Chapter 10
Gases
10.1 Characteristics of Gases
• Unlike liquids and solids, gases
–
–
–
–
Expand to fill their containers.
Are highly compressible.
Have extremely low densities.
Greatly affected by changes in
temperature and pressure
– Behave more ideally at low pressures and
high temperatures
Gases
10.2 Pressure
• Pressure is the
amount of force
applied to an area:
F
P=
A
• Atmospheric
pressure is the
weight of air per
unit of area.
Gases
Units of Pressure
• Pascals
– 1 Pa = 1 N/m2
– Force(N) = mass(kg) x acceleration(m/s2)
– Pressure (Pa=kg·m-1·s-2)
• Bar
– 1 bar = 105 Pa = 100 kPa
Gases
 Units of Pressure
• mmHg or torr
–the difference in the
heights measured in
mm (h) of two
connected columns of
mercury.
• Atmosphere
:1.00 atm = 760 torr
= 101,325 Pa
= 1.01325 bas
Gases
 Manometer
: to measure the
difference in pressure
between atm pressure
and that of a gas in a
vessel.
If atm p = 764.7 torr
Pgas = 764.7 + (136.4-103.8)
= 793.3 torr
Gases
 Standard Pressure
• Normal atmospheric pressure at sea level
is referred to as
standard atmospheric pressure.
• It is equal to
– 1.00 atm
– 760 torr (760 mmHg)
– 101.325 kPa
Gases
10.3 The Gas Laws
Gases
Boyle’s Law
Gases
 Boyle’s Law: Pressure vs Volume
The volume of a fixed quantity of gas at
constant temperature is inversely proportional
to the pressure.
Gases
P and V are Inversely Proportional
PV = k
Since
A plot of V versus P results in a curve.
V = k (1/P)
This means a plot of V versus 1/P will be a
straight line.
Gases
 Charles’s Law: Temperature vs. Volume
• The volume of a fixed
amount of gas at
constant pressure is
directly proportional to
its absolute
temperature.
Gases
Charles’s Law
• So,
V =k
T
• A plot of V versus T
will be a straight line.
Gases
 Avogadro’s Law
• The volume of a gas at constant temperature
and pressure is directly proportional to the
number of moles of the gas.
• Mathematically, this means
V = kn
Gases
10.4 Ideal-Gas Equation
• So far we’ve seen that
V  1/P (Boyle’s law)
V  T (Charles’s law)
V  n (Avogadro’s law)
• Combining these, we get
nT
V
P
V=R
nT
P
Gases
Ideal-Gas Equation
The constant of
proportionality is
known as R, the
gas constant.
Gases
Ideal-Gas Equation
The relationship
nT
V
P
then becomes
nT
V=R
P
or
PV = nRT
Pinitial Vinitial Pfinal Vfinal

ninitialTinitial nfinalTfinal
Gases
Ideal Gas Law
Gases
10.5 Densities of Gases
If we divide both sides of the ideal-gas
equation by V and by RT, we get
n
P
=
V
RT
n=m
m P
=
= d
V RT
dRT
= P
Gases
10.6 Dalton’s Law of Partial Pressures
• The total pressure of a mixture of gases
equals the sum of the partial pressures
that each would exert if it were present
alone.
• In other words,
Ptotal = P1 + P2 + P3 + …
 RT 
 RT 
 RT 
 n1 
  n2 
  n3 
  ..
V
V
V






