CHAPTER 5
THE GASEOUS STATE
Gases
What gases are important for each of the
following: O2, CO2 and/or He?
A.
B.
C.
D.
Gases
What gases are important for each of the
following: O2, CO2 and/or He?
A. CO2
B. O2/CO2
C. O2
D. He
Some Gases in Our Lives
Air:
oxygen O2
nitrogen N2
ozone O3
argon Ar
carbon dioxide CO2 water H2O
Noble gases:
helium He neon Ne krypton Kr xenon Xe
Other gases:
fluorine F2 chlorine Cl2
ammonia NH3
methane CH4
carbon monoxide CO
nitrogen dioxide NO2
sulfur dioxide SO2
I. Characteristics of a Gas
A) Gases assume the shape and
volume of a container.
B) Gases are the most compressible of
all the states of matter.
C) Gases will mix evenly and completely
when confined to the same container.
D) Gases (2 g/L) have lower densities
than liquids or solids (2 g/mL).
II. Historical Perspective
A) It was the first state studied in
detail.
B) It is the easiest state to understand
-- for the purposes of general
chemistry; there is a simple
mathematical equation for the general
description of a gas which works well
in the real world, over a certain range
of temperatures and pressures.
C) The study of gases and its results
formed the primary experimental
evidence for our belief that matter is
made up of particles. MATTER IS
NOT CONTINUOUS.
III. Measurable Properties of a Gas
A) Mass – symbol m, measured in
grams or moles - symbol is n
n = m/M
Where M is the molar mass
(from the periodic table)
B) Pressure - symbol is P
One atmosphere (1 atm)
Is the average pressure of the
atmosphere at sea level .
Is the standard of pressure
 P = Force
Area
1.00 atm = 760 mm Hg = 760 torr = 101.3 kPa
C) Volume - symbol is V
Measured in liters (L), milliliters
(mL), cubic centimeters (cm3), cubic
meters (m3)
D) Temperature - must be in K symbol is T
Temp in Kelvin = Temp in Celsius + 273.15
IV. Measuring the Mass of a Gas is
Difficult.
A) Balloons appear to lose mass when
certain gases are added to them.
WHY?
All expandable containers have this
problem.
B) Constant volume containers, like
glass flasks, have a different problem.
What is that problem? How is it
solved?
How are these problems overcome?
V. Pressure and Its Measurement
A) Pressure is defined as the force
exerted per unit area of surface.
B) Think of a gas confined in a box the top, bottom, and sides of the box
are areas - the gas exerts force on all
sides of the box which are AREAS
C) In the U.S., the units of pressure
seen on tires, tire gauges, reported by
mechanics are _________.
D) Pounds must be a unit of
_________, and square inches is a
unit of _________.
FORCE = MASS X ACCELERATION
WEIGHT = mg = mass x the
acceleration due to gravity
E) In the SI system, the unit of
pressure is the pascal, Pa.
1 Newton is the resultant force which
causes a 1 kilogram mass to accelerate
1 m/sec2 .
A penny on a table exerts a force of
about 100 Pa of pressure – 1 Pa is a
very small unit of pressure.
F) With respect to gases:
1) on weather reports - barometric
pressure is given in __________.
You measure the pressure in mm of Hg
(mm is a unit of length), with a
barometer invented by Torricelli.
(another unit of pressure, the torr, is
named after Torricelli)
a) What is a barometer?
How do you get the
Hg up the tube?
What holds it up
there?
Units of pressure and their
relationships are:
1 atm = 760 mm Hg = 760 torr =
101.3 kPa = 14.7 psi = 29.92 inches
of Hg = 1.013 bars
Learning Check
A. What is 475 mm Hg expressed in atm?
1) 475 atm
2) 0.625 atm 3) 3.61 x 105 atm
B. The pressure of a tire is measured as 29.4 psi.
What is this pressure in mm Hg?
1) 2.00 mm Hg
2) 1520 mm Hg
3) 22,300 mm Hg
Solution
A. What is 475 mm Hg expressed in atm?
485 mm Hg
x
1 atm
= 0.625 atm
760 mm Hg
B. The pressure of a tire is measured as 29.4 psi.
What is this pressure in mm Hg?
29.4 psi x 1.00 atm x 760 mmHg = 1.52 x 103 mmHg
14.7 psi 1.00 atm
VI.MEASURE THE VOLUME OF A
GAS
A) A gas occupies all the volume
enclosing it.
B) How do we know when the flask
is full of gas at the external
pressure?
C) The unit used by chemists is the L.
(ml, cm3 and m3 can also be used)
VII. MEASURING TEMPERATURE
OF A GAS
USE A THERMOMETER TO
MEASURE DEGREES C, then add
273(.15) to change to the KELVIN
scale.
