Chapter 10
Gases and the Atmosphere
Robert Boyle
1627-1691.
Boyle’s Law.
Jacques Charles
1746-1823.
Charles’ Law.
J. Charles 1783.
First ascent in
hydrogen balloon.
1
Characteristics of Gases
• Gases are highly compressible and occupy the full
volume of their containers.
• Gases exert pressure, P = F/A (force/area).
• Gases always form homogeneous mixtures with other
gases.
• Actual gas atoms and molecules only occupy about
0.1 % of the volume of their containers.
• Avogadro’s hypothesis states that equal volumes of
gases at the same pressure and temperature contain
equal number of molecules. (To repeat, not equal
masses but equal numbers of molecules or moles).
2
The Composition of the Atmosphere
Dry Atmosphere at Sea Level (% by Volume)
Nitrogen 78.084
Oxygen 20.948
Argon 0.934
Carbon dioxide 0.033 (increasing yearly)
Neon 0.00182
Hydrogen 0.0010
Helium0.0052
Methane 0.0002*
Krypton 0.0001
Xenon 0.000008
Carbon monoxide, ozone, ammonia,
nitrogen dioxide, sulfur dioxide <0.00001*
* = variable depending upon pollution
Water content in
the atmosphere is
variable in actual
contexts, ranging
to over 5% in hot
steamy climates
to <<1% in dry
arid environments.
3
4
Pressure
760 mm
(at sea level)
Hg
Atmospheric pressure is measured with a barometer
If a tube is inserted into a container of mercury
open to the atmosphere, the mercury will rise 760
mm up the tube (at sea level).
5
Pressure
Atmospheric Pressure and the Barometer
. Standard atmospheric pressure is the pressure
required to support 760 mm of Hg in a column.
Units: 1 atm =
760 mmHg =
760 torr =
1.01325  105 Pa =
101.325 kPa.
6
Pressure - manometers
Patm > Pgas
Patm = Pgas + h2
Pgas > Patm
Pgas = Patm + h3
Pgas = Patm – h2
7
The Gas Laws
The Pressures-Volume Relationship: Boyle’s Law
P is inversely proportional to V (at constant T)
Mathematically:
PV  constant
• A plot of V versus P is a hyperbola.
• Similarly, a plot of V versus 1/P must be a straight line
passing through the origin.
8
The Gas Laws
The Pressures-Volume Relationship: Boyle’s Law
(P vs. V at constant T)
9
The Gas Laws
The Temperature-Volume Relationship: Charles’ Law
(We know that hot air balloons expand when they are
heated.)
The volume of a fixed quantity of gas at constant
pressure increases as the temperature increases.
Mathematically: V
T
 constant
• A plot of V versus T is a straight line.
• When T is measured in C, the intercept on the
temperature axis is -273.15C.
• We define absolute zero, 0 K = -273.15C.
10
The Gas Laws
The Temperature-Volume Relationship: Charles’
Law
11
The Gas Laws
The Quantity-Volume Relationship: Avogadro’s Law
• Gay-Lussac’s Law of combining volumes: at a given
temperature and pressure, the volumes of gases which
react are ratios of small whole numbers.
can’t be: 2 H + O
H2O (Why?)
12
The Quantity-Volume Relationship: Avogadro’s Law
Avogadro’s Hypothesis: equal volumes of any gas at
the same temperature and pressure will contain the
same number of molecules.
Same number
of particles
(same T and P)
V = constant  n
at a constant P and T
13
V = constant  n
at a constant P and T
22.4 L = constant  1 mole
at a 1 atm and 273 K
14
The Ideal Gas Equation
• Summarizing the Gas Laws
Boyle: V  1/P (constant n, T)
Charles: V  T (constant n, P)
Avogadro: V  n (constant P, T).
Combined:
nT
V 
P
Ideal gas equation
R = ideal gas constant
 nT 
V  R

 P 
15
The Ideal Gas Equation
• Ideal gas equation:
PV = nRT
R = gas constant = 0.08206 L•atm/mol-K.
We define STP (Standard Temperature and Pressure)
= 0C (273.15 K)
= 1 atm.
Volume of 1 mol of gas at STP is 22.4 L.
Other units of R (always energy/mol-K):
8.314 J/mol-K (this is the SI unit)
Problem: What is the pressure
of 5.00 g of N2 in a 4.0 L
container at 300K ?
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The Ideal Gas Equation
Relationship Between the Ideal-Gas Equation
and the Gas Laws
• If PV = nRT and n and T are constant, then PV =
constant and we have Boyle’s law.
• Other laws can be generated similarly.
• In general, if we have a gas under two sets of
conditions, then
P1V1 P2V2

