gases. the properties of gases only 4 quantities are needed to define the state of a gas:
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GASESGASES
The Properties of GasesThe Properties of Gases
Only 4 quantities are needed to Only 4 quantities are needed to
define the define the state of a gasstate of a gas: :
a) the a) the quantityquantity of the gas, n (in moles) of the gas, n (in moles)
b) the b) the temperaturetemperature of the gas, T (in of the gas, T (in
KELVIN) KELVIN)
c) the c) the volumevolume of the gas, V (in liters) of the gas, V (in liters)
d) the d) the pressurepressure of the gas, P (in of the gas, P (in
atmospheres)atmospheres)
A gas uniformly fills any container, A gas uniformly fills any container,
is easily compressed & mixes is easily compressed & mixes
completely with any other gas.completely with any other gas.
Gas PressureGas Pressure
A measure of the force that a gas A measure of the force that a gas
exerts on its container. exerts on its container.
Force is the physical quantity that Force is the physical quantity that
interferes with inertia. Gravity is interferes with inertia. Gravity is the the
force responsible for weight.force responsible for weight.
Newton’s 2nd LawNewton’s 2nd Law
Force = mass x acceleration Force = mass x acceleration
N = kg x m/sN = kg x m/s22
PressurePressure
Force / unit areaForce / unit area
N / mN / m22
Barometer -Barometer -
invented by invented by
Evangelista Torricelli Evangelista Torricelli
in 1643; uses the in 1643; uses the
height of a column height of a column
of mercury to of mercury to
measure gas measure gas
pressure (especially pressure (especially
atmospheric)atmospheric)
1 mm of Hg = 1 torr1 mm of Hg = 1 torr
760.00 mm Hg 760.00 mm Hg
= =
760.00 torr 760.00 torr
==
1.00 atm 1.00 atm
= =
101.325 kPa ≈ 10101.325 kPa ≈ 1055 Pa Pa
At sea level, all of the previous At sea level, all of the previous define STANDARD PRESSURE. define STANDARD PRESSURE.
The SI unit of pressure is the The SI unit of pressure is the Pascal Pascal
(Blaise Pascal).(Blaise Pascal).
1 Pa = 1 N / m1 Pa = 1 N / m22
The ManometerThe Manometer
a device for measuring the pressure a device for measuring the pressure
of a gas in a container of a gas in a container
The pressure of the gas is given by h The pressure of the gas is given by h
[the difference in mercury levels] in [the difference in mercury levels] in
units of torr (equivalent to mm Hg).units of torr (equivalent to mm Hg).
a) Gas pressure = atmospheric pressure a) Gas pressure = atmospheric pressure – h– h
b) Gas pressure = atmospheric pressure b) Gas pressure = atmospheric pressure + h+ h
Exercise 1Exercise 1 Pressure Conversions Pressure Conversions
The pressure of a gas is The pressure of a gas is measured measured
as 49 torr. as 49 torr.
Represent this pressure in both Represent this pressure in both
atmospheres and pascals.atmospheres and pascals.
SolutionSolution
6.4 x 106.4 x 10-2-2 atm atm
6.5 x 106.5 x 1033 Pa Pa
ExerciseExercise
Rank the following pressures in Rank the following pressures in
decreasing order of magnitude decreasing order of magnitude
(largest first, smallest last) (largest first, smallest last)
75 kPa 300. torr 75 kPa 300. torr
0.60 atm 350. mm Hg.0.60 atm 350. mm Hg.
GAS LAWSGAS LAWS
THE EXPERIMENTAL BASISTHE EXPERIMENTAL BASIS
BOYLE’S LAW – BOYLE’S LAW – “father of chemistry”“father of chemistry”
The volume of a confined gas is The volume of a confined gas is inversely inversely
proportional to the pressure exerted proportional to the pressure exerted on on
the gas. the gas.
ALL GASES BEHAVE IN THIS MANNER!ALL GASES BEHAVE IN THIS MANNER!
Robert Boyle was Robert Boyle was
an Irish chemist. an Irish chemist.
He studied P V He studied P V
relationships relationships using using
a J-tube set up in a J-tube set up in
the multi-story the multi-story
entryway of his entryway of his
home.home.
P:1/VP:1/Vplot = straight lineplot = straight line
Pressure and volume are Pressure and volume are inverselyinversely
proportional.proportional.
Volume ↑ pressure Volume ↑ pressure (at constant temperature)(at constant temperature)
The converse is also true.The converse is also true.
