Chapter 5!
Gases!
5.1 Pressure!
•  Force = mass x acceleration(F = ma)!
•  SI unit of force: Newton (N)!
•  Pressure = Force / Area!
•  SI unit of pressure: Pascal (Pa)!
Ex. 5.1 A The Units of Force!
•  Let s say that you (with your mass of 68 kg)
are on the moon, where the acceleration
due to gravity is about 1.6 m/s2. !
•  What force would you exert on a scale
( how much would you weigh ) in Newtons
(N) and in pounds?!
(1.00 lb = 4.47 N)!
Ex. 5.1 B The Units of Pressure!
•  Let s say that someone is wearing high
heels with a total area (for both heels) of 1
x 10-4 m2. The force is 670 N. Calculate
the pressure that she exerts.!
•  What would the pressure be if she wore
tennis shoes, total area = 0.035 m2?!
Pressure Units!
•  Air exerts pressure.!
•  Pascals are ridiculously small for
expressing air pressure.!
!!
!1 atm = 760 mm Hg = 760 torr !
!= 29.92 in Hg = 14.7 lb/in2 (psi) !
!= 101325 Pa = 101.325 kPa !
•  Atm - atmosphere!
•  Pa = pascal!
!
Ex. 5.1 C Interconverting the
Units of Pressure!
•  The pressure exerted by a gas is
measured to be 0.985 atm. Convert
this pressure to torr and pascals.!
5.2 Boyle s, Charles , and
Avogadro s Laws!
•  Boyle s Law - the pressure and volume of
a gas are inversely related at constant
temperature.!
•  As pressure goes up, volume goes down;
as pressure goes down, volume goes up!
!
!P V#
!
#
#V P!
5.2 Boyle s Law!
Ex. 5.2 A Boyle s Law!
•  A gas which has a pressure of 1.3
atm occupies a volume of 27 L. What
volume will the gas occupy if the
pressure is increased to 3.9 atm?!
!
!
!
(when a factor is not mentioned in a problem, like temperature, !
assume it is held constant)!
Charles Law!
•  At constant pressure, the volume and temperature of a
gas are directly proportional.!
!
•  As temperature goes up, volume goes up; as
temperature goes down, volume goes down!
!
•  Temperature in Kelvins!!
!T V
#
#
#T V!
Charles Law!
Charles Law!
Charles Law!
Ex. 5.2 C Charles Law!
•  A gas at 30.0OC and 1.00 atm
occupies a volume of 0.842 L. What
volume will the gas occupy at 60.0OC
and 1.00 atm?!
Gay-Lussac s Law!
•At constant volume, when temperature
goes up, pressure goes up; when
temperature goes down, pressure
goes down!
•At constant volume, temperature and
pressure are directly proportional!
!
! !T P
# # #T P!
!
Gay-Lussac s Law!
Gay-Lussac s Law!
•  A sample of gas is initially in a sealed
flask at 50.0°C and 0.50 atm. What is
the pressure when this gas when the
temperature is 78.0°C?!
You can combine all three laws into one
problem (combined gas law).
!
P1V1 P2V2
=
T1
T2
A gas has a volume of 2.35 L and a
pressure of 1.98 atm at 25°C? What is the
volume at STP?!
Avogadro s Law!
•  For a gas at constant T and P, the
volume is directly proportional to the
number of moles of gas (n).!
!
! !
!nV !
!nV!
Ex. 5.2 D Avogadro s Law!
•  A 5.20 L sample at 18.0OC and 2.00
atm pressure contains 0.436 moles of
a gas. If we add an additional 1.27
moles of the gas at the same
temperature and pressure, what will
be the total volume occupied by the
gas?!
5.3 The Ideal Gas Law!
•  Combination of Boyle s, Charles , and
Avogadro s Laws!
!
!
!!
!
!
!PV=nRT!
•  Units of P, V, n, T have to all agree with
units in R (the ideal gas law constant)!
!
!
!R = 0.0821( L atm)/(mol K)!
Ex. 5.3 A Ideal Gas Law!
•  A sample containing 0.614 moles of a
gas at 12.0OC occupies a volume of
12.9 L. What pressure does the gas
exert?!
Ex. 5.3 B Practice with Gas
Laws!
•  A sample of methane gas (CH4) at
0.848 atm and 4.0OC occupies a
volume of 7.0 L. What volume will the
gas occupy if the pressure is
increased to 1.52 atm and the
temperature increased to 11.0OC?!
Ex. 5.3 C More Practice with
the Gas Laws!
•  A 1.6 gram sample of a gas at 104OC
would occupy a volume of 6.8 L at a
pressure of 270 mm Hg. What is the
molar mass of the gas?!
5.4 Gas Stoichiometry!
•  STP - Standard Temperature and Pressure!
!!
!
!
! 0OC and 1.000 atm!
!
•  1 mole of any gas occupies 22.4 L at STP !
!
!-quick conversion between moles !
! and volume of a gas!!
Ex. 5.4 A The Ideal Gas Law
and STP!
•  What volume will 1.18 moles of O2
occupy at STP?!
Ex. 5.4 B Reactions and the
Ideal Gas Law!
