes a change so that its
temperature and pressure become 42oC and 1.7 atm.
What is its final volume?
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Density (d) Calculations
m is the mass of the gas in g
d
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
d is the density of the gas in g/L
M
5.4
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Example 5.5 A chemist has synthesized a
greenish-yellow compound of Cl and O and finds
its density to be 7.71g/L at 36oC and 2.88 atm.
Calculate the molar mass and determine its
molecular formula.
A 2.10 L vessel contains 4.65 g of gas at 1.00
atm and 27.0oC. What is its density and molar
mass?
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Gas Stoichiometry
5.60 g C6H12O6
0.187 mol CO2
V
4.76 L
5.5
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Ideal Gas Law and Reaction Stoichiometry

• Sodium azide (NaN3) is used in some air bags in
  automobiles. Calculate the volume of nitrogen gas
  generated at 21 oC and 823 mm Hg by the
  decomposition of 60.0 g of NaN3 .
• 2 NaN3 (s) 2
  Na (s) 3 N2 (g)

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Daltons Law of Partial Pressures
V and T are constant
P1
P2
Ptotal P1 P2
5.6
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Daltons Law of Partial Pressures

• Definition In a mixture of gases, each gas
  contributes to the total pressure the amount it
  would exert if the gas were present in the
  container by itself. This is called the partial
  pressure of the gas.
• To obtain a total pressure, add all of the
  partial pressures Ptotal p1p2p3...

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Daltons Law of Partial Pressures

• A 2.00 L flask contains 3.00 g of CO2 and 0.10
  g of helium at a temperature of 17.0 oC.
• What are the partial pressures of each gas, and
  the total pressure?
• T 17 oC 273 290 K
• nCO2 3.00 g CO2 x 1 mole CO2 / 44.01 g CO2
• 0.0682 mole CO2
• pCO2 nCO2RT/V
• pCO2
• pCO2 0.812 atm

( 0.0682 mol CO2) ( 0.08206 L atm/mol K) ( 290 K)
(2.00 L)
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Daltons Law Problem - cont.

• nHe 0.10 g He / 1 mole He / 4.003 g He
• 0.025 mole He
• pHe nHeRT/V
• pHe
• pHe 0.30 atm
• PTotal pCO2 pHe 0.812 atm 0.30 atm
• PTotal 1.11 atm

(0.025 mol) ( 0.08206 L atm / mol K) ( 290 K )
( 2.00 L )
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Consider a case in which two gases, A and B, are
in a container of volume V.
nA is the number of moles of A
nB is the number of moles of B
PT PA PB
PA XA PT
PB XB PT
Pi Xi PT
5.6
34
A sample of natural gas contains 8.24 moles of
CH4, 0.421 moles of C2H6, and 0.116 moles of
C3H8. If the total pressure of the gases is 1.37
atm, what is the partial pressure of propane
(C3H8)?
Pi Xi PT
PT 1.37 atm
Xpropane
0.0132
Ppropane 0.0132 x 1.37 atm
0.0181 atm
5.6
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Daltons Law is used for calculations when a gas
is collected over water.Whenever water (or any
liquid) is placed in a closed container some
water will evaporate and reach a state of
equilibrium where the partial pressure of the
water remains constant. This pressure is called
the equilibrium vapor pressure of the liquid. It
depends only on the temperature.
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Bottle full of oxygen gas and water vapor
5.6
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Relative Humidity

• Rel Hum
  x 100
• Example the partial pressure of water at 15oC
  is 6.54 mm Hg, what is the relative humidity?
• Rel Hum (6.54 mm Hg/ 12.79 mm Hg )x100
• 51.1
• What if the temperature is increased to 25oC?

pressure of water in air
maximum vapor pressure of water
38
Collection of Hydrogen Gas over Water - Vapor
Pressure

• 2 HCl(aq) Zn(s) ZnCl2
  (aq) H2 (g)
• Calculate the mass of hydrogen gas collected over
  water if 156 ml of gas is collected at 20oC and
  769 mm Hg.
• PTotal p H2 pH2O pH2 PTotal -
  pH2O
• pH2 769 mm Hg - 17.4 mm Hg
• 752 mm Hg 0.987 atm
• T 20oC 273 293 K
• V 0.156 L

39
Kinetic Molecular Theory of Gases

• A gas is composed of molecules that are separated
  from each other by distances far greater than
  their own dimensions. The molecules can be
  considered to be points that is, they possess
  mass but have negligible volume.
• Gas molecules are in constant motion in random
  directions. Collisions are perfectly elastic.
  Pressure is caused by collisions of molecules
  with the walls of the container.
• Gas molecules exert neither attractive nor
  repulsive forces on one another.
• The average kinetic energy of the molecules is
  proportional to the temperature of the gas in
  kelvins. Any two gases at the same temperature
  will have the same average kinetic energy

5.7
40
Kinetic theory of gases explains the gas laws
and properties of gases

• Compressibility of Gases
• Boyles Law - Why does a decrease in volume cause
  an increase in pressure?
• Charles Law Why does an increase in
  temperature cause an increase in pressure?

5.7
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Velocity and Energy

• Kinetic Energy 1/2mu2
• All gas molecules have the same average kinetic
  energy at the same temperature.
• Therefore heavier molecules must have slower
  average speeds.
• Consider samples of N2 and He gas at the same
  temperature. Which has the higher average
  kinetic energy? Which has the higher average
  speed?

43
Molecular Mass and Molecular Speeds
Problem Calculate the molecular speeds of the
molecules of hydrogen, methane, and carbon
dioxide at 300K! Compare speeds and kinetic
energies.
Next EH assignment due Mar 12 Section 7
Properties of Gases
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Molecular Mass and Molecular Speeds - III
Molecule H2
CH4 CO2
Molecular Mass (g/mol)
2.016 16.04
44.01
Kinetic Energy (J/molecule)
6.213 x 10 - 21 6.0213 x 10 - 21 6.213
x 10 - 21
Velocity (m/s)
1,926 683.8
412.4
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Diffusion vs. Effusion

• Diffusion - One gas mixing into another gas, or
  gases, of which the molecules are colliding with
  each other, and exchanging energy between
  molecules.
• Effusion - A gas escaping from a container into a
  vacuum.
• Grahams Law

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NH3 (g) HCl(g) NH4Cl (s)

• HCl 36.46 g/mol NH3 17.03 g/mol
• RateNH3/ RateHCl 1.463

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Gas diffusion is the gradual mixing of molecules
of one gas with molecules of another by virtue of
their kinetic properties.
NH3 17 g/mol
HCl 36 g/mol
5.7
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Apparatus for studying molecular speed
distribution
5.7
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The distribution of speeds for nitrogen gas
molecules at three different temperatures
5.7
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Deviations from Ideal Behavior
1 mole of ideal gas
Repulsive Forces
PV nRT
Attractive Forces
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For a gas to be an ideal gas its molecules must
have zero volume and there must be no forces
between the molecules.
53
Gases show the greatest deviation from ideal
behavior at1. High pressures2. Low
temperaturesWhy?
54
Effect of intermolecular forces on the pressure
exerted by a gas.
5.8
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The van der Waals Equation
He 0.034
0.0237 Ne
0.211 0.0171 Ar
1.35
0.0322 Kr
2.32 0.0398 Xe
4.19
0.0511 H2
0.244 0.0266 N2
1.39
0.0391 O2
6.49 0.0318 Cl2
3.59
0.0562 CO2
2.25 0.0428 NH3
4.17
0.0371 H2O
5.46 0.0305
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THIS WEEK EXPERIMENT 9 Determination of the Gas
Constant R
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