For a given quantity of a gas at For a given quantity of a gas at
constant temperature, the constant temperature, the product product
of pressure and volume is a of pressure and volume is a
constant. constant.
PV = kPV = k
Therefore, Therefore,
which is the equation for a straight which is the equation for a straight
line of the type y = mx + b line of the type y = mx + b
where m = slope, and b is the where m = slope, and b is the
y-intercept.y-intercept.
Pk
P
kV
1
In this case, In this case,
y = V, x = 1/P y = V, x = 1/P
and b = 0. and b = 0.
Check out the plot Check out the plot
on the left (b). on the left (b).
The data Boyle The data Boyle
collected is collected is graphed graphed
on (a) above.on (a) above.
PP11VV11 = P = P22VV22
is the easiest form of Boyle’s law tois the easiest form of Boyle’s law to
MEMORIZE !MEMORIZE !
Boyle’s Law has been tested for Boyle’s Law has been tested for over three centuries. It holds true over three centuries. It holds true only at low pressuresonly at low pressures. .
A plot of PV A plot of PV
versus P for versus P for
several gases at several gases at
pressures below pressures below
1 atm is pictured 1 atm is pictured to the left.to the left.
An An idealideal gas is gas is
expected to expected to
have a constant have a constant
value of PV, as value of PV, as
shown by the shown by the
dotted line.dotted line.
COCO22 shows the shows the
largest change largest change in in
PV, and this PV, and this
change is change is
actually quite actually quite
small.small.
PV changes PV changes
from about from about
22.39 L·atm 22.39 L·atm at at
0.25 atm to 0.25 atm to
22.26 L·atm 22.26 L·atm at at
1.00 atm.1.00 atm.
Thus, Boyle’s Law is a good Thus, Boyle’s Law is a good
approximation at these approximation at these relatively relatively
low pressures.low pressures.
Exercise 2Exercise 2 Boyle’s Boyle’s Law ILaw I
Sulfur dioxide (SOSulfur dioxide (SO22), a gas that ), a gas that
plays a central role in the plays a central role in the formation formation
of acid rain, is found in the of acid rain, is found in the exhaust exhaust
of automobiles and power of automobiles and power plants.plants.
Consider a 1.53- L sample of Consider a 1.53- L sample of
gaseous SOgaseous SO22 at a pressure of 5.6 x at a pressure of 5.6 x
101033 Pa. Pa.
If the pressure is changed to 1.5 x If the pressure is changed to 1.5 x
101044 Pa at a constant temperature, Pa at a constant temperature,
what will be the new volume of the what will be the new volume of the
gas ?gas ?
SolutionSolution
0.57 L0.57 L
Exercise 3Exercise 3 Boyle’s Boyle’s Law IILaw II
In a study to see how closely In a study to see how closely
gaseous ammonia obeys Boyle’s gaseous ammonia obeys Boyle’s
law, several volume law, several volume measurements measurements
were made at various pressures, were made at various pressures,
using 1.0 mol NHusing 1.0 mol NH33 gas at a gas at a
temperature of 0º C.temperature of 0º C.
Using the results listed below, calculate Using the results listed below, calculate the the
Boyle’s law constant for NHBoyle’s law constant for NH33 at the various at the various
pressures.pressures.
Experiment Experiment Pressure (atm) Pressure (atm) Volume (L)Volume (L)
11 0.1300 0.1300 172.1 172.1
22 0.2500 0.2500 89.28 89.28
33 0.3000 0.3000 74.35 74.35
44 0.5000 0.5000 44.49 44.49
55 0.7500 0.7500 29.55 29.55
66 1.000 1.000 22.08 22.08
SolutionsSolutions
experiment 1 is 22.37experiment 1 is 22.37
experiment 2 is 22.32experiment 2 is 22.32
experiment 3 is 22.31experiment 3 is 22.31
experiment 4 is 22.25experiment 4 is 22.25
experiment 5 is 22.16experiment 5 is 22.16
experiment 6 is 22.08experiment 6 is 22.08
PLOT the values of PLOT the values of
PV for the previous PV for the previous
six experiments. six experiments.
Extrapolate it back Extrapolate it back
to see what PV to see what PV
equals at 0.00 atm equals at 0.00 atm
pressure.pressure.
Compare it to Compare it to the PV vs. P the PV vs. P graph at the graph at the right.right.
What is the y-intercept for all What is the y-intercept for all of these gases?of these gases?
Remember, gases behave most Remember, gases behave most
ideally at low pressures. ideally at low pressures.
You can’t get a pressure lower You can’t get a pressure lower than than
0.00 atm!0.00 atm!
