Kinetic Molecular Theory

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Kinetic Molecular Theory

• This theory (KMT) explains the effects of temp.
  and pressure on matter through 3 basic
  assumptions
• All matter is composed of small particles.
• These particles are in constant random motion.
• All collisions are perfectly elastic.
• there is no change in the total kinetic energy of
  the 2 particles before and after the collision.
• assumed that the gas particles attraction for
  each other is negligible
• The motion of the particles varies w/ changes in
  temperature, of particles, and particle mass.

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Measuring Pressure of a Trapped Gas
Use a manometer device used to measure gas
pressure Open-armed manometer if gas end lower
than open end, Pgas Pair diff. in height of
Hg if gas end higher than open end, Pgas Pair
diff. in height of Hg Closed-armed manometer Pgas
difference in height of mercury
Barometer special closed-armed manometer
designed to measure air pressure. Developed by
Evangelista Torricelli (1644)
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Torricelli Barometer
The air pushes down on the mercury in the dish.
The space above the mercury is nothing. So the
mercury rises to the point that the forces of air
pressure and gravity are equal. Normal
atmospheric pressure pushes the mercury column to
a height of 76.0 cm (760. mm). So 1.00 atm of
pressure 760. mmHg 760. Torr 101,325 Pa
101.325 kPa
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The Maxwell-Boltzmann Distribution
(Kinetic Energy)
Fig. E07.4.1 The number of particles at speed v
varies with the absolute temperature, as the
shape of the curve changes. However, the
distribution really has the same profile the
distribution is pushed to the left and upward as
temperature decreases, and is pushed to the right
and down as the temperature increases.
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Simple Gas Laws
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Simple Gas Laws - Examples
1.53 dm3 of sulfur dioxide gas at 5.60 kPa is
contracted to 0.571 dm3. What is the new
pressure (in atm)?
Gas at 15.0 0C has a volume of 2.58 dm3. If the
gas is heated to 38.0 0C, what is the new volume?
A sample of diborane (B2H6) gas has a pressure of
345 torr at -15 0C and 3.48 dm3. If the
temperature of the gas is increased to 36 0C and
the pressure is increased to 0.632 atm, what is
the volume of the gas?
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IDEAL GASES
In the early part of the 19th Century,
Amadeo Avogadro demonstrated the relationship
between the number of particles and gas volume.
As amount of gas increases volume increases
proportinally (at constant P and T)
that is, V/n a.
As a result of this, equal volumes of gases at
the same temperature and pressure have the same
What do we ignore w/ these?
number of particles.
At standard temperature and pressure (STP)
1 mol of any gas has a volume equal to
22.4 L
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V k/P
Charles Law
Boyles Law
V bT
kba constant,
R
Avogadros Law
V an

T
n
R
Therefore,
V
R
(Tn/P),
or
P
V

THE IDEAL GAS LAW!!
Lets try a problem
A sample of hydrogen gas has a volume of 8.56 L
at 0 0C and 1140 mmHg. How many grams of gas are
present?
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If you have 2L of H2(g) and 1L of O2(g), at the
same temperature and pressure, why is there twice
as much H2?
Because there are 2X as many particles.
If you mixed the two gases and the total pressure
of the mixture was 99 kPa, what is the partial
pressure of each gas?
O2 would be 33kPa.
H2 would be 66kPa,
This is
Daltons Law of Partial Pressures.
Do you remember what to do if a gas is collected
over water?
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Magnesium metal reacts with aqueous HCl to
produce hydrogen gas. The gas is collected over
water at 25 0C and 747 mmHg and is found to have
a volume of 3.557 L. How many grams of Mg were
used in the reaction? n.b. Assume 100 yield.
Partial pressure of water at 298 K 23.8 mmHg
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REAL GASES
An ideal gas is a hypothetical concept. No gas
exactly follows the Ideal Gas Law, though many do
at high temperatures and low pressures, i.e.
normal conditions.
As long as these conditions exist, the law works
well,
But at high pressures and/or low temperatures,
modifications must be made to the equation.
An equation for real gases was developed in 1873
by Johannes van der Waals using experimental
values.
Pobs a(n/Vi)2 x (Vobs nb) nRT
a is in
atm L2/mol2
b is in
L/mol