A Gas
-
Uniformly fills any container.
-
Mixes completely with any other gas
-
Exerts pressure on its surroundings.
Pressure
-
is equal to force/unit area
-
SI units = Newton/meter2 = 1 Pascal (Pa)
-
1 standard atmosphere = 101,325 Pa
-
1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr
A simple manometer –
measures the pressure of a gas
in a contained (in mm Hg =
Torr)
a) Gas pressure = atmospheric
pressure – h, b) Gas pressure
= atmospheric pressure + h
Atmospheric
pressure (Patm)
Atmospheric
pressure (Patm)
05_48
h
Gas
pressure (Pgas)
less than
atmospheric
pressure
(Pgas) = (Patm) - h
(a)
h
Gas
pressure (Pgas)
greater than
atmospheric
pressure
(Pgas) = (Patm) + h
(b)
Boyle’s Law*
Experiment
b)
A plot V versus 1/P gives a straight
line and the slope gives the value of
the contant k
05_50
100
40
slope = k
V(in3)
Volume doubles as the pressure is
halved
P (in Hg)
a)
50
20
P
P
2
0
0
20
40
60
0
0.01
0.02
0.03
1/P (in Hg)
V
2V
V(in3)
(a)
(b)
05_1541
Pext
Pext
Volume is decreased
Boyle’s Law*
Generalization
Pressure × Volume = Constant (T = constant)
P1V1 = P2V2
V ∝ 1/P
(T = constant)
(T = constant)
(*Holds precisely only at very low pressures.)
A gas that strictly obeys
Boyle’s Law is called an
ideal gas.
Charles’s Law
He
05_53
6
5
CH4
4
V(L)
A plot V versus T gives a straight line as
shown for several gases. The solid lines
represent experimental measurements.
The dashed lines represent extrapolation
of the data into regions where these gases
would become liquids or solids
3
H2O
2
H2
1
N2O
-300
-200
-273.2 ºC
-100
0
100
200
T(ºC)
The volume of a gas is directly proportional to
temperature, and extrapolates to zero at zero Kelvin.
V = bT (P = constant)
b = a proportionality constant
300
Charles’s Law
V1
V2
=
T1
T2
( P = constant)
05_1543
Pext
T1
T2
Pext
Energy (heat) added
V1
V2
Gas stoichiometry
Avogadro’s Law
For a gas at constant temperature and
pressure, the volume is directly proportional
to the number of moles of gas (at low
pressures).
V = an
a = proportionality constant
V = volume of the gas
n = number of moles of gas
Ideal Gas Law
-
An equation of state for a gas.
-
“state” is the condition of the gas at a
given time.
PV = nRT
Ideal Gas Law
PV = nRT
R = proportionality constant
= 0.08206 L atm Κ−1 mol−1
P = pressure in atm
V = volume in liters
n = moles
T = temperature in Kelvins
Holds closely at P < 1 atm
Standard Temperature
and Pressure
“STP”
P = 1 atmosphere
T = 0°C
The molar volume of an ideal gas is 22.42
liters at STP
Dalton’s Law of
Partial Pressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P3 + . . .
Kinetic Molecular Theory
1. Volume of individual particles is ≈ zero.
2. Collisions of particles with container
walls cause pressure exerted by gas.
3. Particles exert no forces on each other.
4. Average kinetic energy ∝ Kelvin
temperature of a gas.
The Meaning of Temperature
(KE)avg
05_59
Relative number of N2 molecules
with given velocity
Kelvin temperature is an index of
the random motions of gas
particles (higher T means greater
motion.)
3
= RT
2
273 K
1273 K
2273 K
0
1000
2000
V e lo c ity (m /s )
3000
A plot of the relative number of N2 molecules that
have a given velocity at three temperatures. Note that
as the temperature increases both the average volocity
(maximum on curves) and the spread of velocities
increase
Diffusion: describes the mixing of
gases. The rate of diffusion is the
rate of gas mixing.
Effusion: describes the passage of gas
into an evacuated chamber.
05_60
Pinhole
Gas
Vacuum
Effusion:
Rate of effusion for gas 1
=
Rate of effusion for gas 2
M2
M1
Diffusion:
Distance traveled by gas 1
=
Distance traveled by gas 2
M2
M1
Real Gases
0 5 _ 63
Plots PV/nRT versus P for
nitrogen gas at three
temperatures.
203 K
1 .8
PV
nRT
293 K
1 .4
673 K
1 .0
Id e a l
gas
0 .6
0
200
400
600
800
P (a tm )
Plots PV/nRT versus P for
several gases (at 200 K).
05_62
CH4
N2
2 .0
H2
PV
nRT
CO2
1 .0
Id e a l
gas
0
0
200
400
600
800
1000
P (a tm )
The ideal gas model works only for low pressures and
high temperatures
Real Gases
Must correct ideal gas behavior when
at high pressure (smaller volume)
and low temperature (attractive
forces become important).
Real Gases
Van der Waals’ equation
[ Pobs + a ( n / V ) ] × (V − nb ) = nRT
2
↑
corrected pressure
Pideal
↑
corrected volume
Videal
Chemistry in atmosphere
05_68
0.4
Other
pollutants
0.3
NO2
0.2
O3
NO
Time of day
6:00
4:00
2:00
Noon
10:00
8:00
0
6:00
0.1
4:00
3O2(g) → 2O3(g)
0.5
Concentration (ppm)
2NO2(g) → 2NO(g) + 2O(g)
2O (g) + 2O2(g) → 2O3(g)
2NO(g) + O2(g) → 2NO2(g)
Molecules of unburned
fuel (petroleum)