Chapter 10

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Chapter 10
GASES
Aim:
Examine the physical characteristics of gases and
the transformations that occur among them
CONTENTS:
10.1- Characteristics of Gases
10.2- Pressure
10.3- Gas Law
10.4- Ideal Gas Equation
11.5- Further Application of the Ideal-Gas
Equation
10.6- Gas Mixtures and Partial Pressures
10.7- Kinetic Molecular Theory
10.8- Molecular Effusion and Diffusion
10.9 Real Gases:Deviation from Ideal Behavior
10.1 Characteristics of Gases:
 Gases are highly compressible and occupy the full volume
of their containers
 When a gas is subject to an increasing pressure, its volume
decreases
 Gases always form homogeneous mixture with other
gases.
10.2 Pressure:
 Pressure = force/area : F/S = mS
is the acceleration
Unit: kg.m/s2.m2 or N/m2
SI unit: Pascal (1 Pa = 1 N/m2)
Units of Pressure
1 pascal (Pa)
1 N*m-2 = 1 kg*m-1*s-2
1 atmosphere (atm)
1.01325*105 Pa
1 atmosphere (atm)
760 torr
1 bar
105 Pa
Atmospheric Pressure and the Barometer :
Due to earth gravity, the atmosphere exerts a pressure on the
Earth’surface .
Atmospheric pressure can be measured by a mercury
barometer.
1 atm = 760 mmHg = 760 torr = 101,325 Pa
Open end Manometer:
U-shaped tubes containing mercury
Pgas= Patm - P
Pgas= Patm + P
10.3 Gas Law
Four variables are usually sufficient to define the state (i.e.
condition) of a gas:




Temperature, T
Pressure, P
Volume, V
Quantity of matter, usually the number of moles, n
The equations that express the relationships among P, T, V and n
are known as the gas laws
The Pressure-Volume Relationship: Boyle's Law
Robert Boyle (1627-1691)
Studied the relationship between the pressure exerted on a gas and
the resulting volume of the gas. He utilized a simple 'J' shaped tube
and used mercury to apply pressure to a gas:


He found that the volume of a gas decreased as the pressure was
increased
Doubling the pressure caused the gas to decrease to one-half its
original volume
Boyle's Law:
The volume of a fixed quantity of gas maintained at constant temperature
is inversely proportional to the pressure


The value of the constant depends on the temperature and the amount
of gas in the sample
A plot of V vs. 1/P will give a straight line with slope = constant
The Temperature-Volume Relationship: Charles's Law
The relationship between gas volume and temperature was discovered in
1787 by Jacques Charles (1746-1823)





The volume of a fixed quantity of gas at constant pressure increases
linearly with temperature
The line could be extrapolated to predict that gasses would have zero
volume at a temperature of -273.15°C (however, all gases liquefy or
solidify before this low temperature is reached
In 1848 William Thomson (Lord Kelvin) proposed an absolute
temperature scale for which 0°K equals -273.15°C
In terms of the Kelvin scale, Charles's Law can be restated as:
The volume of a fixed amount of gas maintained at constant pressure is
directly proportional to its absolute temperature

Doubling the absolute temperature causes the gas volume to double

The value of constant depends on the pressure and amount of gas
The Quantity-Volume Relationship: Avogadro's Law
The volume of a gas is affected not only by pressure and temperature, but by
the amount of gas as well.

Avogadro's hypothesis: Equal volumes of gases at the same
temperature and pressure contain equal numbers of molecules

1 mole of any gas (i.e. 6.02 x 1023 gas molecules) at 1 atmosphere
pressure and 0°C occupies approximately 22.4 liters volume

Avogadro's Law: The volume of a gas maintained at constant
temperature and pressure is directly proportional to the number of
moles of the gas