VIII. THE RELATIONSHIP
BETWEEN PRESSURE AND
VOLUME OF A GAS AT
CONSTANT TEMPERATURE
A) Boyle's Law Apparatus
show relationship.
B) What kind of a graph
do we get when we plot the
V vs. P data?
What name do we give to this curve?
V1 x P1 = Area1
V2 x P2 = Area2
Area1 = Area2
V1 x P1 = V2 x P2
THE LARGER THE P1 the smaller
the V1
Let's say that P X V = 30
If P is 5 then V is _______
If P is 10 then V is ______
If P is 15 then V is ______
As P decreases V increases; or as P
increases, V decreases.
C) What kind of a graph do we get if
we plot 1/V vs P?
What kind of curve is this?
EXAMPLE PROBLEMS
1) A sample of gas occupies a volume
of 20.0 L at 1.50 atm. What will the
volume be if the pressure changes to
0.250 atm and the temperature and
the amount of gas remain the same?
The pressure went down, so the
volume must go up. So the final
volume must be 6 times larger.
2) A sample of gas occupies a volume
of 25.0 L at 1.00 atm. What will the
pressure be if the volume changes to
5.00 L ? The temperature and the
amount of gas remain the same.
V is going down, P must go up
3) What volume will 22.4 L of H2 gas
measured at 1.00 atm occupy at a
pressure of 1900. mm of Hg with the
temp. and amt. of gas remaining
constant?
IX. TEMPERATURE EFFECTS AND
CHARLES’ LAW
A) When we plot volume in L vs. T in
degrees C for a constant amount of
gas at constant P, we obtain what kind
of graph?
-273 oC or 0 K is
absolute zero;
the lowest
possible
temperature.
B) We see that when we extrapolate
this line to where it intersects the x
axis, we will obtain a temperature of
-273oC (zero Kelvin).
C) What are the implications of this?
What happens in reality? What is the
difference between a real gas and an
ideal gas?
D) If we plot T in oC vs V we get a
straight line, it follows the general
formula____________.
oC
= mV + (-273)
oC
+273 = mV
Kelvins = mV
KELVINS ARE PROPORTIONAL
TO VOLUME
SAMPLE PROBLEMS
1) A sample of gas occupies a volume
of 20.0 mL at 25oC and 1.00 atm.
What is its volume at 50oC at the
same pressure?
If it were a balloon, what would have
happened to it? LARGER OR
smaller?
Will it be twice as big? Is the
temperature twice as big?
X. COMBINED GAS LAW
A sample of gas occupies a volume of
30.0 mL at 25oC and 0.600 atm. What
is its volume at STP (standard
temperature and pressure  0oC or
273K and 1.00 atm or 760 mm Hg)?
XI. REACTIONS INVOLVING GASES
A) Gay-Lussac's and Avogadro's Laws
1) 1808 - Joseph-Louis Gay-Lussac
published the results of some
experiments on reactions of gases
which resulted in the Gay-Lussac Law
of Combining Volumes. When gases
react, the volumes of the product and
reactant gases at a given temp and
pressure are in the ratios of small
whole numbers.
2 liters of CO gas react with 1 liter of
O2 gas to yield 2 liters of CO2 gas.
2 CO(g) + 1 O2(g)  2 CO2(g)
2) HOW CAN THIS BE POSSIBLE?
B) Avogadro's Law - EQUAL
VOLUMES OF DIFFERENT GASES
CONTAIN EQUAL NUMBERS OF
MOLECULES WHEN MEASURED
AT THE SAME TERMPERATURE
AND PRESSURE.
1) The volume of a gas is directly
proportional to the number of
molecules (moles) of gas at the same T
and P.
2) One mole of any gas occupies the
same volume for a given T and P and
contains the same number of particles
- atoms - molecules.
3) This volume is called the molar
volume and is 22.414 L for an ideal gas
at 0oC and 1 atm.
4) V is directly proportional to n at
constant P and T.
5) Some real gas volumes at STP are:
O2-22.397 L; N2-22.402 L; H-22.433L
XII. THE IDEAL GAS EQUATION
A) At the beginning of our study of
gases, we said that there was a simple
mathematical relationship which
describes a gas: the equation of state
for an ideal gas.
B) That equation is: PV = nRT
This equation is for an ideal gas: one
which follows Boyle's, Charles’ and
Avogadro's Laws perfectly. No real
gas does this exactly!
When P is low and T is high, real
gases behave this way. It keeps scuba
divers and people needing oxygen gas
alive, and other processes using gases
at normal T and P working correctly.
