Chapter 10
Gases
Contents
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10.1- Characteristics of Gases
10.2- Pressure
10.3- Gas Laws
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
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Characteristics of Gases
• Gases are highly compressible and
occupy the full volume of their
containers.
When a gas is subjected to pressure,
its volume decreases.
• Gases always form homogeneous
mixtures with other gases.
• Gases have extremely low densities
(At sea level and 20 °C, air has a density of approximately 0.0012 kg/dm3)
Some Common Gases
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Pressure
• Pressure is the force acting on an
object per unit area:
• Pressure = force/area : F/S = m.g/S
• g is the gravity acceleration (9.8 m/s2)
• Unit: kg.m/s2.m2 or N/m2 or Pa
Units of Pressure
1 pascal (Pa)
1 Pa = 1 N/m2
1 atmosphere (atm)
1.01325*105 Pa=760 Torr
1 bar
105 Pa
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Atmospheric Pressure
Due to Gravity, atmosphere exerts a pressure on the earth’s surface
called atmospheric pressure
A column of air 1 m2 in cross section exerts a force of 1 atm
• How much pressure does an
elephant with a mass of 2000 kg and
a total footprint area of 5000 cm2
exert on the ground, assuming that
the force of gravity is 9.8 m/s2 ?
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Barometer
• Atmospheric pressure can be measured by a
mercury barometer.
1 atm = 760 mmHg
• A barometer
measures atmospheric
pressure as a mercury column height
Manometer
• a manometer measures gas pressure as a difference in
mercury column heights
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The Gas Laws
• Four variables are usually sufficient
to define the state (i.e. condition) of
a gas:
• T,P,V, and n
• Equations that express the
relationships among P, T, V and n
are known as the gas laws
Boyle’s Law
Boyle found that the volume of a gas decreased as the
pressure was increased (more mercury).
Doubling the pressure caused the gas to decrease to onehalf its original volume.
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Boyle’s Law: Plot of
Pressure vs. Volume
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
Application:
weather balloons
Charles's Law
• Charles’s Law: the volume of a fixed quantity
of gas at constant pressure increases as the
temperature increases.
• Mathematically:
V = constant × T
• Hot air balloons shrink when they are cooled
down.
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Charles's Law :
Absolute zero ?
Is it real?
A plot of V versus T is a straight line
The line could be extrapolated to predict that gasses would have
zero volume at a temperature of -273.15°C
We define absolute Temperature as 0 K = -273.15°C.
Avogadro’s Law
• 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
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Ideal Gas Equation
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Summarizing the gas laws
-Boyle’s law: V ~ 1/P (at constant T and n)
-Charles’s law: V~ T (at constant n and P)
-Avogadro’s 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, then :
PV = nRT
P=pressure
T=temperature in Kelvin
R is the molar gas constant
Value of Gas Constant
9
Ideal Gas Assumption
(the kinetic molecular theory)
theory)
• 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.
• The gas molecules move randomly and
the attractive and repulsive forces
between the molecules are considered
negligible
Combined Gas Law:
•In general, if we have a gas under two sets of
conditions, then
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Example
• A 25.0 mL sample of gas is enclosed
in a flask at 22°C. If the flask was
placed in an ice bath at 0°C, what
would the new gas volume be if the
pressure is held constant?
Answer
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Gas Densities and Molar
Mass
• 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
• 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?
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Answer
Gas Mixtures and Partial
Pressures
• Dalton’s 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
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Assumption
If we assume that each gas is ideal
and behaves independently of others,
then:
The partial pressure of each gas in the
mixture is equal to the total pressure
multiplied by the mole fraction.
Example
• A 10.73 g sample of PCl5 (g) is placed in a
4.00 L flask at 200°C.
a) What is the initial pressure of the gas
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)?
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Answer
Collecting Gases Over
Water
CaCO3(s) + 2 HCl → CaCl2 + CO2(g) +
PT = PCO2 + PH2O = Patm
H2 O
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Example
A given volume of CO2(g) was collected over
water by adding a concentrated solution of HCl
to 0.30 g of CaCO3(s) at a temperature of 17°C
and a barometric pressure of 646 torr. The
vapor pressure of water at 17°C is 14.5 torr and
R, the gas constant, is 0.082 L.atm/mol-K.
What is the volume of the gas CO2 collected if the
reaction is complete?
Kinetic Molecular Theory
• Theory developed to explain gas
behavior.
• Theory of moving molecules
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Postulates
ASSUMPTIONS:
- Gases consist of a large number of
molecules in constant random motion.
- Gas molecules are abstract points without
volumes.
- no attractive forces.
- average kinetic energy of molecules is
proportional to the absolute temperature.
- the total kinetic energy is constant at
constant temperature.
Molecular 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 a tiny hole.
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Effusion
Graham's law represents the relationship
between rates of effusion for two different
molecules (under same P and T):
• 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"
Effusion
• Massive molecules effuse slower
than lighter ones
• For instance a balloon filled with
helium deflates more rapidly
than balloon filled with air
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Example
• Ne(g) effused through a pinhole in
4.5 second. How long will it take an
equivalent amount of Ar(g) to effuse
under the same conditions?
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
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Deviation From Ideal
Behavior
Ideal gas molecules:
• abstract points without volume.
• no attractive forces.
Real gas molecules:
• actual molecules (occupy space).
• attract each other.
Deviation From Ideal
Behavior
• The quantity (pV)/(nRT) = Z is called the
COMPRESSIBILITY FACTOR and should be unity
for an Ideal Gas):
At lower pressure, the deviation from ideal
behavior is typically small, and the ideal gas law
can be used to predict behavior with little error.
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Deviation From Ideal
Behavior
• Deviation from ideal behavior can also be shown
for a given Nitrogen gas as a function of
temperature:
• As temperature is decreased below a critical
value, the deviation from ideal gas behavior
becomes severe, because the gas CONDENSES to
become a LIQUID
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Van der Waals Equation
• 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:
Pideal × Vavailable = nRT
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Van der Waals Equation
• 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:
Pideal × Vavailable = nRT
Pcontainer
n
+ a 
V 
2
Vcontainer − nb
Van der Waals Equation
• 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:
2


 P + a n  (V − nb ) = nRT

 V  

• 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
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Example
• 88 mL of CO2(g) were collected over
water by adding 5.0 ml of 4 M HCl to
0.30 g of CaCO3(s) (molar mass = 100
g/l) at the temperature of 17°C and the
barometric pressure of 646 torr .
• Assuming that the reaction is complete
a. Write the chemical reaction that involves
the release of CO2 (g)
b. If the vapor pressure of water at 17°C is
14.5 torr, determine the gas constant R
(apply the Van der Waals equation)
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