Charles’ LawCharles’ Law
If a given quantity of gas is held If a given quantity of gas is held at at
a constant pressure, then its a constant pressure, then its
volume is directly proportional to volume is directly proportional to
the absolute temperature. the absolute temperature.
Must use KELVIN !Must use KELVIN !
Jacques Charles was a French Jacques Charles was a French
physicist and the first person to physicist and the first person to fill a fill a
hot “air” balloon with hydrogen hot “air” balloon with hydrogen gas gas
and made the first solo balloon and made the first solo balloon
flight!flight!
V:T plot = straight lineV:T plot = straight line
VV11TT22 = V = V22TT11
Temperature ↑ Volume ↑ Temperature ↑ Volume ↑
at constant pressureat constant pressure
This figure shows the plots of V vs. T This figure shows the plots of V vs. T (Celcius) for several gases. (Celcius) for several gases.
The solid lines The solid lines represent represent experimental experimental measurements on measurements on gases. The gases. The
dashed dashed lines represent lines represent extrapolation of extrapolation of the data into the data into regions where regions where these gases these gases
would would become liquids or become liquids or solids.solids.
Note that the samples Note that the samples of of
the various gases the various gases
contain different contain different
numbers of moles.numbers of moles.
What is the What is the
temperature when temperature when
the volume the volume extrapolates to zeroextrapolates to zero??
Exercise 4Exercise 4 Charles’s Charles’s LawLaw
A sample of gas at 15º C and 1 A sample of gas at 15º C and 1 atm atm
has a volume of 2.58 L. has a volume of 2.58 L.
What volume will this gas What volume will this gas occupy at occupy at
38º C and 1 atm?38º C and 1 atm?
SolutionSolution
2.79 L2.79 L
Gay-Lussac’S Law Gay-Lussac’S Law of Combining of Combining VolumesVolumesVolumes of gases always Volumes of gases always
combine combine
with one another in the ratio of with one another in the ratio of
small whole numbers, as long as small whole numbers, as long as
volumes are measured at the volumes are measured at the same same
T and P.T and P.
PP11TT22 = P = P22TT11
Avogadro’s HypothesisAvogadro’s Hypothesis
Equal volumes of gases under Equal volumes of gases under the the
same conditions of temperature same conditions of temperature and and
pressure contain equal pressure contain equal numbers of numbers of
molecules.molecules.
Avogadro’s LawAvogadro’s Law
The volume of a gas, at a given The volume of a gas, at a given
temperature and pressure, is temperature and pressure, is
directly proportional to the quantity directly proportional to the quantity
of gas.of gas.
V:nV:n
n n ↑↑ Volume Volume ↑↑
at constant T & Pat constant T & P
Here’s an easy way to Here’s an easy way to MEMORIZE all this….MEMORIZE all this….
Start with the combined gas Start with the combined gas law: law:
PP11VV11TT22 = P = P22VV22TT11
Memorize it.Memorize it.
Next,Next,
put the guy’s names in put the guy’s names in alphabetical alphabetical
order. order.
Boyle’s uses the first 2 variables, Boyle’s uses the first 2 variables,
Charles’ the second 2 variables & Charles’ the second 2 variables &
Gay-Lussac’s the remaining Gay-Lussac’s the remaining
combination of variables. What combination of variables. What
ever doesn’t appear in the ever doesn’t appear in the formula, formula,
is being held CONSTANT!is being held CONSTANT!
These balloons These balloons
each hold 1.0 L of each hold 1.0 L of
gas at 25gas at 25°°C and 1 C and 1
atm. Each balloon atm. Each balloon
contains 0.041 mol contains 0.041 mol
of gas, or 2.5 x 10of gas, or 2.5 x 102222
molecules.molecules.
Exercise 5Exercise 5 Avogadro’s Law Avogadro’s Law
Suppose we have a 12.2-L sample Suppose we have a 12.2-L sample
containing 0.50 mol oxygen gas containing 0.50 mol oxygen gas
(O(O22) at a pressure of 1 atm and a ) at a pressure of 1 atm and a
temperature of 25º C. temperature of 25º C.
If all this OIf all this O22 were converted to were converted to
ozone (Oozone (O33) at the same ) at the same temperature temperature
and pressure, what would be and pressure, what would be the the
volume of the ozone ?volume of the ozone ?
