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05/04/16

Gases
Chapter 5

1
Copyright © The McGraw-Hill Companies, Inc
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States of matter

http://www
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co
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jpg

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Gases move continuously
in arbitrary (random) directions

https://en
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org/wiki/File:Translational_motion
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• 

Gases are the most compressible state of matter
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• 

Gases have much lower densities than liquids and solids
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revisegcsephysics
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uk/images/
states_of_matter_big
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325 kPa
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1 Bar = 100 kPa = 0
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2 atm

0
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What is it in a) torr, b) atm, c) kPa
Ans: a) 489 torr b) 0
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15 kPa

Exercise question:
The pressure of a gas sample was measured to be 701
mmHg
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922 atm c) 86
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1
The pressure outside a jet plane flying at high altitude falls
considerably below standard atmospheric pressure
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What is the pressure in atmospheres in the cabin if the
barometer reading is 688 mmHg?

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Example 5
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15

16

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Avogadro’s Law
V α number of moles (n)
V = constant x n

Constant temperature
Constant pressure

V1 / n1 = V2 / n2

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Summary of Gas Laws
Boyle’s Law

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Charles’s Law

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Avogadro’s Law

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Ideal Gas Equation
Boyle’s law: P α 1 (at constant n and T)
V
Charles’s law: V α T (at constant n and P)
Avogadro’s law: V α n (at constant P and T)
Vα

nT
P

V = constant x

nT
nT
=R
P
P

R is the gas constant

PV = nRT
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The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP)
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414 L
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414L)
PV
=
nT
(1 mol)(273
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082057 L • atm / (mol • K)
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PV = nRT

ideal gas equation

R : ideal gas constant

R = 0
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314

L
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mol

J
K
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g
...
g
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2
Sulfur hexafluoride (SF6) is a
colorless and odorless gas
...

Calculate the pressure (in atm)
exerted by 1
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43 L at 69
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SF6

Example 5
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Is the gas undergoing a change in any of its properties?
What equation should we use to solve for the pressure?
What temperature unit should we use?

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Example 5
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Rearranging Equation (5
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3
Calculate the volume (in L) occupied by 7
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NH3

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Example 5
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40 g of NH3?
Solution
Recognizing that 1 mole of an ideal gas occupies 22
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03 g), we write the
sequence of conversions as

Example 5
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Here the
problem can also be solved by first converting 7
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Try it
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40 g of NH3 is smaller than its molar mass,
its volume at STP should be smaller than 22
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Therefore,
the answer is reasonable
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2 g of methane
gas (CH4) at 25°C and 698 mmHg
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0 L tank containing
100 g of butane (C4H10) gas at 20
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Ans: 4
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Hint:
1
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  STP (standart temperature and pressure)
2
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4 L

Exercise question:
Calculate the molar volume of butane (C4H10) gas at STP
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4 L
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Exercise question:
11
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6 L

Exercise question:
Calculate the volume occupied by 3
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Ans: 1
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4
A small bubble rises from the bottom of a lake, where the
temperature and pressure are 8°C and 6
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0 atm
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1 mL
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4
Strategy In solving this kind of problem, where a lot of
information is given, it is sometimes helpful to make a sketch of
the situation, as shown here:

What temperature unit should be used in the calculation?

Example 5
...
9)

We assume that the amount of air in the bubble remains
constant, that is, n1 = n2 so that

which is Equation (5
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Example 5
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4 atm
V1 = 2
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0 atm
V2 = ?
T2 = (25 + 273) K = 298 K

Rearranging Equation (5
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4
Check We see that the final volume involves multiplying the
initial volume by a ratio of pressures (P1/P2) and a ratio of
temperatures (T2/T1)
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Because the pressure decreases and temperature increases as
the bubble rises, we expect the bubble’s volume to increase
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Exercise question:
A sample of N2 gas occupies 2
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If the gas is in
a container that can contract or expand at constant
pressure, at what temperature will the N2 occupy 4
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n and P are constant
2
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40x103 mL at 25°C and 760
mmHg
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8 L

Density (d) Calculations
PM
d=m =
V
RT

m is the mass of the gas in g
M is the molar mass of the gas

Molar Mass (M ) of a Gaseous Substance

M=

dRT
P

d is the density of the gas in g/L

40

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Example 5
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71 g/L at 36°C and 2
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Calculate the molar mass of the compound and determine its
molecular formula
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5
Strategy
Because Equations (5
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12) are rearrangements of
each other, we can calculate the molar mass of a gas if we
know its density, temperature, and pressure
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What temperature unit should we use?