Doubling the number of moles of gas will cause the volume to double
if T and P remain constant
10.4- The ideal Gas Equation
Summarizing the gas laws
-Boyle’s law: V ~ 1/P (at constant T and n)
-Charles law: V~ T (at constant n and P)
-Avogadro law: V~ n (at constant T and P)
The combination of those equations give a general gas law:
V~ nT/P if R is the proportionality constant :
Ideal gas law or equation of state for an ideal gas:
PV = nRT
Where:
P=pressure in atm
T=temperature in kelvins
R is the molar gas constant, where R=0.082058 L*atm*mol-1*K-1.
The Ideal Gas Law assumes several factors about the molecules of gas. The
volume of the molecules is considered negligible compared to the volume of
the container in which they are held. We also assume that gas molecules
move randomly an the attractive and repulsive forces between the molecules
are considered negligible.
Combined Gas Law:
Example Problem: A 25.0 mL sample of gas is enclosed in a flask at 22
degrees celsius. If the flask was placed in an ice bath at 0 degrees celsius,
what would the new gas volume be if the pressure is held constant?
10.5 Further Application of Ideal-Gas Equation
The ideal gas law can be used to determine the density of a gas
,the molar mass, or the volumes of gases.
From n = PV/RT  m = M PV/RT where M is the molar mass
, the density is d = m/V = P M /RT
Example Problem: A gas exerts a pressure of 0.892 atm in a 5.00 L container
at 15 degrees celsius. The density of the gas is 1.22 g/L. What is the
molecular weight of the gas?
Gas Mixtures and Partial Pressures
What happens when several gases are mixed in one container?
Dalton Law: the total pressure exerted on a container by several different
gases, is equal to the sum of the pressures exerted on the container by each
gas.
Where:
Pt=total pressure in atm
P1=partial pressure, in atm, of gas "1"
P2=partial pressure, in atm, of gas "2" …and so on
. We
assume that each gas is ideal and behaves independently
of others.
Where:
X1=mole fraction of gas "1"
The partial pressure of each the gas in the mixture is equal to the total
pressure multiplied by the mole fraction.
Example Problem: A 10.73 g sample of PCl5 is placed in a 4.00 L flask at
200 degrees celsius.
a) What is the initial pressure of the flask before any reaction takes place?
b) PCl5 dissociates according to the equation: PCl5(g) --> PCl3(g) + Cl2(g). If
half of the total number of moles of PCl5(g) dissociates and the observed
pressure is 1.25 atm, what is the partial pressure of Cl2(g)?
Collecting Gases Over Water
Example: Decomposition of CaCO3 in presence of
Concentrated solution of HCl
CaCO3
HCl
Beaker
CaCO3(s) + 2 HCl  CaCl2 + CO2(g) + H2O
PT = pCO2 + pH2O = Patm
10.7 Kinetic Molecular Theory
Theoretical model to explain the behavior of ideal gases
Postulates :
1.Gases are composed of particles that are in constant, random motion.
2.Volume of individual molecules is negligible compared to the volume
of the container.
3. intermolecular forces are negligible.
4. Each molecule has different energy.
5.The average kinetic energy of the particles is proportional to the
absolute temperature.
10.8 Molecular Effusion & Diffusion
The average kinetic energy of a gas is related to its mass :
E= 1/2 mu2 where u is root mean square (rms)
u = (3RT/ M)1/2
Graham’s Law of Effusion:
The shape of a gas is determined entirely by the container in which the gas is
held. Sometimes, however, the container may have small holes, or leaks.
Molecules will flow out of these leaks, in a process called effusion.
Effusion: is the escape of gas through tiny hole.
Thomas Graham (1830):
Because massive molecules travel slower than lighter molecules, the rate of
effusion is specific to each particular gas. We use Graham's law to
represent the relationship between rates of effusion for two different
molecules .
Where:
r1=rate of effusion in molecules per unit time of gas "1"
r2=rate of effusion in molecules per unit time of gas "2"
u1=molecular mass of gas "1"
u2=molecular mass of gas "2"
For instance a balloon filled with helium deflates more
rapidly than ballon filled with air
Diffusion
Diffusion: the spread of one substance throughout a space, or a second
substance .
Diffusion is faster for lighter molecules.
Diffusion is slowed by gas molecules colliding with each other
10.9 Real Gases: Deviation From Ideal Behavior
An ideal gases are those that fit the assumptions of the ideal gas law:
Ideal gas molecules are:
 abstract points without volume.
 no attractive forces.
Real gas molecules:
 actual molecules (occupy space).
 attract each other.
When pressure is high or temperature is low, gases deviate farther from
the ideal state. To account for these changes, a common equation used to
better represent a real gas is the van der Waals equation:
a accounts for molecular attraction
a (L2.atm/mol2) is proportional to the strength of the attractive forces.
b accounts for volume of molecules .
b (L/mol) is a measure of the actual volume occupied by the molecules
He
O2
NH3
H2O
CH4
C2H6
CH3OH
C2H5OH
a (L2.atm/mol2)
b (L/mol)
0.034
1.36
4.17
5.46
2.25
5.489
9.523
12.02
0.0237
0.0318
0.0371
0.0305
0.0428
0.06380
0.06702
0.08407
The table below shows values for a and b of several different compounds and elements.
(P+ an2/V2) ( V-nb) = nRT
Presence of 2 correction terms:
Previously, we considered only ideal gases, those that fit the assumptions of the ideal gas
law. Gases, however, are never perfectly in the ideal state. All atoms of every gas have
mass and volume. When pressure is low and temperature is high, gases behave similarly
to gases in the ideal state. When pressure and temperature increase, gases deviate farther
from the ideal state. We have to assume new standards, and consider new variables to
account for these changes. A common equation used to better represent a gas that is not
near ideal conditions is the van der Waals equation, seen below.
Where the van der Waals constants are:
a accounts for molecular attraction
b accounts for volume of molecules
The table below shows values for a and b of several different compounds and elements.
Species a (dm6*bar*mol-2) b (dm3*mol-1)
Helium
0.034598
0.023733
Hydrogen
0.24646
0.026665
Nitrogen
1.3661
0.038577
Oxygen
1.3820
0.031860
Benzene
18.876
0.11974
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