Gases Chapter 9

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Gases Chapter 9
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What parameters do we use to describe
gases? pressure force/unit area 1 atm 101
kPa volume liters (L) Temperature K
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What is meant by volume? In principle, the
actual molecular volume of a gas is so small in
comparison to the volume it will occupy that we
treat gases at mathematical points.
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How do we measure pressure? above 1
atmosphere below 1 atmosphere A column of air 1
m2 has a mass of 10,300 kg, producing a
pressure of 101 kPa due to gravity (14.7
pounds/in2)
1 atm 76 cm Hg 101 kPa
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Boyles Law is concerned with the relationship of
pressure and volume using a fixed amount of gas
( a fixed number of mols of gas) PV constant
at constant temperature
Avogadros Law is concerned with the relationship
between the number of molecules or mols (n) and
the volume of a gas under conditions of constant
pressure and temperature V ? n at constant
pressure and temperature
Charles Law is concerned with the relationship
of temperature and volume when dealing with a
constant amount of gas (mols) V ? T when T is
expressed in K. The K temperature scale is
derived from the behavior of gases if V ? T then
V kT where k is a constant at constant pressure
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Ideal gas law PV nRT where R is a constant
R 0.0821 L.atm/K.mol Note that at constant
n and T, PV constant Boyles Law Note
that at constant P and T V/n
constant Avogadros Law Note that at constant P
and n, V/T constant Charless Law
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Standard conditions of pressure and temperature T
0 C (273 K) Pressure 1 atm What volume does a
mol of any ideal gas occupy at STP? PV nRT
V 1mol(0.0821 Latm/Kmol)(273 K)/(1 atm) V
22.4 L This means that equal volumes of gases
under identical conditions of temperature and
pressure contain equal number of molecules
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What is the difference between an ideal gas and a
real gas?
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• The ideal gas equation was generated from the
  kinetic theory of gases making the following
  assumptions
• The molecules could be treated as points (ie
  molecular volume 0)
• There are no attractive interactions between
  molecules.
• Gas particles move around at random
• Collision of gas molecules with the wall are
  totally elastic
• The kinetic energy of the gas particle is ? to
  temperature (K)
• In general, the ideal gas law works best at low
  pressures and high temperatures

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Real Gases van der Waals equation (P
an2/V2)(V-nb) n RT an2/V2 corrects for
intermolecular attractions nb corrects for the
real volume of molecules
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Daltons Law of partial pressures
Total atmospheric pressure 1 atm How much of
the pressure is contributed by N2?
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Pressure is a consequence of molecules colliding
with each other and the walls of the container
062
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For air if If PTV nTRT
and nT (no2 n N2 ...) at constant T,
PTV (no2 n N2 ...)RT Since the actual
volume of the molecules is small in comparison to
the volume occupied by the gas, all molecule
occupy the same volume V. The contribution to
the total pressure is dependent on the number of
collision of each gas with the wall and this is
dependent on the number of molecule of each gas.
Hence P (PN2 PO2 ...) PO2V nO2RT
PN2V nN2RT ...
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Temperature a measure of the average kinetic
energy of molecules
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Distribution of molecular speeds as a function of
temperature
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What are some of the consequences associated with
the fact that molecules at the same temperature
have different speeds?
Diffusion mixing of gases Effusion escape
through a small opening
The size of the pinhole needs to be
small 07
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. . . . . . .
. . . . . .. . . . . .
.. . . . .
Two molecules of different mass at the same
temperature effusing through an opening
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. . . . . . . . .
. . . . . .
. . . . . . .
. . . . . .. . . . . .
.. . . . .
Two molecules of different mass at the same
temperature effusing through an opening
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From the kinetic theory of gases speed of a
molecule u (3RT/M)1/2 For two gases at the
same temperature 1/2maua2 1/2mbub2 ua
average speed of molecule a ub average
speed of molecule b ma /mb ub2 /ua2 The rate
at which molecule a hits the pinhole ? u if the
comparisons are made at the same concentration
and temperature. ub /ua (ma /mb )1/2
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• Solving some problems involving gases
• A sample of gas at 25 C and 2 atm pressure in a
  5 L vessel was found to have a mass of 18 g. What
  is its molecular weight?
• PV n RT
• 2 atm5 L n0.0821 (Latm/K mol)298 K
• n 10/(0.0821298) mol 0.4087
• n wt/ mw 0.4087 18g/mw
• mw 44 g/mol

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Suppose the gas at the right exerted a pressure
of 15 cm as shown. Would the pressure of the gas
be greater or less than 1 atm? How many atm of
pressure is the gas exerting?
15.2 cm
1 atm 76 cm
76 - 15.2 60.8
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Suppose we have a sample of equal amounts of H2
and D2 in a vessel and a small opening is
introduced. What will be the initial rates of
effusion? uH2/uD2 mD2/mH2 (4/2)0.5
1.42 Will the relative rate change with time?
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What is the density of natural gas (CH4) at
STP? PV nRT density is g/mL or g/L We know
the molar volume of any gas is 22.4 L at STP How
many g of methane in a mole? 16g/22.4 L 0.714
g/l or 7.1410-4 g/mL or PV (wt/mw)RT
mwP/RT (wt/V)
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The surface temperature of Venus is about 1050 K
and the pressure is about 75 Earth atmospheres.
Assuming these conditions represent a Venusian
STP, what is the standard molar volume of a gas
on Venus? PV nRT 75 atmV 1mol0.0821(Latm/K
mol)1050 K V 1.15 L
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Natural gas is a mixture of a number of
substances including methane (mol fraction,
0.94) ethane (mol fraction, 0.04) propane (mol
fraction, 0.015). If the total pressure of the
gases is 1.5 atm, calculate the actual pressure
contributed by each of the gases described. mol
fraction mol A/(mol A mol B ....) PT 1.5
P CH4 PC2H6 ... Px V nxRT nCH4/nC2H6
PCH4/PC2H6 0.94/.04 CH4 0.941.5 C2H6
0.041.5 C3H8 0.0151.5