SolutionSolution
8.1 L 8.1 L
The Ideal Gas LawThe Ideal Gas Law
Four quantities describe the Four quantities describe the state of state of
a gas: a gas:
pressure, volume, temperature, pressure, volume, temperature, and and
# of moles (quantity).# of moles (quantity).
Combine all 3 laws…Combine all 3 laws…
V : V : nT nT
PP
Replace the : with a constant, R, Replace the : with a constant, R, and and
you get:you get:
PV = nRTPV = nRT
The Ideal Gas Law!The Ideal Gas Law!It is an Equation of State.It is an Equation of State.
R = 0.8206 L R = 0.8206 L •• atm/mol atm/mol •• K K
Useful only at low pressures and Useful only at low pressures and high high
temperatures! Guaranteed points temperatures! Guaranteed points on on
the AP Exam!the AP Exam!
These next exercises can all be These next exercises can all be
solved with the ideal gas law. solved with the ideal gas law.
BUT, you can use another if you BUT, you can use another if you
like!like!
Exercise 6Exercise 6 Ideal Gas Law I Ideal Gas Law I
A sample of hydrogen gas (HA sample of hydrogen gas (H22) has ) has
a volume of 8.56 L at a temperature a volume of 8.56 L at a temperature
of 0º C and a pressure of 1.5 atm. of 0º C and a pressure of 1.5 atm.
Calculate the moles of HCalculate the moles of H22 molecules molecules
present in this gas sample.present in this gas sample.
SolutionSolution
0.57 mol0.57 mol
Exercise 7Exercise 7 Ideal Gas Law II Ideal Gas Law II
Suppose we have a sample of Suppose we have a sample of ammonia ammonia
gas with a volume of 3.5 L at a gas with a volume of 3.5 L at a pressure of 1.68 atm. The gas is pressure of 1.68 atm. The gas is compressed to a volume of 1.35 L at a compressed to a volume of 1.35 L at a constant temperature. constant temperature.
Use the ideal gas law to calculate the Use the ideal gas law to calculate the final pressure.final pressure.
SolutionSolution
4.4 atm4.4 atm
Exercise 8Exercise 8 Ideal Gas Law III Ideal Gas Law III
A sample of methane gas that A sample of methane gas that has a has a
volume of 3.8 L at 5º C is heated volume of 3.8 L at 5º C is heated to to
86º C at constant pressure. 86º C at constant pressure.
Calculate its new volume.Calculate its new volume.
SolutionSolution
4.9 L4.9 L
Exercise 9Exercise 9 Ideal Gas Law IV Ideal Gas Law IV
A sample of diborane gas (BA sample of diborane gas (B22HH66), ), a a
substance that bursts into flame substance that bursts into flame
when exposed to air, has a when exposed to air, has a pressure pressure
of 345 torr at a temperature of of 345 torr at a temperature of
––15º C and a volume of 3.48 L.15º C and a volume of 3.48 L.
If conditions are changed so If conditions are changed so that that
the temperature is 36º C and the temperature is 36º C and the the
pressure is 468 torr, what will pressure is 468 torr, what will be be
the volume of the sample ?the volume of the sample ?
SolutionSolution
3.07 L3.07 L
Exercise 10Exercise 10 Ideal Gas Law V Ideal Gas Law V
A sample containing 0.35 mol argon A sample containing 0.35 mol argon
gas at a temperature of 13º C and a gas at a temperature of 13º C and a
pressure of 568 torr is heated to pressure of 568 torr is heated to
56º C and a pressure of 897 torr. 56º C and a pressure of 897 torr.
Calculate the change in volume that Calculate the change in volume that
occurs.occurs.
SolutionSolution
decreases by 3 Ldecreases by 3 L
Gas StoichiometryGas Stoichiometry
Use:Use:
PV = nRT PV = nRT
to solve for the volume of one to solve for the volume of one mole mole
of gas at STP.of gas at STP.
Look familiar?Look familiar?
This is the This is the molar volumemolar volume of a gas of a gas at at
STP. Work stoichiometry problems STP. Work stoichiometry problems
using your favorite method, using your favorite method,
dimensional analysis, mole map, the dimensional analysis, mole map, the
table way…just work FAST! Use the table way…just work FAST! Use the
ideal gas law to convert quantities ideal gas law to convert quantities
that are NOT at STP.that are NOT at STP.
Exercise 11Exercise 11 Gas Stoichiometry I Gas Stoichiometry I
A sample of nitrogen gas has a A sample of nitrogen gas has a
volume of 1.75 L at STP. volume of 1.75 L at STP.
How many moles of NHow many moles of N22 are are present ?present ?
