Kinetic Gas Theory including Ideal Gas Equation. Temperature, Volume, Applications Boyle's Law, Charles' Law and Avogadro's Law. Ideal Gas Theory, Dalton's Partial Pressure

1. THE GAS LAWS
Made by – VIKASH PRASAD

2. Opening thoughts…
Have you ever:
Seen a hot air balloon?
Had a soda bottle spray all over you?
Baked (or eaten) a nice, fluffy cake?
These are all examples of gases at work!
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3. Important Characteristics of Gases
1) Gases are highly compressible
An external force compresses the gas sample and decreases its
volume, removing the external force allows the gas volume to
increase.
2) Gases are thermally expandable
When a gas sample is heated, its volume increases, and when it is
cooled its volume decreases.
3) Gases have high viscosity
Gases flow much easier than liquids or solids.
4) Most Gases have low densities
Gas densities are on the order of grams per liter whereas liquids
and solids are grams per cubic cm, 1000 times greater.
5) Gases are infinitely miscible
Gases mix in any proportion such as in air, a mixture of many gases.

4. Properties of Gases
We can predict the behavior of gases based
on the following properties:
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Pressure
Volume
Amount (moles)
Temperature

5. Units of Pressure
1 pascal (Pa) = 1 N/m2
1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa
Barometer
Pressure = Force
Area

6. Volume
Volume is the three-dimensional space inside the
container holding the gas. The SI unit for volume is
the cubic meter, m3. A more common and
convenient unit is the liter, l.
Think of a 2-liter bottle of soda to get an
idea of how big a liter is.
(OK, how big two of them are…)
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7. Amount (moles)
Amount of substance is tricky. As we’ve already learned, the
SI unit for amount of substance is the mole, mol. Since we
can’t count molecules, we can convert measured mass (in kg)
to the number of moles, n, using the molecular or formula
weight of the gas.
By definition, one mole of a substance contains
approximately 6.022 x 1023 particles of the substance.
You can understand why we use mass and moles!
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8. Temperature
Temperature is the measurement with which you’re
probably most familiar (and the most complex to describe
completely). For these lessons, we will be using
temperature measurements in Kelvin, K.
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The Kelvin scale starts at Absolute 0, which is
-273.15°C. To convert Celsius to Kelvin, add
273.15.

9. Boyle’s Law
 This law is named for Charles Boyle, who studied
the relationship between pressure, p, and
volume, V, in the mid-1600s.
 He determined that for the same amount of a
gas at constant temperature,
p * V = constant
 This defines an inverse relationship:
when one goes up, the other
comes down.
pressure
volume
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10. Boyle’s Law at Work…
Doubling the pressure reduces the volume by half. Conversely, when the volume
doubles, the pressure decreases by half.
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11. Application of Boyle’s Law
Boyle’s Law can be used to predict the interaction of
pressure and volume.
p1 * V1 = p2 * V2
p1 = initial pressure
V1 = initial volume
p2 = final pressure
V2 = final volume
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12. Boyle’s Law
• Hyperbolic Relation Between Pressure and Volume
p
T1 T2 T3 T3 >T2>T1
V
pp –– VV DDiiaaggrraamm
isotherms
(courtesy F. Remer)

13. Boyle’s Law: Summary
 Pressure * Volume = Constant
 p1 * V1 = p2 * V2
 With constant temperature and amount of
gas, you can use these relationships to
predict changes in pressure and volume.
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14. Charles’ Law
 This law is named for Jacques Charles, who
studied the relationship volume, V, and
temperature, T, around the turn of the 19th
century.
 He determined that for the same amount of a
gas at constant pressure,
V / T = constant
 This defines a direct relationship:
an increase in one results in an
increase in the other.
volume
temperature
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15. Charles’ Law
• Linear Relation Between Temperature and Pressure
P
V1 V iissoocchhoorrss 2
0 100 200 300
T (K)
PP –– TT DDiiaaggrraamm
V3
V1 <V2 <V3
(courtesy F. Remer)

16. Charles’ Law
Real data must be
obtained above
liquefaction
temperature.
Experimental curves for
different gasses,
different masses,
different pressures all
extrapolate to a
common zero.

