Download Topic 3.3 Kinetic Model of Ideal Gas

Topic 3.3 Kinetic Model of Ideal Gas
Name _____________________
Read Tsokos pp 174-180
Read Cutnell pp 414-419, 426
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Mathematic Physics: The mole
Mole, molar mass and avogadro consatnt
A detailed analysis of the physics behind the macroscopic behavior of
materials must invlove knowing how many atoms of molecules exist in a given
sample of a substance. The numbers involved are extreamly large, so it
helps to have a unit that deals with large numbers of particles. The amount
of substance can then be measured in terms of a fixed number of atoms or
molecules. Th eunit used for the amount of substance is the mole.
A mole of any substance will always contain the same number of
particles, but the mass will vary depending on th eparticular substance
considered. The mole can be thought of as a very large number. It is
defined as the amount substance that contains the same number of
elementary units as there are atoms in 12 g of carbon-12. The amount of
particles in one mole is called the Avogadro consatnt, and is equal to
6.02x1023.
The word “molar” just means “one mole”, so the molar mass of any
substance is the mass per mole. For example, 1 mole of water molecules
(H2O) has a mass of 18 g, whereas 1 mole of oxygen (O2) has a mass of 32 g.
These masses can be worked out from the individul molar masses for the
elements involved (the molar mass of the element hydrogen is 1 g, and for
oxygen it is 16 g).
Note that these is a difference between the organized KE that a
moving object’s particles must possess (which equals the KE of the object
as a whole) and the random thermal kinetic energy that particles must
possess (which is part of the internal energy of the object and is related to
its temperature)
Find the molar mass of the following substance with the periodic tabel:
1. H2
2. H2SO4
3. NaCl
4. HCl
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Ideal Gas behavior and Pressure
Ideal Gas
The kinetic theory views all matter as consisting of individual atoms
and molecules. Certain microscopic assumptions need to be made in order to
be able to deduce the macroscopic behavior of a gas. For an ideal gas,
these are as follows:
 The molecules are assumed to behaved in an idealized way: that is,
Newton’s laws of mechanics apply to the individual molecule’s motion.
 Th eintermolecular forces are assumed to be negligible (except duirng
a collision)
 The molecules are assumed to be spherical and their volume negligible
(compared with the volume occupied by the whole gas)
 The molecules are assumed to be in a random motion.
 Th ecollisions between molecules are assumed to be perfectly elastic.
 The time taken for a collision is assumed to be negligible.
Pressure: Macroscopic and microscopic views
From the macroscopic point of view, a general definition of pressure is as
follows:
𝑃=
𝐹⊥
𝐴
Where
𝐹⊥ is force exerted, measured in N.
𝐴 is the normal area over which the froce acts, measured in m2
𝑃 is the pressure, measured in Nm
–2
(or pascals, Pa)
1 Pa = 1 Nm –2
In the above equation for pressure, area is at right angles to the direction
in which the force acts. If a force does not act at 90o to the surface, then
the pressure is calculated using the component of the force that is at 90o
to the surface.
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Gas Pressure
Gas pressure can be understood by considering the large number of
collisions that take place between the molecules of the gas and the walls
of the container:
o
When a gas molecule hits the walls of the container, it bounces
off.
o
The momentum of the gas molecule has changed during this
collision, and Newton’s second law applied to this situation means
that there must have been a force on the molecule from the wall.
o
Newton’s third law applied to this situation means that there must
have been a force on the wall from the molecule.
o
Each time a molecule collides with the wall, there will be a small
force from the molecule on the wall.
o
In a given time, there will be a certain number of collisions.
o
The average result of all of thse individual molecular collision
forces acting for a short time will be a constant force on the wall
of the container.
o
The value of the constant force on the wall divided by its area is
the pressure that the gas exerts on the wall of the container.
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Ideal Gas Law PV = nRT
A gas exerts a pressure on every surface of its container: this pressure
depends on the mass of the gas, its volume, and its temperature. The
macroscopic behaviour of an ideal gas can be understood in terms of the
motion of the molecules of the gas. In the first three of the following
scenarios, one variable has been changed and all but one of the other ones
are kept constant.
1. Idea gases increase in pressure when more gas is introduced into
the contanier. The increase is mass of the gas means that there are
more gas molecules in the container, and therefore an increase in
the number of collisions that take place in a given time. The force
from each molecule remains the same, but an increased number of
collisions in a given time means that the pressure increases.
2. Ideal gases increase in pressure when their volume decreases. The
decrease in volume means that molecules hit a given area of the
walls more often. The force from each molecule remains the same,
but an increased number of collisions in a given time means that the
pressure increases.
3. Ideal gases increase in pressure when their temperature increases.
The increased temperature means the molecules are moving faster,
and thus they hit the wall more often. The force from each
molecule goes up on average and an increased of collisions in a given
time means that the pressure increases.
4. In this final example, an isolated sample of gas is compressed. Ideal
gas increase in temperature when their volume is decreased. As the
volume is reduced, the walls of the container move inwards. The
molecules are colliding with a moving wall and will, on average, speed
up. Faster-moving molecules mean that the average kinetic energy
per molecule has increases – that is, the temperature has increased.
The smaller volume and higher temperature mean the pressure must
have increased.
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