SolutionSolution
7.81 x 107.81 x 10-2-2 mol N mol N22
Exercise 12Exercise 12 Gas Stoichiometry II Gas Stoichiometry II
Quicklime (CaO) is produced by Quicklime (CaO) is produced by the the
thermal decomposition of thermal decomposition of calcium calcium
carbonate (CaCOcarbonate (CaCO33). ).
Calculate the volume of COCalculate the volume of CO22 at at STP STP
produced from the decomposition produced from the decomposition of of
152 g CaCO152 g CaCO33 by the reaction: by the reaction:
CaCOCaCO33((ss) → CaO() → CaO(ss) + CO) + CO22((gg))
SolutionSolution
34.1 L CO34.1 L CO22 at STP at STP
Exercise 13Exercise 13 Gas Stoichiometry III Gas Stoichiometry III
A sample of methane gas having a A sample of methane gas having a volume of 2.80 L at 25º C and 1.65 volume of 2.80 L at 25º C and 1.65 atm was mixed with a sample of atm was mixed with a sample of oxygen gas having a volume of oxygen gas having a volume of
35.0 L 35.0 L at 31º C and 1.25 atm. The mixture at 31º C and 1.25 atm. The mixture was then ignited to form carbon was then ignited to form carbon dioxide and water. dioxide and water.
Calculate the volume of COCalculate the volume of CO22 formed formed
at a pressure of 2.50 atm and a at a pressure of 2.50 atm and a
temperature of 125º C.temperature of 125º C.
SolutionSolution
2.47 L2.47 L
The Density of Gases The Density of Gases
d = d = m m = = P(FW) P(FW) {for ONE {for ONE V RT mole of gas}V RT mole of gas} = = FW FW 22.4 L22.4 LAND…AND… Molar Mass = FW = Molar Mass = FW = dRT dRT
PP
““Molecular Mass Kitty Molecular Mass Kitty Cat”Cat”
All good cats put dirt [dRT] over All good cats put dirt [dRT] over
their pee [P]. their pee [P].
Corny, but you’ll thank me Corny, but you’ll thank me later! later!
Just remember that densities of Just remember that densities of
gases are reported in g/L gases are reported in g/L NOTNOT
g/mL.g/mL.
What is the approximate molar What is the approximate molar mass mass
of air? _________of air? _________
The density of air is approximately The density of air is approximately _______ g/L. _______ g/L.
List 3 gases that float in air:List 3 gases that float in air:
List 3 gases that sink in air:List 3 gases that sink in air:
Exercise 14Exercise 14 Gas Density/Molar Gas Density/Molar MassMassThe density of a gas was measured The density of a gas was measured
at 1.50 atm and 27º C and found to at 1.50 atm and 27º C and found to
be 1.95 g/L. be 1.95 g/L.
Calculate the molar mass of the Calculate the molar mass of the
gas.gas.
SolutionSolution
32.0 g/mol32.0 g/mol
Gas Mixtures and Gas Mixtures and Partial PressuresPartial Pressures
The pressure of a The pressure of a
mixture of gases mixture of gases
is the sum of the is the sum of the
pressures of the pressures of the
different components different components
of the mixture:of the mixture:
PPtotaltotal = P = P11 + P + P22 + . . . P + . . . Pnn
John Dalton’s Law of Partial John Dalton’s Law of Partial
Pressures also uses the concept Pressures also uses the concept of of
mole fraction, X.mole fraction, X.
XXAA = = moles of A moles of A _ _
moles A + moles B + moles C + . moles A + moles B + moles C + . . .. .
so now, so now,
PPAA = X = XAA P Ptotaltotal
The partial pressure of each gas in a The partial pressure of each gas in a
mixture of gases in a container mixture of gases in a container
depends on the number of moles of depends on the number of moles of
that gas. The total pressure is the that gas. The total pressure is the
SUM of the partial pressures and SUM of the partial pressures and
depends on the total moles of gas depends on the total moles of gas
particles present, no matter what particles present, no matter what
they are!they are!
Exercise 15Exercise 15 Dalton’s Law I Dalton’s Law I
Mixtures of helium and oxygen Mixtures of helium and oxygen are are
used in scuba diving tanks to used in scuba diving tanks to help help
prevent “the bends.”prevent “the bends.”
For a particular dive, 46 L He at 25º C For a particular dive, 46 L He at 25º C and 1.0 atm and 12 L Oand 1.0 atm and 12 L O22 at 25º C and at 25º C and 1.0 atm were pumped into a tank with 1.0 atm were pumped into a tank with a volume of 5.0 L. a volume of 5.0 L.