R
If n1=n2 then
n1T1 n2T2
Problem: 3.0 mL of a gas at 300 K and 3.4 atm is
heated to a temp of 450 K and pressure of 5.5 atm.
What is its volume?
17
Further Applications of The Ideal-Gas
Equation
Gas Densities and Molar Mass
Rearranging the ideal-gas equation with
M as molar mass we get:
n
P

V
RT
or:
Solving for molar mass,
dRT
M
P
nM
PM
d 
V
RT
Problem: a gas in a 5-L container
At 350 K and 1.4 atm pressure has
a mass of 6.85 g. What is its MW?
What might the gas be?
18
Gas Mixtures and Partial Pressures
• Since gas molecules are so far apart, we can assume
they behave independently.
Dalton’s Law: in a gas mixture the total pressure is given
by the sum of partial pressures of each component:
Ptotal = P1 + P2 + P3 + …
For one gas in the mixture, its pressure fraction is the
same as its mole fraction:
Pi/Ptotal = ni/ntotal = Xi
19
Gas Mixtures and Partial Pressures
Collecting Gases over Water
It is common to synthesize gases and collect them by
displacing a volume of water.
To calculate the amount of gas produced, we need to
correct for the partial pressure of the water:
Ptotal = Pgas + Pwater
20
Gas Mixtures and Partial Pressures
Collecting Gases over Water
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22
Collecting Gases over Water
Example:
Zn(s) + H2SO4 (aq)
ZnSO4(aq) + H2(g)
159 mL wet H2 collected over water at 24oC.
Barometric pressure = 738 torr
How many g of Zn are consumed?
(vapor pressure of water at 24oC = 22.38 Torr)
23
Kinetic-Molecular Theory (KMT)
• Theory of moving molecules, explains gas behavior,
gives us an understanding of temperature and
pressure effects on the molecular level.
• Assumptions:
(1) Gases consist of a large number of molecules in constant
random motion.
(2) Volume of individual gas particles is negligible compared to
volume of container (point particles).
(3) Intermolecular forces (forces between gas molecules) are
negligible.
(4) All particle collisions with walls are elastic (no loss of energy).
(5) All energy and momenta conserved.
24
Kinetic-Molecular Theory (KMT)
Pressure of a gas results from
the number of collisions per unit
time on the walls of container.
The energy of gas molecules
depends only on temperature.
Thus, heavier molecules move
more slowly (at the same
temperature).
25
Kinetic-Molecular Theory
For gases, there is a range of velocities and energies at
each temperature.
N2
0oC
100oC
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Molecular Effusion and Diffusion
Graham’s Law of Effusion
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Molecular Effusion and Diffusion
at 25oC
Light molecules move faster and therefore
effuse (move through a pinhole) and diffuse
(mix together) faster.
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COMBINE ALL CONCEPTS:
Two 1-L flasks, one with N2 at STP, the other with CH4
at STP. How do these systems compare with respect
to:
(a) number of molecules?
(b)density?
(c) average kinetic energy?
(d)rate of effusion?
(e) pressure?
(f) temperature?
29
Real Gases: Deviations from Ideal
Behavior
Pressure and Temperature effects:
• From the ideal gas equation, we have
PV
n
RT
For 1 mol of ideal gas, PV/RT = 1 for all pressures.
In a real gas, PV/RT varies from 1 significantly.
The higher the pressure the greater the deviation
from ideal behavior.
The lower the temperature, the greater the deviation
from ideal behavior
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Real Gases: Deviations from Ideal
Behavior (Temperature and Pressure Effects)
• As temperature increases, the gas molecules move
faster and further apart.
• Also, higher temperatures mean more energy
available to break intermolecular forces.
• Therefore, the higher the temperature, the more ideal
the gas.
• As pressure increases, gas molecules are closer
together making the gas less ideal.
• Therefore, the lower the pressure, the more ideal the
gas.
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Real Gases: Deviations from Ideal
Behavior
The van der Waals Equation
• We add two terms to the ideal gas equation, one to
correct for volume of molecules, and the other to
correct for intermolecular attractions
• The correction terms generate the van der Waals
equation:
2
nRT n a
P
 2
V  nb V
where a and b are empirical constants.
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