Transcript DO NOW - Nancy Brim Chemistry

THE PROPERTIES OF GASES
A gas uniformly fills any container, is easily
compressed and mixes completely with any
other gas.
 Only four quantities define the state of a
gas:
a. the quantity of the gas, n (in moles)
b. the temperature of the gas, T (in
KELVINS)
c. the volume of the gas, V (in liters)
d. the pressure of the gas, P (in atmospheres)

PRESSURE
A measure of the force that a gas exerts on
its container.
 Force is the physical quantity that interferes
with inertia.
 Gravity is the force responsible for weight.
 Newton’s 2nd Law: Force = m × a
 The units of force follow: N = kg × m/s2
 Pressure - Force ÷ unit area; N/m2

PRESSURE

Standard Pressure
◦
◦
◦
◦

760.00 mm Hg
760.00 torr
1.00 atm
101.325 kPa ≈ 105 Pa
The SI unit of pressure is the Pascal; 1 Pa =
1 N/m2
PRESSURE

Pressure is measured in a variety of units.
UNIT
ABBREVIATION
COMPARE TO 1
ATM
kPa
101.3 kPa
mmHg
760.0 mmHg
Torr
torr
760.0 torr
Atmosphere
atm
1.0 atm
Pounds per square
inch*
psi
14.7 psi
Kilopascal
Millimeters of
mercury
*We will use all of these but psi.
PRESSURE
Barometer - measures gas pressure
(especially atmospheric). 1 mm of Hg = 1
torr
 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).

PRESSURE
PRACTICE ONE
The pressure of a gas is measured as 49
torr. Represent this pressure in both
atmospheres and pascals.
PRACTICE TWO
Rank the following pressures in decreasing
order of magnitude (largest first, smallest
last): 75 kPa, 300. torr, 0.60 atm, and 350.
mm Hg.
THE GAS LAWS
1.
Boyle’s Law: V and P;
inversely proportional.
2.
3.
4.
Charles’ Law: T and V;
directly proportional.
Gay-Lussac’s Law: P and T;
directly proportional.
Avogadro’ Principle: moles and P or V;
directly proportional.
BOYLE’S LAW
BOYLE’S LAW
THE LAW: the volume of a confined gas is
inversely proportional to the pressure exerted
on the gas: P1V1 = P2V2
P ∝ 1/V plot = straight line
GOOD HABITS
EVERY TIME you do a gas laws problem:
1.
2.
3.
Write what you know and what you are
trying to find
Write the formula
Plug in the numbers with units and solve
with the correct number of sig figs.
PRACTICE THREE
Consider a 1.53L sample of gaseous SO2 at a pressure of 5.6 ×
1O3 Pa. If the pressure is changed to 1.5 × 104 Pa at a constant
temperature, what will be the new volume of the gas ?
PRACTICE FOUR

Using the results listed below, calculate
the Boyle’s law constant for NH3 at the
various pressures.
Experiment
1
2
3
4
5
6
Pressure (atm) Volume (L)
0.1300
172.1
0.2500
89.28
0.3000
74.35
0.5000
44.49
0.7500
29.55
1.000
22.08
PV vs. P

What is the yintercept? How
about the 3rd graph
on page two?

Molar Volume of a
gas: 22.42L
CHARLES’ LAW
CHARLES LAW

THE LAW: If a given quantity of gas is held
at a constant pressure, then its volume is
directly proportional to the absolute
temperature.
V1T2 = V2T1
You must use the Kelvin!
K = °C + 273
CHARLES’ LAW
Where do all the
gases cross the xintercept?
 If the volume is
zero, what is the
temperature?


