Kinetic Molecular Theory

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Kinetic Molecular Theory

• Matter is composed of tiny particles (atoms,
  molecules or ions) with definite and
  characteristic sizes that never change.
• The particles are in constant random motion, that
  is they possess kinetic energy. Ek 1/2 mv2
• The particles interact with each other through
  attractive and repulsive forces (electrostatic
  interactions), that is the possess potential
  energy. U mgh
• The velocity of the particles increases as the
  temperature is increased therefore the average
  kinetic energy of all the particles in a system
  depends on the temperature.
• The particles in a system transfer energy form
  one to another during collisions yet no net
  energy is lost from the system. The energy of
  the system is conserved but the energy of the
  individual particles is continually changing.

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PRESSURE

• A physical property of matter that describes the
  force particles have on a surface. Pressure is
  the force per unit area, P F/A
• Pressure can be measured in
• atmosphere (atm)
• millimeters of mercury (mmHg)
• (torr) after Torricelli, the inventor of the
  mercury barometer (1643)
• pounds per square inch (psi)
• 1 atm 760 mmHg 760 torr 14.69 psi

3
TEMPERATURE

• A physical property of matter that determines the
  direction of heat flow.
• Measured on three scales.
• Fahrenheit oF Celsius
  oC
• Kelvin K
• oF (1.8 oC) 32 oC (oF - 32)/1.8
• K oC 273.15

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• EMPIRICAL GAS LAWS
• Boyles Law P1V1 P2V2
• Charles Law V1 / T1 V2 / T2
• Combined Gas Law P1V1 / T1 P2 V2 / T2

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Empirical Gas Laws

• 1. At 25oC, a sample of N2 gas under a pressure
  of 689 mmHg occupies 124 mL in a piston-cylinder
  arrangement before compression. If the gas is
  compressed to 75 of its original volume, what
  must be the new pressure (in atm) at 25oC?
• First make a list of the measurements made
• P1689 mmHg V1 124 mL
• P2 ? V2 75 V1
• From the variables, choose the appropriate
  equation, in this case Boyles Law P1V1P2V2
• (689 mmHg) (124 mL) P2 (0.75 x 124 mL)
• Solve for P2
• P2 (689mmHg) (124 mL) / (93 mL) 919 mmHg
• Now convert to atm
• 919 mmHg (1 atm / 760 mmHg) 1.21 atm

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Empirical Gas Laws

• 2. The gas in a Helium filled ball at 25oC
  exerts a volume of 4.2 L. If the ball is placed
  in a freezer and the volume decreases to 1/8 of
  its original value, what is the temperature
  inside the ball?
• First make a list of the measurements made
• V14.2 atm T1 25 oCc 273.15 298.15
• V2 1/8 P1 T2 ?
• From the variables, choose the appropriate
  equation, in this case Charles Law V1/T1V2/T2
• (V1) / (298 K) (1/8 V1) / T2
• Solve for T2
• T2 (298 K) (1/8 V1) / (V1) 298 / 8
  37.3 K or -235 oC
• 3. A balloon containing 6.50 grams of NH3 has a
  volume of 10.30 L at a temperature of 20.0oC and
  a pressure of 689.2 torr. What would be the
  pressure of NH3 if the volume decreased to 2.50 L
  without a change in temperature?

Pressure of NH3 2.84 x 103 torr.
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COMBINED GAS LAW

• A gas occupies a volume of 720 mL at 37oC and 640
  mmHg pressure. Calculate the volume the gas would
  occupy at 273 K and 1 atm.
• P1V1 / T1 P2V2 / T2
• rearranged to solve for V2 is
• V2 P1 V1 T2 / P2 T1
• V2 (640 mmHg)(720 mL) (273 K) / (760 mmHg)
  (310 K)
• V2 534 mL

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COMBINED GAS LAW

• A gas occupies a volume of 720 mL at 37oC and 640
  mmHg pressure.
• Calculate the pressure if the temperature is
  increased to 1000oC the volume expands to 900
  mL.
• Calculate the temperature if the pressure is
  decreased to 10 torr the volume is reduced to
  500 mL.

P2 2.1 x 103 mmHg
T2 3.4 K or -270 oC
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PRACTICE PROBLEM 20a
1. You prepared carbon dioxide by adding
aqueous HCl to marble chips, calcium carbonate.
According to your calculations, you should obtain
79.4 mL of carbon dioxide at 0 oC and 760 mmHg.
How many milliliters of gas would you obtain at
27oC at the same pressure? 2. Divers working
from a North Sea drilling platform experiences
pressures of 50 atm at a depth of 5.0 x 102 m.
If a balloon is inflated to a volume of 5.0 L
(the volume of a lung) at that depth at a water
temperature of 4.0oC, what would the volume of
the balloon be on the surface (1.0 atm) at a
temperature of 11 oC? 3. What volume would
5.30 L of H2 gas at 0 oC and 760 mmHg occupy if
the temperature was increased to 70oF and the
pressure to 830 torr? 4. The pressure gauge
reads 125 psi on a 0.140-m3 compressed air tank
when the gas is at 33.0 oC. To what volume will
the contents of the tank expand if they are
released to an atmospheric pressure of 751 torr
and a temperature of 13oC? 5. A gas has a
volume of 397.0 mL at 14.70 atm. What will be
its pressure (in torr) if the volume is changed
to 4.100 L?
87.3 mL
256 L
5.23 L
1.126 m3
1082 torr
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PRACTICE PROBLEM 20a

• 6. Which of the following statements is false?
• a) If the Celsius temperature is doubled, the
  pressure of a fixed volume of gas would double.
• b) All collisions between gas molecules are
  perfectly elastic (no energy is lost) according
  to KMT.
• c) The volume of gas is inversely proportional
  to the temperature of gas present (P constant)
• d) Gases are capable of being greatly
  compressed.
• 7. Which of the following statements are true?
• a) In a large container of O2 gas the pressure
  exerted by the oxygen will be greater at the
  bottom of the container.
• b) Of the three states of matter, gases are the
  most compact and the most mobile.
• c) The formula of ozone is 3 O2.
• d) Molecules of O2 gas and H2 gas at the same
  temperature will have the same average kinetic
  energies and the same average velocities.

C
D
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GROUP STUDY PROBLEMS
1. A sample of O2 gas initially at 0oC and 1.0
atm is transferred from a 2-L container to a 1-L
container at constant temperature. a) What
effect does this change have on the average
kinetic energy of the gas molecules? b) What
effect does the total number of collisions of O2
molecules with the container walls in a unit
time? 2. At constant pressure, a student needed
to decrease a volume of 155 mL of Ne gas by
32.0. To what temperature, (in oC), must the
gas be cooled if the initial temperature was
21oC? 3. A sample of CO2 gas has a volume of
125.0 L at a pressure of 789 torr and a
temperature of 30oC. What will be the
temperature if the pressure was increased to 900
torr the volume decreased to 95.0 L? 4. F2 gas,
which is dangerously reactive, is shipped in
steel containers of 30.0 L capacity, at a
pressure of 10.0 atm at 26.0 oC. What should be
the volume of the tank if the pressure is
increased to 820.0 torr the temperature is 43.0
oC?