 RT 
 RT 
 ( n1  n2  n3 ..)
  nt 

 V 
 V 
• Mole fraction
Gases
 Partial Pressures
2 KClO3(s)  2 KCl (s) + 3 O2(g)
• When one collects a gas over water, there is
water vapor mixed in with the gas.
Ptotal =Pgas+PH2O
Gases
10-7 Kinetic-Molecular Theory
• model that aids in our understanding
of what happens to gas particles as
environmental conditions change.
• Gases are in continuous, random
motion.
• The combined volume of all the
molecules of the gas is negligible
relative to the total volume in which the
gas is contained.
• Attractive and repulsive forces
between gas molecules are negligible.
• Collisions are elastic: P constant
Gases
Molecular Motion
Gases
Kinetic Energy and Temperature
Gases
Main Tenets of Kinetic-Molecular Theory
Energy can be
transferred between
molecules during
collisions, but the
average kinetic energy
of the molecules does
not change with time, as
long as the temperature
of the gas remains
constant.
Gases
Main Tenets of Kinetic-Molecular Theory
The average kinetic
energy of the
molecules is
proportional to the
absolute
temperature.
Gases
10.8 Effusion & Diffusion
Effusion is the escape of gas
molecules through a tiny hole
into an evacuated space.
Gases
Effusion
The difference in the rates of effusion for
helium and nitrogen, for example, explains
why a helium balloon would deflate faster.
Gases
 Diffusion
Diffusion is the spread of
one substance throughout
a space or throughout a
second substance.
Gases
Pressure – Assessing Collision Forces
• Translational kinetic energy,
• Frequency of collisions,
2
1
Et  mu
2
N
 u
V
• Impulse or momentum transfer,
I  mu
• Pressure proportional to impulse times
2
frequency
N
P
V
mu
Gases
Pressure and Molecular Speed
P
• Three dimensional systems lead to:
1N
m u2
3V
um is the modal speed
uav is the simple average
urms  u 2
Gases
Average Kinetic Energy(Et) & T
Et 
2
1
mu
2
 mu
2
=
3PV
3nR T

N
N
Et = 3 R T
2NA
• Average kinetic energy is directly proportional to
temperature!
• all gases have the same value of ET at a given T.
Gases
Average Speed
Assume one mole:
1
PV  N A m u 2
3
3RT  N A m u 2
 PV=RT
 N A m=M
3RT  M u 2
u rms
3RT

M
Gases
Molecular Speeds
• The speed of gas molecules is related
to mass and the temperature of the gas.
• The root-mean speed is calculated from:
rms 
3RT
M
Note units: M (kg/mol) and R (8.314 kg m2/s2mol K)
Gases
Sample Problem
Calculate the rms speed of nitrogen at
300. K.
rms 

3RT
M
 3   8.314 kg m2 / mol K   300. K 
 0.028 kg/mol
 517 m/s
Gases
Graham's Law of Effusion
KE1 = KE2
1/2 m1v12 = 1/2 m2v22
=
v22
v12
r1

r2
M2
M1
m1
m2
Gases
Sample Problem
A tank contains He and O2 gases. How
much more rapidly would the He effuse
through a pin hole inMthe tank?
re1

re2
reHe

reO2
2
M1
32.0
4.00
 2.83
He would effuse 2.83 times faster than O2
Gases
10.9 Real Gases: Deviations from Ideal
Behavior
In the real world, the
behavior of gases
only conforms to the
ideal-gas equation
at relatively high
temperature and low
pressure.
Gases
Real Gases
Even the same gas
will show wildly
different behavior
under high pressure
at different
temperatures.
N2
Gases
Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular
model (negligible volume of gas molecules
themselves, no attractive forces between gas
molecules, etc.) break down at high pressure
Gases
and/or low temperature.
Corrections for Nonideal Behavior
• The ideal-gas equation can be adjusted to
take these deviations from ideal behavior into
account.
– occupy discrete volumes
Vavailable  Vcontainer  nb
– interact with one another
n
n
Pactual  Pideal  a[ ]2 , Pideal =Pactual +a[ ]2
V
V
• The corrected ideal-gas equation is
known as the van der Waals equation.
Gases
The van der Waals Equation
n2
(P  a 2 )(v  nb)  nRT
V
nRT
n2
P
a 2
V  nb
V
Gases
Homework
• 필수 숙제: 14, 42, 62, 84, 98, 110, 125
• 추가 연습
18, 30, 40, 44, 54, 58, 64, 68, 83
Gases