# Chemical Bonding - Lesson 1 - Derivation of the Ideal Gas Law by a.mustafasipsak

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```									     Derivation of the                                  We have now identified the models of
how we look at atoms and molecules,
Ideal Gas Law                                studied reactions they undergo and have
learned how energy is involved in these
processes. Now we will turn our study to
the different phases in which matter exists.
You will find that these units on
phases of matter and the kinetic-molecular
theory will be quite extensively tested in the
multiple-choice section of the national AP
exam; especially the unit on gases. Be
forewarned.
Get out AP equation sheet

Characteristics of Gases
1. Non metallic compounds
Factors the Influence
2. Simple formulas w/ low M.W.                            Gas Behavior
3. A.k.a. Vapors for substances that are
normally (s) or (l) at room temp.               •Temperature (T)
4. Expand to fill their container                      = The indirect measure of the
5. Highly compressible                                 average kinetic energy of a
6. Form homogeneous mixtures
collection of particles (on the
7. Relatively far apart (behave                        Kelvin scale, K)
independent of other molecules)

•Volume (V)                                         •Pressure (P)
= The total space of a container that
= The measure of the number of
gases occupy due to the free random
motion of the gas molecules                          collisions between gas particles
(reported in liters, L)                              and a unit area of the walls of its
container (reported in KPa or
•Number of moles (n)                                   atm)
= The total number of gas                               P=F/A    having the units (N/m2)
molecules in a collection of
particles. (reported in moles, mol)                        1N/m2 = 1 Pascal (Pa)

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Pressure of air is measured                        Pressure
Pressure
with a BAROMETER                             Column height measures
Column height measures
pressure of the
pressure of the
atmosphere
atmosphere
•• 1 standard atm
1 standard atm
= 760 mm Hg
= 760 mm Hg
= 760 torr
= 760 torr
(developed by Torricelli in 1643)               = 29.92 inches Hg
= 29.92 inches Hg
= 14.70 psi
= 14.70 psi
Hg rises in tube until force
= about 34 feet of water
= about 34 feet of water
of Hg (down) balances the
•• SI unit is PASCAL, Pa,
SI unit is PASCAL, Pa,
force of atmosphere
– where 1 atm = 101.325 kPa
– where 1 atm = 101.325 kPa
(pushing up).

Aneroid Barometer   In order to measure the pressure
exerted by an enclosed gas, scientist
use a device called an manometer.
Two types of manometers:
1. Open-end manometer- used for gas
pressures near 1 atm.
2. Closed-end manometer- used for
gas pressures greatly over or under
1 atm.

1.The pressure of a gas is                       The Classical Gas Laws
measured at 49.0 torr in an
open-end manometer. Describe
•Boyle’s Law
this pressure in the units of
atmospheres and describe the                        The volume of a
mercury level in the manometer                 fixed quantity of gas at
in respect to the pressure of the              constant temperature is
gas and the atmosphere.                        inversely proportional           Robert Boyle
to the pressure               (1627-1691). Son of
Earl of Cork,
Ireland.

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(L, atm)         •Boyle’s Law
The volume of a        2. Baby George was given a 4.53 dm3
V = 1/P            fixed quantity of gas at         helium filled metallic balloon on a
constant temperature is
VP = k             inversely proportional to        bright, sunny day when the
the pressure                     barometric pressure was 768 torr.
V1P1 = V2P2
That night a storm front moved in
y=mx+b                     and the pressure dropped to 732 torr.
1                   What is the expected volume of the
V = m          + b
P                   balloon at these new barometric
k                 conditions?
or       V =
P

(L, K)
•Charles’ Law
V = k’ T
The volume of
V1/ T1 = V2/ T2
a fixed amount of
gas maintained at
constant pressure is
proportional to its         Jacques Charles (1746-
1823). Isolated boron       •Charles’ Law
absolute                      and studied gases.
The volume of a fixed amount of gas maintained at
temperature.                      Balloonist.
constant pressure is proportional to its absolute temperature.

He
3. Baby George received a larger 6.19
Y=mx+b                                          dm3 helium filled metallic balloon
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V=mT+b                                 CH4      on top of Pike's Peak at noon when
4      V = k’ T                                       the temperature was 200C. That
night, the temperature dropped to -
V(L)

3                                           H2O
100C. What volume did the balloon
2                                           H2        occupy at that temperature?
1                                           N2O

-200     0           200
T(0C)

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• The volume of a gas at constant temperature
and pressure is directly proportional to the
number of moles of the gas.
Hypothesis
• Mathematically, this means   V = kn
At constant temperature and
V1/ n1 = V2/ n2                     pressure, equal volumes of gases
contain equal number of particles
It was found that one mole of any
gas occupies a volume equal to
22.414 L at STP, or 0oC and 1 atm

Y=mx+b                                           Ideal-Gas Equation
V=mn+b
V = k’’ n                                • So far we’ve seen
that V ∝ 1/P (Boyle’s law)
V                                                          V ∝ T (Charles’s law)
• Combining these, we
get              nT
V∝
P
n

Ideal-Gas Equation                           “R” is the ideal gas constant
describing the volume of one mole of a gas
The relationship            nT                 at 1 atm and 0oC
V∝                                                    L ⋅ atm
P                         R = 0 . 0821
mol ⋅ K
then becomes                nT
V=R                                                L ⋅ kPa
P                            = 8.314
mol ⋅ K
or
PV = nRT                                                          L ⋅ torr
= 62.36
mol ⋅ K
With the addition of a proportionality constant             = 8.314          J
(R).                                                                       mol • K

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4. A sample of hydrogen gas has            Relevance of the Ideal Gas Law
a volume of 8.56 L at a                     The Ideal gas law provides a
temperature of 0oC and a                constant set of conditions to which we
pressure of 1.5 atm. Calculate          can compare any gas sample.
the mass of hydrogen present                However, if any one variable is
in the sample.                          held constant, the combined gas law
can be utilized, where:

P1V1/ n1T1 = P2V2/ n2T2

5. A sample of diborane gas (B2H6), a
substance that burst into flame when
exposed to air, has a pressure of 345
torr at a temperature of –15.0oC and
a volume of 3.48 L. If the conditions
changed the temperature to 36.0oC
and the pressure to 468 torr, what
will be the volume?

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