Gases
Gases
All elements that are gases at standard
conditions are nonmetals
All compounds that are gases at standard
conditions are covalent compounds
Gases of all elements/compounds have
similar physical properties.
Substances that are liquid and solid at
standard condition can exist as gases – they
are usually called vapors (water vapor)
Kinetic Molecular Theory
An explanation of the characteristics
and properties of gases (and how
they differ from liquids and solids)
Postulates (assumptions)
Gases are composed of a large number of particles
(atoms/molecules) that behave like hard, spherical
objects in a state of constant, random motion
These particles have insignificant volume compared to
the total volume of the gas. The particles are much
smaller than the average distances between them.
Most of the volume of a gas is empty space between
the molecules.
There is no force or attraction between the gas
particles or between the particles and the walls of the
container.
When particles of a gas collide a small amount of
energy may transfer from one particle to another
but the average kinetic energy of the gas remains
constant. (Energy is conserved)
The average kinetic energy of a collection of gas
particles depends only on the temperature of the
gas. (Samples of different gases at the same temp
have the same average kinetic energy)
Properties of Gases
Pressure
Caused by the collision of gas particles with the walls of
their container. The magnitude depends on how often
and how forcefully the particles strike the walls.
Temperature (absolute - in Kelvin)
A measure of the average kinetic energy of the particles.
Motion increases with increasing temp.
Volume
Since a gas is mostly empty space it can be readily
compressed to a smaller volume or can expand to fill
any larger volume. (Takes the volume of its container)
Diffusion - The spontaneous spreading out of a gas to fill
a container uniformly
Density
Very low! The mass of a gas occupies a much greater
volume than an equal mass of the same liquid or solid.
Mixtures
All gases that do not chemically react with each
other can form homogeneous mixtures
High entropy
Ideal Gas
Conforms exactly to all aspects of the kinetic theory
Does NOT exist. Real gases have attractions between
particles and the particles have volume.
Real gases exhibit ideal behavior when
Temperature is high (particles have enough energy to
overcome any attractions)
Pressure is low (particles are so far apart their individual
volume is insignificant).
Real gases have near ideal behavior at room conditions.
The most ideal gases have the weakest IMFs
(use molar mass as a tie-breaker when ranking)
most ideal
least ideal
Real Gases
He
N2
CO2
H2O
 no bonds
 nonpolar
 nonpolar with polar bonds
 polar
Pressure Exerted by Gases
Pressure is due to collisions between gas
molecules and the container walls
Pressure = force / area
Units are: lb/in2 (psi), g/cm2 , atmospheres
(atm), mm Hg, Torr, pascals (Pa), kilopascals
(kPa), bar
Unit relationships (used for converting units)
1.00 mm Hg = 13.6 mm H2O
1 mm Hg = 1 Torr
1 atm = 760 mm Hg
1.00 atm = 14.7 lb/in2
1.00 atm = 1.01  105 Pa
1 in2 column of
air (mass = 14.7 lb)
1 atm of pressure =14.7
lb/in2
Measuring the pressure of
collected gases
Principle: Pressure on a gas = the pressure of a gas
As long as the balloon is not inflating/deflating PA = PB
Measuring Equipment
Eudiometer: gas measuring tube
Manometer: instrument which allows for
the determination of the pressure of a gas
sample
Barometer: instrument for measuring air
pressure
Manometer - measuring the pressure
of collected gases
(a) Pgas = Ph1
(b) Pgas = Patm – Ph2
(c) Pgas = Patm15+ Ph3
Barometer – measuring air pressure
Hg can move
in and out of
the tube
Standard Temperature
a reference temperature which is 0oC or 273 K
NOT the same as standard state (25oC or 298 K)
Standard Pressure
a reference pressure which is 1 atm or its
equivalent
Molar Volume of a gas
The volume of 1 mole of a gas at standard
temperature and pressure (STP)
22.4 L/mole (at 273 K and 1 atm)
17
Boyle’s Law
Gas Pressure vs. Gas Volume
As the container size decreases, the
particles collide with the walls more
frequently thus raising the pressure
Qualitatively:
P ↑ , V ↓ or P↓ , V ↑
temperature and moles held constant
Gas Pressure vs. Gas Volume
As volume
increases,
pressure
decreases.
19
Boyle’s P-V
PV=k
(at constant temp and moles)
P1V1=k and P2V2=k (*k depends on temp and moles)
thus
P1V1 = P2V2
Inverse variation:
Movie
Amonton’s Law
(a.k.a. Nobody’s Law - Not in your book)
Gas Pressure vs. Gas Temperature
Increasing the temperature increases the KE
of the molecules. With higher velocities,
the molecules hit the walls more often and
harder: more pressure (if volume held
constant)
qualitatively: T ↑ , P ↑ or T↓ , P ↓
volume and moles held constant
Amonton’s: P-T
T/P = k ONLY if temp is Kelvin
T1P2 = T2P1
Represents a direct variation: graph is a straight
line
P
Charles’s Law
Gas Volume vs. Gas Temperature
Increasing the temperature increases the KE of the
molecules. The faster moving molecules will hit the
walls more often and harder. If the pressure is held
constant and the volume is not, the volume will
increase.
Qualitatively:
T ↑ , V ↑ or T ↓ , V ↓
pressure and moles held constant
Charles’s Law
Gas Temperature vs. Gas Volume
T/V = k
T1V2 = T2V1 (Temp in Kelvin!!!)
Direct variation: graph is a straight line
Charles’s Law
As temperature
increases, volume
increases
Absolute zero can be
determined by
determining T when
volume is zero.
25
COMBINED GAS LAW
This law combines Boyle’s, Amonton’s and Charles’s
Laws into one law.
It allows you to do calculations for situations in
which only the amount of gas is constant
P1V1 = P2V2
P1T2 = P2T1
V1T2 = V2T1
P1V1T2 = P2V2T1
If you remember only this one equation – you should
be able to derive all 3 of the gas laws!
Law of Combining Volumes:
Gay-Lussac:
Gas volumes during a chemical reaction are
proportional to the coefficients of the
balanced equation.
2 H2(g) + O2(g)  2H2O(g)
2L + 1L = 2 L
Avogadro’s Hypothesis
Avogadro used Gay-Lussac’s work and
realized:
Equal volumes of gases at the same
temperature and pressure contain equal
numbers of molecules. (it doesn’t matter what
gas it is – H2, H2O, CO2, etc)
Ex: 22.4L of any gas at 273K and 1atm
contains 6.02x1023 particles (1 mole).
Avogadro’s Law
Gas Volume vs. Amount of Gas
Increasing number of molecules will increase
collisions and will increase volume if pressure is
held constant
qualitatively: n ↑ , V ↑ or n ↓ , V ↓
P and T held constant
quantitatively:
V/n = k
V1n2 = V2n1
Avogadro’s Law
Gas Volume vs. Amount of Gas
Rearranging the equation:
V1n2 = V2n1
𝑽𝟏
𝑽𝟐
=
𝒏𝟏
𝒏𝟐
So volume and mole ratios are equivalent to one
another.
Ideal Gas Law
o
o
o
o
o
combines all of the above into one equation or
relationship
PV = nRT
P is pressure
V is volume
n is the number of moles of gas
T is the temperature in KELVIN
R is the universal gas constant
Value of the Gas Constant (R)
♦
PV
(1.00 atm)(22.4 L)
L atm
R=
=
= 0.0821
nT (1.00 mole)(273 K)
mole K
other values of R
1.987 cal/mol K
8.314 J/mol K
8.314 m3 Pa/mol K
62.36 L torr/mol K
• Units must cancel when using this equation!
32
Other Applications of the Ideal
Gas Law
The ideal gas equation can be stated in other
ways incorporating other variables while still
keeping the same general relationship
𝑔𝑅𝑇
𝑃𝑉 =
𝑚𝑚
𝑚𝑚𝑃
𝐷=
𝑅𝑇
g = grams
D = density
mm = molar mass
van der Waals Equation
(Ideal vs. Real Gases)
Corrects the ideal gas equation for the "problems" of
real gases