•  A sample containing 15.0 g of dry ice (CO2(s)) is
put into a balloon and allowed to sublime
according to the following equation: !
!
!
!
!CO2(s)  CO2(g). !
!
How big will the balloon be (i.e., what is the volume
of the balloon), at 22.0OC and 1.04 atm, after all of
the dry ice has sublimed?!
Ex. 5.4 C Practice with the
Ideal Gas Law!
•  0.500 L of H2(g) are reacted with
0.600 L of O2(g) at STP according to
the equation below. !
2H2 (g) + O 2 ( g) " 2H 2O(g)
What volume will the H2O occupy at
1.00 atm and 350OC?!
Density relationship derived.!
Ex. 5.4 D Density and Molar
Mass!
•  A gas at 34.0OC and 1.75 atm has a
density of 3.40 g/L. Calculate the
molar mass of the gas.!
5.5 Dalton s Law of Partial
Pressures!
•  For a mixture of gases in a container, the total
pressure is the sum of the pressures that each
gas would exert if it were alone.!
!
!!
!
!Ptotal = P1 + P2 + P3 + …!
!
!Ptotal = (n1 + n2 + n3 + …)(RT/V)!
!
•  Key problem solving strategy: use the IGL (Ideal
Gas Law) to interconvert between pressure and
moles of each gas.!
Ex. 5.5 A Partial Pressure!
•  A volume of 2.0 L of He at 46OC and
1.2 atm pressure was added to a
(metal) vessel that contained 4.5 L of
N2 at STP. What is the total pressure
and partial pressure of each gas at
STP after the He is added?!
Note that the volume is constant.!
Mole fraction!
•  Once you have either the number of
moles OR the pressure of all
components of your system, you can
calculate the mole fraction of each
component.!
ni
Pi
"i =
=
ntotal Ptotal
Ex. 5.5 B Mole Fraction and
Partial Pressure!
a)  Calculate the number of moles of N2
and He present in the previous
example (5.5 A).!
b)  Calculate the mole fractions of N2
and He given the following data
from Example 5.5 A.!
i.  Mole data!
ii.  Pressure data!
Ex. 5.5 C Vapor Pressure!
•  The vapor pressure of water in air at
28OC is 28.3 torr. Calculate the mole
fraction of water in a sample of air at
28OC and 1.03 atm pressure.!
5.6 Kinetic Molecular Theory of
Gases!
1.  The volume of the individual particles of
a gas can be assumed to be negligible.!
2.  The particles are in constant motion. The
collisions of the particles with the walls of
the container are the cause of the
pressure exerted by the gas.!
3.  The particles are assumed to exert no
forces on each other.!
4. The average kinetic energy of a
collection of gas particles is directly
proportional to the Kelvin temperature
of the gas.!
!
The KMT is a model - tries to explain
ideal gas behavior.!
•  Temperature – proportional to the
average kinetic energy of a gas (not a
measure of heat)!
– Linear relationship!
!
•  Root mean square velocity - average
velocity of gas particles!
•  Remember: vrms is an average!!
•  Gas particles collide with each other and
exchange energy after traveling a very short
distance (mean free path = 10-8 m)!
•  Particles are speeding up and slowing down all
the time - there is a large range of velocities in a
container of gas.!
•  There s a wider range at higher temp.!
Maxwell Boltzmann Distribution!
•  Curve that shows speed distribtution in
gases at certain temperatures (K.E)!
K.E = ½ mv2 Maxwell Boltzmann Distribution!
•  Temp Dependence!
More varied speeds
at higher temps
Maxwell Boltzmann Distribution!
•  Constant Temp!
To have the
same K.E.
must be moving
at different
speeds
5.7 Effusion and Diffusion!
•  Diffusion - mixing of gases.!
•  Effusion - gas moves through a small
opening into an evacuated chamber.!
Ex. 5.7 Graham s Law of
Effusion!
•  Which molecule effuses faster He or
NO2 ?!
Diffusion !
•  Gases travel very rapidly - hundreds
of meters per second.!
•  They mix rather slowly, because gas
particles don t travel in straight lines.!
When Gases Aren t Ideal!
•  Our IGL assumptions were!
–  that the gas particles don t take up space (they do)!
–  Gas particles don t interact with each other (they do)!
!
!
!
•  When these assumptions fail, we have to correct the P and V.!
Volume Correction!
Because gas molecules do take up space,
the free volume of the container is not as
large as it would be if it were empty.!
!
High pressure (molecules are close together and
collide with each other more than container) :: not
normal on earth!
!
Volume Correction!
Because gas molecules do take up space, !
!
!
!
!
High pressure!
Pressure Correction!
Because gas molecules can interact with
each other, they do not collide with the walls
of the container as much as we might think.!
!
•  Low temperature (molecules moving
slowly and interact with each other in
proximity) :: start to condense!
Pressure Correction!
Gas molecules can interact with each other!
!
!
!
Low T!
!
Condensation!
Real Gas Behavior!
Which gas is the
most polar?!
A
B
PV/RT
ideal
C
Pressure
Real Gas Deviations!
Low P!
-attractions!
matter!
!
High P!
-volume
matters !