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Example 5
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12)

Alternatively, we can solve for the molar mass by writing

From the given density we know there are 7
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Example 5
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5
We can determine the molecular formula of the compound by
trial and error, using only the knowledge of the molar masses of
chlorine (35
...
00 g)
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45 g, which is too low,
while the molar mass of a compound made up of two Cl atoms
and one O atom is 86
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Thus, the compound must contain one Cl atom and two O
atoms and have the formula ClO2, which has a molar mass of
67
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Exercise question:
0
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892 g
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0°C and a pressure of 9
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(1
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7 psi)
Ans: 1
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0°C and
a pressure of 4
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38 g/L

46

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Exercise question:
A 0
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0 mL at 0
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3 °C
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M = g/mol, mol = PV/RT
2
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275 g/L at
STP)
Ans: 28
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6
Sodium azide (NaN3) is used in some
automobile air bags
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Calculate the volume of N2 generated
at 80°C and 823 mmHg by the
decomposition of 60
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An air bag can protect
the driver in an
automobile collision
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6
Strategy From the balanced equation we see that
2 mol NaN3 ≏ 3 mol N2 so the conversion factor between NaN3
and N2 is

Because the mass of NaN3 is given, we can calculate the
number of moles of NaN3 and hence the number of moles of N2
produced
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Example 5
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0 g NaN3 using the following sequence of conversions

so that

The volume of 1
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94 atm pressure
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46 kg

Example question:
CaCO3 was the major component of blackboard chalks in the past
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3 atm pressure and 25 °C to produce a piece of
chalk weighing 5
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CO2 (g) + Ca(OH)2 (aq) ⟶ CaCO3 (s) + H2O (l)
(Assume that 85% of the chalk is calcium carbonate
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83 L
52

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Dalton’s Law of Partial Pressures
V and T are constant

P2

P1

Ptotal = P1 + P2
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Consider a case in which two gases, A and B, are in a
container of volume V
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7
A mixture of gases contains 4
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74 mole
of argon (Ar), and 2
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Calculate the partial pressures of the gases if the total pressure
is 2
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Example 5
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14), the partial pressure of
Ne (PNe) is equal to the product of its mole fraction (XNe) and
the total pressure (PT)

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Example 5
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13), we calculate the mole fraction of Ne as
follows:

Therefore,

Example 5
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21 + 0
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586) atm = 2
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Exercise question:
From data gathered by Voyager 1, scientists have
estimated that a 55 g sample of the atmosphere of Titan
(Saturn's largest moon) contains 44
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22 g Ar, and
the remaining is CH4
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Calculate the partial pressure (in torr) of
each of these gases in Titan's atmosphere (1 torr=1 mmHg)
Ans: 1002 torr N2, 147 torr Ar, and 71 torr CH4

Example question:
The exhaled air (breath) of a man was found to contain (in mole %)
15
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7% CO2, 75% N2 and 5
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Calculate the partial
pressure, in mmHg, of each gas if the breath has 1
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59
Ans: 120 mmHg O2, 29 mmHg CO2, 598 mmHg N2 and 41 mmHg H2O

Collecting a Gas over Water

2KClO3 (s)

2KCl (s) + 3O2 (g)

PT = PO2 + PH2 O

60

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Vapor of Water and Temperature

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Example 5
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15
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Calculate the mass (in grams) of oxygen gas obtained
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4 mmHg
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8
Strategy To solve for the mass of O2 generated, we must first
calculate the partial pressure of O2 in the mixture
...
8
Therefore,

From the ideal gas equation we write

where m and
are the mass of O2 collected and the molar
mass of O2, respectively
...
8
Rearranging the equation we obtain

Check The density of the oxygen gas is (0
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128 L), or
1
...
8)
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5 mmHg total
pressure
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PH2O at 30°C is 31
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See Table 5
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M (NH4NO2) = 64 g/mol

Ans: 0
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0 °C
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0 kPa
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79 mmHg, 1 atm = 101
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7 mmHg

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Kinetic Molecular Theory of Gases
1
...
The molecules can be considered to be points;
that is, they possess mass but have negligible volume
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  Gas molecules are in constant motion in random directions,
and they frequently collide with one another
...