P


n 2a 
+ 2  V - nb  = n R T
V 
𝑛2 𝑎
𝑉2
Real gases have attractions between molecules –
corrects
for this.
Real gas molecules have an actual volume – nb corrects for
this.
your textbook has a chart of van der Waals constants
(a and b) for several common real gases on page 412
Dalton's Law of Partial Pressure
Total number of collisions is based on total number of
molecules. Collisions from one kind of gas molecule
are based only on that kind of molecule.
The total pressure of a mixture of gases is the sum of
the pressures of each individual gas (each gas is said to
have a partial pressure)
Ptot = P1 + P2 + P3 + …..
Dalton’s Law Application #1
Dalton's Law can be stated in a slightly different
way emphasizing one component of the gas
mixture
 ngas 1 
Pgas 1 = 
Ptotal

 ntotal 
 ngas 1 
 ntotal 


the ratio
is called the "mole fraction" of the
gas and is symbolized by Xgas 1
substituting in the above equation we get:
Pgas 1 = (Xgas 1) ( Ptotal )
this works because the total pressure depends on
the total moles of all the gases
36
Dalton’s Law Application #2
Dalton’s Law is especially useful when
collecting a gas by water displacement
1. A gas collected by water displacement will have
some water vapor mixed in with the gas
2. Since we want only the pressure of the gas:
Ptot = Pgas + PH2O  Pgas = Ptot – PH2O
3. Values for water vapor pressure are in Appendix
B (page 1058) of your text
Graham's Law
Related to the rate at which gases:
diffuse (spread to fill a volume)
effuse (move through a small opening in their container)
Lighter particles (low MM)  move faster!
most often stated as:
rategas 1
=
rategas 2
can also use density:
rategas 1
=
rategas 2
molar massgas 2
molar massgas 1
densitygas 2
densitygas 1
Root-mean-square (rms) speed
The speed (velocity) of molecules with
exactly the average kinetic energy
KE= ½ mv2
Some molecules in a gas sample move faster
Some molecules in a gas move slower
rms speed is close to the average speed
Root mean square (rms) speed (symbolized by )
 =
3RT
molar mass
kg  m 2
use R value of 8.314 J/mol-K (J=
)
2
s
T is in Kelvin
and molar mass MUST be in kg
rms speed () decreases with increasing molar
mass (heavier particles move slower!)
40