17. Partial Pressure
Partial Pressure
Pressure each gas in a mixture would exert if it
were the only gas in the container
Dalton's Law of Partial Pressures
The total pressure exerted by a gas mixture is
the sum of the partial pressures of the gases in
that mixture.
PT = P1 + P2 + P3 + .....

18. Charles’ Law at Work…
As the temperature increases, the volume increases. Conversely, when the
temperature decreases, volume decreases.
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19. Application of Charles’ Law
Charles’ Law can be used to predict the interaction
of temperature and volume.
V1 / T1 = V2 / T2
V1 = initial volume
T1 = initial temperature
V2 = final volume
T2 = final temperature
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20. Charles’ Law: Summary
 Volume / Temperature = Constant
 V1 / T1 = V2 / T2
 With constant pressure and amount of gas,
you can use these relationships to predict
changes in temperature and volume.
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21. Avogadro’s Law
V a number of moles (n)
V = constant x n
V1/n1 = V2/n2
Constant temperature
Constant pressure

22. Ideal Gas Equation
Boyle’s law: V a (at constant n and T) 1P V a
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
nT
P
V = constant x = R
nT
P
nT
P
R is the gas constant
PV = nRT

23. Dalton’s Law of Partial Pressures
V and T
are
constant
P1 P2 Ptotal = P1 + P2

24. Kinetic Molecular Theory
• The Kinetic Molecular Theory is a single set of descriptive
characteristics of a substance known as the Ideal Gas.
• All real gases require their own unique sets of descriptive
characteristics. Considering the large number of known
gases in the World, the task of trying to describe each one
of them individually would be an awesome task.
• In order to simplify this task, the scientific community has
decided to create an imaginary gas that approximates the
behavior of all real gases. In other words, the Ideal Gas is
a substance that does not exist.
• The Kinetic Molecular Theory describes that gas. While the
use of the Ideal Gas in describing all real gases means
that the descriptions of all real gases will be wrong, the
reality is that the descriptions of real gases will be close
enough to correct that any errors can be overlooked.

25. The Nature of Gases
Three basic assumptions of the kinetic
theory as it applies to gases:
1. Gas is composed of particles- usually
molecules or atoms
–Small, hard spheres
–Insignificant volume; relatively far apart
from each other
–No attraction or repulsion between
particles

26. The Nature of Gases
2. Particles in a gas move rapidly in
constant random motion
–Move in straight paths, changing direction
only when colliding with one another or
other objects
–Average speed of O2 in air at 20 oC is an
amazing 1660 km/h! (1.6km=1mile)

27. The Nature of Gases
3. Collisions are perfectly elastic- meaning
kinetic energy is transferred without loss from
one particle to another- the total kinetic
energy remains constant
Newtonian Cradle-
Where the collisions between the balls elastic?
Yes, because kinetic energy was transferred with
each collision

28. THE KINETIC THEORY OF GASES
Remember the assumptions
• Gas consists of large number of particles (atoms
or molecules)
• Particles make elastic collisions with each other
and with walls of container
• There exist no external forces (density constant)
• Particles, on average, separated by distances
large compared to their diameters
• No forces between particles except when they
collide

29. Ideal Gas Model
Kinetic Molecular Theor y (KMT) for an ideal gas
states that all gas particles:
• are in random, constant, straight-line motion.
• are separated by great distances relative to their
size; the volume of the gas particles is considered
negligible.
• have no attractive forces between them.
• have collisions that may result in the transfer of
energy between gas particles, but the total energy
of the system remains constant.

30. Deviations from ideal behaviour
• A real gas is most like an ideal gas when the real
gas is at low pressure and high temperature.
• At high pressures gas particles are close therefore the
volume of the gas particles is considered.
• At low temperatures gas particles have low kinetic
energy therefore particles have some attractive force
• Example
• Dry ice, liquid oxygen and nitrogen

31. Compression and expansion of adiabatically
isolated gas is accompanied by its heating
and cooling.