Calculate the partial pressure of each Calculate the partial pressure of each gas and the total pressure in the tank gas and the total pressure in the tank at 25º C.at 25º C.
SolutionSolution
PPHeHe = 9.3 atm = 9.3 atm
PPO2O2 = 2.4 atm = 2.4 atm
PPTOTALTOTAL = 11.7 atm = 11.7 atm
Exercise 16Exercise 16 Dalton’s Law II Dalton’s Law II
The partial pressure of oxygen was The partial pressure of oxygen was
observed to be 156 torr in air with a observed to be 156 torr in air with a
total atmospheric pressure of 743 total atmospheric pressure of 743
torr. torr.
Calculate the mole fraction of OCalculate the mole fraction of O22
present.present.
SolutionSolution
0.2100.210
Exercise 17Exercise 17 Dalton’s Law III Dalton’s Law III
The mole fraction of nitrogen in the The mole fraction of nitrogen in the
air is 0.7808. air is 0.7808.
Calculate the partial pressure of NCalculate the partial pressure of N22
in air when the atmospheric in air when the atmospheric
pressure is 760. torr.pressure is 760. torr.
SolutionSolution
593 torr593 torr
Water DisplacementWater Displacement
It is common to collect a gas by It is common to collect a gas by water water
displacement, which means some of displacement, which means some of
the pressure is due to water vapor the pressure is due to water vapor
collected as collected as
the gas was the gas was
passing passing
through! through!
You must correct for this. You must correct for this.
You look up the partial pressure You look up the partial pressure due due
to water vapor by knowing the to water vapor by knowing the
temperaturetemperature..
Exercise 8Exercise 8 Gas Collection over Gas Collection over WaterWaterA sample of solid potassium A sample of solid potassium
chlorate (KClOchlorate (KClO33) was heated in a ) was heated in a
test tube (see the figure above) and test tube (see the figure above) and
decomposed by the following decomposed by the following
reaction:reaction:
2 KClO2 KClO33((ss) → 2 KCl() → 2 KCl(ss) + 3 O) + 3 O22((gg))
The oxygen produced was collected The oxygen produced was collected
by displacement of water at 22º C by displacement of water at 22º C
at a total pressure of 754 torr. The at a total pressure of 754 torr. The
volume of the gas collected was volume of the gas collected was
0.650 L, and the vapor pressure of 0.650 L, and the vapor pressure of
water at 22º C is 21 torr.water at 22º C is 21 torr.
Calculate the partial pressure of OCalculate the partial pressure of O22
in the gas collected and the mass of in the gas collected and the mass of
KClOKClO33 in the sample that was in the sample that was
decomposed.decomposed.
SolutionSolution
Partial pressure of OPartial pressure of O22 = 733 = 733 torrtorr
2.12 g KClO2.12 g KClO33
KINETIC MOLECULAR KINETIC MOLECULAR THEORY OF GASESTHEORY OF GASES
Assumptions of the Assumptions of the MODEL:MODEL:
1. All particles are in constant, 1. All particles are in constant, random, motion.random, motion.2. All collisions between particles are 2. All collisions between particles are perfectly elastic.perfectly elastic.3. The volume of the particles in a 3. The volume of the particles in a gas is negligible.gas is negligible.4. The average kinetic energy of the 4. The average kinetic energy of the molecules is its Kelvin temperature.molecules is its Kelvin temperature.
This neglects any intermolecular This neglects any intermolecular
forces as well. forces as well.
Gases expand to fill their container, Gases expand to fill their container,
solids/liquids do not.solids/liquids do not.
Gases are compressible, Gases are compressible, solids/liquids solids/liquids
are not appreciably compressible.are not appreciably compressible.
This helps explain:This helps explain:
Boyle’s Law Boyle’s Law P & V P & V
If the volume is decreased, that If the volume is decreased, that means that the gas particles will means that the gas particles will hit the wall more often, thus hit the wall more often, thus increasing pressure.increasing pressure.
Boyle’s Law Boyle’s Law P & V P & V
VnRTP
1)(
Constant
Charles’ Law: V & TCharles’ Law: V & T
When a gas is heated, the speeds When a gas is heated, the speeds
of its particles increase, thus of its particles increase, thus
hitting the walls more often and hitting the walls more often and
with more force. with more force.
The only way to keep the P The only way to keep the P
constant is to increase the constant is to increase the
volume of the container.volume of the container.
TP
nRV
Constant
Charles’ Law: V & TCharles’ Law: V & T
Gay-Lussac’s Law: P & Gay-Lussac’s Law: P & TT
When the temperature of a gas When the temperature of a gas
increases, the speeds of its particles increases, the speeds of its particles
increase. The particles are hitting increase. The particles are hitting
the wall with greater force and the wall with greater force and
greater frequency. greater frequency.
