Transcript AP CHEMISTRY Chapter 5 Gases Slides with gray backgrounds are not tested on the AP test.

AP CHEMISTRY
Chapter 5
Gases
Slides with gray backgrounds are not tested on
the AP test.
Gas Pressure
This is a schematic diagram showing gas molecules (purple) in
a container. The molecules are constantly moving in random
directions. When a molecule hits the container wall (green), it
exerts a tiny force on the wall. The sum of these tiny forces,
divided by the interior surface area of the container, is the
pressure. (Longer arrows indicate higher velocities, shorter
arrows indicate lower velocities)
Barometer invented by
Evangelista Torricelli
in 1643; uses the
height of a column
of mercury to
measure gas
pressure (especially
atmospheric)
The Manometer
a device for measuring the pressure
of a gas in a container
The pressure of the gas is given by h
[the difference in mercury levels] in
units of torr (equivalent to mm Hg).
Open-tube
manometer
a) Gas pressure = atmospheric pressure – h
b) Gas pressure = atmospheric pressure + h
1 mm of Hg = 1 torr
760.00 mm Hg
=
760.00 torr
=
1.00 atm
=
101.325 kPa
Know
these!
kPa is not
tested on the
AP exam
SI unit of pressure is N/m2 or
Pascal (Pa)
Memory Trick: We Boyle
Peas and Vegetables
Boyle’s Law
1st quantitative study of gases, 1600s.
Pressure and volume are inversely
related.
P1 = V2
P2 V1
P1V1= P2V2
Ideal gas- gas that obeys Boyle’s law
An ideal gas is expected to
have a constant value of PV,
as shown by the dotted line.
CO2 shows the largest
change in PV, and this
change is actually quite
small.
Charles’ Law 1700’s
-volume of a gas is directly
proportional to Kelvin
temperature
V1 = V2 Temp must be in Kelvin!!!!!!
T1 T2
Memory Trick: Charlie Brown’s
Xmas is on TV
0
The volume of a gas at absolute zero is
zero.
Avogadro’s Law
-equal volumes of gases at
the same temperature and
pressure contain the same # of
particles
-for a gas at constant temp.
and pressure, the volume is
directly proportional to the # of
moles of gas
Gay-Lussac’s Law
Pressure of a gas is directly proportional
to Kelvin temperature
P1 = P2 Temp must be in Kelvin!!!!!!
T1 T2
“GayLe drives a
PT cruiser”
Combined Gas Law
P1V1 = P2V2
T1
T2
“Peas and Vegetables on the Table”
This can be used to come up with Boyle’s, Charles’,
or Gay-Lussac’s Law. Simply cover up the factors
that are constant.
Ideal Gas Law
Combining Boyle’s, Charles’,
and Avogadro’s laws we get
PV= nRT.
R = 0.08206 (Latm)/(Kmol)
(proportionality constant)
Most gases behave ideally at
pressures less than 1 atm.
We can use the ideal gas law for all gas
law problems by putting changing variables
on one side and the constant on the other.
Ex. If P&V change w/ others constant:
P1V1 = nRT and P2V2 = nRT
so P1V1 = P2V2
If V&T change with others constant:
V1 = nR and V2 = nR so V1 = V2
T1 P
T2 P
T1 T2
The gas pressure inside an aerosol can is
1.5 atm at 25oC. Assuming that the gas is
ideal, what would the pressure be if the can
were heated to 452oC?
P1=1.5 atm
P2 = ?
P1
T1

P2
T2
P2 
T1 = 25oC+273 = 298K
T2 = 452oC + 273 = 725K
P1T 2
T1
P2 
(1.5atm)(7 25K)
P2 = 3.6 atm
298K
A quantity of helium gas occupies a volume
of 16.5 L at 78°C and 45.6 atm. What is the
volume at STP?
P1 = 45.6 atm V1 = 16.5L T1 = 78°C + 273 = 351K
P2 = 1 atm
V2 = ?
T2 = 0°C + 273 = 273K
P1V1
T1
V2 

P2V 2
T2
V2 
P1V1T 2
T1 P2
(4 5 . 6 ) (16.5)(273 )
(351)(1)
V2 = 585L
Many gases are shipped in high-pressure
containers. If a steel tank whose volume is 50.0L
contains O2 gas at a total pressure of 1550 kPa at
23oC, what mass of oxygen does it contain?
P = 1550 kPa/101.3 = 15.3atm V = 50.0L n = ?
R = 0.08206(Latm)/(Kmol) T = 23oC + 273 = 296K
PV = nRT
(15.3)(50.0) = n (0.08206)(296)
n = 31.5mol O2
31.5 mol O 2