C) We have looked at the relationship
between V & P, V & T, and V & n
separately. Now we can put them all
together using the gas constant, R.
D) We can use the following
relationship to find R for an ideal gas:
1.000 mol of an ideal gas at 273.15 K
and 1.000 atm occupies 22.414 L.
What is the value of R?
If you use 3 significant figures, as we
will usually do
We can see that the value of R changes
depending on the units of pressure and
volume which are used. mol and K
stay the same.
E) We can solve a variety of problems
with the Ideal Gas Equation.
1) Calculate the volume of 2.63 mol of
O2 gas at 25oC and 0.986 atm
pressure. Assume O2 behaves as an
ideal gas under these conditions.
2) Calculate the density of N2 in grams
per Liter at 25oC and 0.968 atm.
From this we see how chemists could
obtain the molar masses of substances
which were gases or could easily be
changed to the gaseous form before the
invention of the mass spectrometer.
In a future lab you will find the molar
mass of a volatile liquid using the Ideal
Gas Equation.
3) Calculate the approximate molar
mass of a gas which has a density of
1.429 g/L at STP.
4) Calculate the approximate molar
mass of a gas which has a density of
1.782 g/L at 27oC and 670 mm Hg.
XIII. MIXTURES OF GASES
A) Many studies involve mixtures of
gases which do not react, for example
air.
B) What is the relationship between
the total pressure of the gas mixture
and the pressure of each component of
the mixture?
C) Dalton's Law of Partial Pressures
1) The total pressure of a mixture of
ideal gases is the sum of the pressures
that each gas would exert if it were
present alone.
You will use this important concept in
the laboratory when you collect a gas
over water -
Pbar = Pinside = Pgas + Pwater vapor
Pgas = Pbar - Pwater vapor
XIV. DIFFUSION OF GASES
A) In 1832, Graham studied the rates
of diffusion of gases: the speeds at
which gases move through each other.
SPEED is a difficult concept. What
does speed mean to you???
You should think of miles per hour - a
distance in the numerator and a time
in the denominator.
What is the
distance?
What is the
time?
What is the
fraction?
Distance
time
B) Effusion - a process in which a gas
flows through a small hole and is
theoretically simpler than diffusion
since we don't have to be concerned
with molecules hitting each other and
zigzagging across the room.
C) Graham's Law of Effusion - Under
the same conditions of pressure and
temperature, the rates of effusion of
gases are inversely proportional to the
square roots of their molar masses.
D) What does this mean?
E) How many times faster does H2
effuse than O2 at the same temperature
and pressure?
The rate of effusion of H2 is 4 times
faster than the rate of effusion of O2.
If it takes 205 seconds for 1.50 L of an
unknown gas to effuse through a
porous cup, and 95 seconds for the
same volume of N2 at the same T and
P, what is the approximate molar mass
of the gas?
XV. MOLECULAR BEHAVIOR OF
GASES
A) We have now considered in detail
the ideal gas law which was formulated
from experimental evidence.
B) Starting in the 1850's, Boltzmann
in Germany and Maxwell in England
found that properties of gases could
be satisfactorily explained in terms of
the motion of the individual gas
molecules.
C) This gave rise to what we call the
Kinetic Molecular Theory of Gases.
D) This theory applies to an Ideal
Gas perfectly.
E) The Kinetic Molecular Theory has
5 postulates about the nature of an
ideal gas.
1) Gases are composed of molecules
whose size is negligible compared with
the average distance between them.
(Ideal gas molecules are point masses.)
2) Gas molecules are in constant
motion, in random directions, and at
various speeds. (Properties of a gas
that depend on motion like pressure
are the same in all directions.)
3) Ideal gas molecules exert neither an
attractive force nor repulsive force on
each other.
4) When molecules collide with one
another, the collisions are elastic.
What does this mean?
5) The average kinetic energy of the
molecules is proportional to the
temperature on the Kelvin scale.
What does this mean?
All gases at the same temperature on
the K scale have the same average
kinetic energy.
K.E. = 1/2 mv2 or 1/2 mu2 where v is
velocity and is a vector quantity, and u
is speed which is a scaler quantity.
Two gases at the same T have the
same average K.E.
If one gas is heavier than the other,
what must be different if the average
K.E. must be the same?
This is the basis for Graham's Law.
avg. KEA = avg. KEB
1/2 mAu2A = 1/2 mBu2B
mAu2A = mBu2B
F) Distribution of Molecular Speeds
1) According to KMT, in a given
sample of gas, the speeds of the
molecules vary over a wide range of
values - a few are moving very slow, a
few are moving very fast, most have
intermediate speeds.
2) Graphically we represent it as:
3) If we raise the temperature, then
the curve moves to the right and
lowers.