Since the volume remains the Since the volume remains the same, same,
this would result in increased this would result in increased gas gas
pressure.pressure.
Gay-Lussac’s Law: P & Gay-Lussac’s Law: P & TT
TV
nRP
Constant
Avogadro’s Law: V & nAvogadro’s Law: V & n
An increase in the number of particles An increase in the number of particles
at the same temperature would cause at the same temperature would cause
the pressure to increase, if the volume the pressure to increase, if the volume
were held constant. were held constant.
The only way to keep constant The only way to keep constant P is P is
to vary the V.to vary the V.
Avogadro’s Law: V & nAvogadro’s Law: V & n
nP
RTV
Constant
Dalton’s Law Dalton’s Law
The P exerted by a mixture of gases The P exerted by a mixture of gases
is the SUM of the partial pressures is the SUM of the partial pressures
since gas particles are independent since gas particles are independent
of each other and the volumes of of each other and the volumes of
the individual particles the individual particles DO NOT DO NOT
matter.matter.
Distribution of Distribution of Molecular SpeedsMolecular Speeds
Plot # of gas molecules having Plot # of gas molecules having
various speeds vs. the speed and various speeds vs. the speed and
you get a curve. you get a curve.
Changing the temperature affects Changing the temperature affects
the shape of the curve, NOT the the shape of the curve, NOT the
area beneath it. area beneath it.
Change the # of molecules and all Change the # of molecules and all
bets are off!bets are off!
Maxwell’s equationMaxwell’s equation
FW
RTuu rms
32
Use 8.314510 J/K• mol for this equation—the “energy” R since it’s really kinetic energy that is at work here!
Exercise 19Exercise 19 Root Mean Square Root Mean Square VelocityVelocityCalculate the root mean square Calculate the root mean square
velocity for the atoms in a velocity for the atoms in a sample sample
of helium gas at 25º C.of helium gas at 25º C.
SolutionSolution
1.36 x 101.36 x 1033 m/s m/s
If we could If we could
monitor the monitor the path path
of a single of a single
molecule it molecule it
would be very would be very
erratic.erratic.
Mean Free PathMean Free Path
the average distance a particle the average distance a particle
travels between collisions. travels between collisions.
It’s on the order of a tenth of a It’s on the order of a tenth of a
micrometer. WAY SMALL! micrometer. WAY SMALL!
Examine the effect of temperature Examine the effect of temperature
on the numbers of molecules with a on the numbers of molecules with a
given velocity as it relates to given velocity as it relates to
temperature. temperature.
HEAT ‘EM UP, SPEED ‘EM UP!!HEAT ‘EM UP, SPEED ‘EM UP!!
Drop a vertical line Drop a vertical line
from the peak of from the peak of
each of the three each of the three
bell shaped curves—bell shaped curves—
that point on the x-that point on the x-
axis represents the axis represents the
AVERAGE velocity of AVERAGE velocity of
the sample at that the sample at that
temperature. temperature.
Note how the bells are “squashed” Note how the bells are “squashed”
as the temperature increases. You as the temperature increases. You
may see graphs like this on the AP may see graphs like this on the AP
exam where you have to identify exam where you have to identify
the highest temperature based on the highest temperature based on
the shape of the graph!the shape of the graph!
Graham’s Law of Graham’s Law of Diffusion and EffusionDiffusion and Effusion
Effusion is closely related to Effusion is closely related to diffusion.diffusion.
DiffusionDiffusion
is the term used to describe the is the term used to describe the
mixing of gases. mixing of gases.
The The raterate of diffusion is the of diffusion is the raterate of of
the mixing. the mixing.
EffusionEffusion
is the term used to describe the is the term used to describe the
passage of a gas through a tiny passage of a gas through a tiny
orifice into an evacuated chamber orifice into an evacuated chamber as shown above.as shown above.
The rate of effusion measures The rate of effusion measures the the
speed at which the gas is speed at which the gas is
transferred into the chamber.transferred into the chamber.
The rates of effusion of two gases The rates of effusion of two gases
are inversely proportional to the are inversely proportional to the
square roots of their molar masses square roots of their molar masses
at the same temperature and at the same temperature and
pressure.pressure.
FW
FW = 2 gas ofeffusion of Rate
1 gas ofeffusion of Rate
1
2
REMEMBER,REMEMBER,
raterate is a change in a quantity is a change in a quantity
over time, over time,
NOT just the time!NOT just the time!