3
...

4
...
Any two gases at
the same temperature will have the same average kinetic
energy
KE = ½ mu2
67

Kinetic theory of gases and …
•  Compressibility of Gases
•  Boyle’s Law
P α collision rate with wall
Collision rate α number density
Number density α 1/V
P α 1/V

•  Charles’s Law
P α collision rate with wall
Collision rate α average kinetic energy of gas molecules
Average kinetic energy α T
PαT
68

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Kinetic theory of gases and …
•  Avogadro’s Law
P α collision rate with wall
Collision rate α number density
Number density α n
Pαn

•  Dalton’s Law of Partial Pressures
Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the
presence of another gas
Ptotal = ΣPi

69

The distribution of speeds
of three different gases
at the same temperature

The distribution of speeds
for nitrogen gas molecules
at three different temperatures

urms =

3RT
√M
70

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Example 5
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Example 5
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16)
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314 J/K · mol and,
because 1 J = 1 kg m2/s2, the molar mass must be in kg/mol
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003 g/mol, or 4
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Example 5
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16),

Using the conversion factor 1 J = 1 kg m2/s2 we get

Example 5
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02 g/mol, or 2
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A quick way to check the answers is to note
that the ratio of the two urms values (1
...
6)
should be equal to the square root of the ratios of the molar
masses of N2 to He, that is,

...

r1
r2

=

√

M2
M1

molecular path

NH4Cl

NH3
17 g/mol

HCl
36 g/mol
75

Example question:
a) What is the root-mean-square (average) speed, in m/s,
of an O2 gas molecule at -100 °C, 25 °C and 100 °C?
b) How long will it take for O2 molecule to travel from
Famagusta to Nicosia (60 km) at 25 °C? (Assume it will
have no collisions on its path)
Hint: m/s is an SI unit, therefore, use R and M with SI units
Ans: a) 367, 482 and 539 m/s at -100 °C, 25 °C and 100 °C, respectively b) 28
...
What is this element?
Hint: Calculate molar mass
Ans: He

76

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Gas effusion is the process by which gas under pressure
escapes from one compartment of a container to another by
passing through a small opening
...
10
A flammable gas made up only of
carbon and hydrogen is found to
effuse through a porous barrier in
1
...

Under the same conditions of
temperature and pressure, it
takes an equal volume of bromine
vapor 4
...

Calculate the molar mass of the
unknown gas, and suggest what
this gas might be
...
Gas
molecules move from a
high-pressure
region (left) to a lowpressure
one through a pinhole
...
10
Strategy The rate of diffusion is the number of molecules
passing through a porous barrier in a given time
...

Therefore, the rate is inversely proportional to the time required
for diffusion
...
17) can now be written as r1/r2 = t2/t1 =
,
where t1 and t2 are the times for effusion for gases 1 and 2,
respectively
...
10
Solution From the molar mass of Br2, we write

Where
is the molar mass of the unknown gas
...
01 g and that of
hydrogen is 1
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Exercise question:
A sample of unknown gas effuse through a porous
container 1
...

Estimate the molar mass of the unknown gas
...
What is it for Xe?
Ans: 54
...
0
n=
RT

Repulsive Forces

Attractive Forces

82

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Effect of intermolecular forces on the pressure exerted by a gas
...
11
Given that 3
...
20 L at 47°C, calculate
the pressure of the gas (in atm) using
(a) the ideal gas equation and
(b) the van der Waals equation
...
11
Strategy
To calculate the pressure of NH3 using the ideal gas equation,
we proceed as in Example 5
...

What corrections are made to the pressure and volume terms in
the van der Waals equation?

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Example 5
...
20 L
T = (47 + 273) K = 320 K
n = 3
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0821 L · atm/K · mol
Substituting these values in the ideal gas equation, we
write

Example 5
...
18)
...
18) separately
...
4, we have
a = 4
...
0371 L/mol
so that the correction terms for pressure and volume are

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Example 5
...
89 atm)(5
...
130 L) = (3
...
0821 L·atm/K·mol)(320 K)

P = 16

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