32.0 g O 2
1 mol O 2

1010 g O2
Molar Volume = 22.42 L of an
ideal gas at STP
(Some gases behave more
ideally than others.)
STP = 0oC and 1 atm
CaH2 reacts with H2O to produce H2 gas.
CaH2(s) + 2H2O(l)  2H2(g) + Ca2+(aq) + 2OH-(aq)
Assuming complete rxn with water, how many grams of
CaH2 are required to fill a balloon to a total pressure of
1.12 atm at 15oC if its volume is 5.50 L?
P = 1.12 atm V= 5.50 L T= 15oC + 273 = 288K
n= ? R = 0.08206 Latm/Kmol
PV=nRT (1.12)(5.50)=n(0.08206)288
n = 0.2606 mol H2
0.2606 mol H2 1 mol CaH2 42.10g CaH2
2 mol H2
1 mol CaH2
= 5.49g CaH2
How many liters of N2 are required to
produce 115 g of NH3 at STP?
N2 + 3H2  2NH3
115g NH3 1 mol NH3 1 mol N2 22.42L N2
17.04g NH3 2 mol NH3 1 mol N2
= 75.7 L N2
Molecular Weight and Density of a Gas
n = mass
so P = mRT
MW
V(MW)
Since m/V = density (g/L),
P = dRT
MW
MW = dRT
P
“Molecular Weight Kitty Cat”
Meow = dirt/pee
Calculate the molar mass of a gas if 0.608g
occupies 750 mL at 385 mm Hg and 35oC.
V = 750 mL = 0.75L P = 385/760 = 0.507 atm
T = 35oC + 273 = 308 K
d = 0.608g/0.75L = 0.811g/L
MW = dRT/P
MW = (0.811)(0.08206)(308) = 40.4
0.507
g/mol
Dalton’s Law of Partial Pressures
For a mixture of gases in a container, the
total pressure exerted is the sum of the
pressures that each gas would exert if it were
alone.
Ptot = P1 + P2 + P3 + …
Ptot = n1RT + n2RT + n3RT +…
V
V
V
Ptot = ntotal (RT)
(It doesn’t matter what the gas is.)
V
Mole Fraction
-the ratio of the number of
moles of a given component in a
mixture to the total number of
moles in the mixture.
 is used to symbolize mole
fraction.
1 =
n1
n1 + n2 + n3 + ...
The partial pressure of a
particular component of a
gaseous mixture is the mole
fraction of that component times
the total pressure.
P1 = 1 (Ptotal)
When gases are collected over
water, we must adjust for the
pressure of the water vapor.
PH2O + Pgas = Ptotal
If a 0.20 L sample of O2 at 0oC and 1.0 atm pressure
and a 0.10 L sample of N2 at 0oC and 2.0 atm
pressure are both placed in a 0.40 L container at 0oC,
what is the total pressure in the container?
P1V1=P2V2
1.0(0.20) = P2 (0.40) P2 = 0.50 atm = PO2
(2.0)(0.10) = P2 (0.40) P2 = 0.50 atm = PN2
PO2 + PN2 = Ptotal
0.50 + 0.50 = 1.00 atm
Kinetic Molecular Theory of
Gases
-a simple model that attempts to
explain properties of an ideal gas
Gases consist of particles which have the
following properties:
1. The particles are so small compared to the
distances between them that the volume of the
individual particles can be assumed to be
negligible (zero).
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; they are assumed neither
to attract nor to repel each other.
4. The average kinetic energy of a collection
of gas particles is assumed to be directly
proportional to the Kelvin temperature of the
gas.
-real gases don’t conform to these
assumptions!!!
Kelvin temp. is an index of the
random motions of the particles of a
gas, with higher temp. meaning
greater motion.
Since we are working
with energy, we need the
energy R, not the gas R.
Temp must be in Kelvin.
KE (avg) = 3/2 RT
Formula is not on AP exam.
R = 8.314 J/K mol
Units of KE are J/mol
KE = 1/2 mv2
Remember that mass
has to be in kg and
velocity in m/s!
Real gases have many collisions
between particles. The average
distance a particle travels between
collisions in a particular gas sample
is called the mean free path. These
collisions produce a huge variation
in velocities. As temperature
increases, the range of velocities is
greater.
Path of One
Particle in a
Gas
A Plot of the Relative
Number of O2
Molecules That Have a
Given Velocity at STP
A Plot of the Relative
Number of N2
Molecules That Have a
Given Velocity at Three
Temperatures
This is called a
Boltzmann
Distribution
graph
Effusion and Diffusion
Diffusion- mixing of gases
Effusion- the passage of a gas
through a tiny orifice into an
evacuated chamber
The Effusion of a Gas into an Evacuated Chamber
Graham’s Law of Effusion
-The rate of effusion of a gas is
inversely proportional to the square root
of the mass of its particles.
____
Rate of effusion for gas 1 = MW2
Rate of effusion for gas 2
 MW1
MW1 and MW2 represent the molar
masses of the gases. These calculations
are not tested on
the AP test.
-lighter gases effuse &
diffuse faster than heavier gases
HCl(g) and NH3(g) Meet in a Tube
Because NH3 has a lower molar mass than HCl,
it moves faster and farther in the tube. Solid
NH4Cl is formed closer to the HCl.
Real gases
*No gas exactly follows the ideal
gas law.
*A real gas exhibits behavior
closest to ideal behavior at low
pressures and high temperatures.
Students also behave most ideally under these
conditions. (Summer vacation!)
At high temperatures, there is
less interaction between particles
because they are moving too fast.
At high concentrations, gases
have much greater attractive forces
between particles. This causes
particles to hit the walls of the
container with less force (producing
less pressure than expected).
At high pressure (small
volume), the volume of the particles
becomes significant, so that the
volume available to the gas is
significantly less than the container
volume.
Attractive forces are greatest for
large, complex molecules and polar
molecules.
Volume Taken up by Gas Particles
We can use the Van der Waals
equation to adjust for departures
from ideal conditions.
PV = nRT becomes:
[Pobs + a(n/V)2]V-nb = nRT
corrected
pressure
corrected
volume You don’t need
to memorize
this!