Exercise 20Exercise 20 Effusion Rates Effusion Rates
Calculate the ratio of the effusion Calculate the ratio of the effusion
rates of hydrogen gas (Hrates of hydrogen gas (H22) and ) and
uranium hexafluoride (UFuranium hexafluoride (UF66), a gas ), a gas
used in the enrichment process to used in the enrichment process to
produce fuel for nuclear reactors.produce fuel for nuclear reactors.
SolutionSolution
13.213.2
ExerciseExercise
A pure sample of methane is found A pure sample of methane is found
to effuse through a porous barrier in to effuse through a porous barrier in
1.50 minutes. Under the same 1.50 minutes. Under the same
conditions, an equal number of conditions, an equal number of
molecules of an unknown gas effuses molecules of an unknown gas effuses
through the barrier in 4.73 minutes. through the barrier in 4.73 minutes.
What is the molar mass of the What is the molar mass of the
unknown gas?unknown gas?
DiffusionDiffusion -- This is a classic! -- This is a classic!
Distance traveled by NH3 Distance traveled by NH3 = =
Distance traveled by HCl Distance traveled by HCl
urmsurms for NHfor NH33 = =
urms for HClurms for HCl
5.117
5.36
3
NH
HCl
FW
FW
The observed ratio is LESS than a The observed ratio is LESS than a
1.5 distance ratio. Why?1.5 distance ratio. Why?
This diffusion is slow considering This diffusion is slow considering
the molecular velocities are 450 and the molecular velocities are 450 and
660 meters per second. Which one 660 meters per second. Which one
is which?is which?
This tube contains air and all those This tube contains air and all those collisions slow the process down in collisions slow the process down in the real world. the real world.
Speaking of real world….Speaking of real world….
REAL, thus NONIDEAL GASESREAL, thus NONIDEAL GASES
Most gases behave ideally until Most gases behave ideally until you you
reach high pressure and low reach high pressure and low
temperature. temperature.
(By the way, either of these can (By the way, either of these can
cause a gas to liquefy, go figure!)cause a gas to liquefy, go figure!)
van der Waals Equationvan der Waals Equation
corrects for negligible volume of corrects for negligible volume of
molecules and accounts for inelastic molecules and accounts for inelastic
collisions leading to intermolecular collisions leading to intermolecular
forces (his real claim to fame)forces (his real claim to fame)
a and b are van der Waals constants. a and b are van der Waals constants.
No need to work problems, it’s the No need to work problems, it’s the
concepts that are important!concepts that are important!
nRT = bn] - [V ])V
na( + [P 2
Notice, pressure is increased Notice, pressure is increased
(intermolecular forces lower real (intermolecular forces lower real
pressure, you’re correcting for pressure, you’re correcting for this) this)
and volume is decreased (corrects and volume is decreased (corrects
the container to a smaller “free” the container to a smaller “free”
volume).volume).
The following graphs are The following graphs are classics and make great classics and make great multiple choice questions on multiple choice questions on the AP exam.the AP exam.
When PV/nRT =1.0, the gas is When PV/nRT =1.0, the gas is ideal.ideal.
All of these are All of these are
at 200K. Note at 200K. Note
the P’s where the P’s where
the curves crossthe curves cross
the dashed the dashed line [ideality].line [ideality].
This graph is just for nitrogen This graph is just for nitrogen gas. gas.
Note that although nonideal Note that although nonideal
behavior is behavior is
evident at each evident at each
temperature, temperature,
the deviations the deviations
are smaller at are smaller at
the higher Ts.the higher Ts.
Don’t underestimate the power Don’t underestimate the power of of
understanding these graphs. We understanding these graphs. We
love to ask questions comparing love to ask questions comparing the the
behavior of ideal and real gases. behavior of ideal and real gases.
It’s not likely you’ll be asked an It’s not likely you’ll be asked an
entire free-response gas problem on entire free-response gas problem on
the real exam in May. the real exam in May.
Gas Laws are tested extensively in Gas Laws are tested extensively in
the multiple choice since it’s easy to the multiple choice since it’s easy to
write questions involving them! write questions involving them!
You will most likely see PV=nRT as You will most likely see PV=nRT as
one part of a problem in the free-one part of a problem in the free-
response, just not a whole problem!response, just not a whole problem!
GO FORTH AND RACK UP THOSE GO FORTH AND RACK UP THOSE
MULTIPLE CHOICE POINTS!!MULTIPLE CHOICE POINTS!!
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