-273.15ºC or 0K
PRACTICE FIVE
A sample of gas at 15ºC and 1 atm has a
volume of 2.58 L. What volume will this
gas occupy at 38ºC and 1 atm ?
GAY-LUSSAC’S LAW
GAY-LUSSAC’S LAW
THE LAW: An increase in temperature
increases the frequency of collisions
between gas particles. In a given volume,
raising the KELVIN temperature also
raises the pressure.
P1 T2 = P2T1
You must use Kelvin!
AVOGADRO’S LAW
Volume:
Mass:
Quantity:
Pressure:
Temperature:
22.42L
39.95g
1 mol
1 atm
273K
22.42L
32.00g
1 mol
1 atm
273K
22.42L
28.02g
1 mol
1 atm
273K
AVOGADROS’S LAW




The volume of a gas, at a given temperature
and pressure, is directly proportional to the
quantity of gas.
Equal volumes of gases under the same
conditions of temperature and pressure contain
equal numbers of molecules.
In gas law problems, moles is designated by
an “n”.
One mole of a gas has a volume of 22.42 L
(dm3) at STP. It also has 6.02 x 1023 particles
of that gas.
PRACTIVE SIX
Suppose we have a 12.2-L sample containing
0.50 mol oxygen gas (O2) at a pressure of 1
atm and a temperature of 25ºC. If all this O2
were converted to ozone (O3) at the same
temperature and pressure, what would be
the volume of the ozone ?
HINT
PTV
HINT
PVT

Put the scientists' names in alphabetical
order. Boyle’s uses the first 2 variables,
Charles’ the second 2 variables and GayLussac’s the remaining combination of
variables.
COMBINED GAS LAW
From the Boyle’s, Charles’, and Gay-Lussac’s
laws, we can derive the
Combined Gas Law:
P1V1 T2 = P2V2 T1
Mnemonic: Potato and Vegetable on top of
the Table for P1V1 = P2V2
T1
T2
STANDARDS
T = 0°C = 273 K
V = 22.4 L (at STP)
P = 1.00 atm = 101.3 kPa
= 760.0 mm Hg = 760.0 torr
Remember only kPa has limited
sigfigs.
PUTTING IT ALL TOGETHER
Simulation on gas laws:
Structure and Properties of Matter
IDEAL GAS LAW
Ideal Gas Equation:
PV = nRT
“R” is the universal gas constant.
V ∝ (nT)/P
replace ∝ with constant, R
UNIVERSAL GAS CONSTANTS
R = 0.08206 L• atm
mol • K
R = 62.36 L•mmHg
mol • K
R = 62.36 L • torr
mol • K
R = 8.314 L • kPa
mol • K
Why are
there four
constants?
IDEAL GAS LAW
Remember:
1. Always change the temperature to
KELVINS and convert volume to
LITERS
2. Check the units of pressure to make
sure they are consistent with the “R”
constant given or convert the pressure
to the gas constant (“R”) you want to
use.
PRACTICE SEVEN
A sample of hydrogen gas (H2) has a volume of
8.56 L at a temperature of 0ºC and a pressure
of 1.5 atm. Calculate the moles of H2 molecules
present in this gas sample.
PRACTICE EIGHT
Suppose we have a sample of ammonia gas with a
volume of 3.5 L at a pressure of 1.68 atm. The gas
is compressed to a volume of 1.35 L at a constant
temp. Use the ideal gas law to calculate the final
pressure.
PRACTICE NINE
A sample of methane gas that has a volume of 3.8
L at 5ºC is heated to 86ºC at constant pressure.
Calculate its new volume.
PRACTICE TEN
A sample of diborane gas (B2H6) has a pressure of
345 torr at a temp. of -15ºC and a volume of 3.48
L. If conditions are changed so that the temp. is
36ºC and the pressure is 468 torr, what will be the
volume of the sample?
PRACTICE ELEVEN
A sample containing 0.35 mol argon gas at a temp.
of 13ºC and a pressure of 568 torr is heated to
56ºC and a pressure of 897 torr. Calculate the
change in volume that occurs.
GAS STOICHIOMETRY
VOLUME
1 mol
22.42 L @ STP
1 mole
1 mole
PARTICLES
MOLE
MASS
6.02 x 1023
molar mass
Use the ideal gas law to convert
quantities that are NOT at STP.
HINT

You must have a balanced equation to do
a stoichiometry problem.
PRACTICE TWELVE
Use PV = nRT to solve for the volume of
one mole of gas at STP.
PRACTICE THIRTEEN
A sample of nitrogen gas has a volume of
1.75 L at STP. How many moles of N2 are
present?
PRACTICE FOURTEEN
Calculate the volume of CO2 at STP made
from the decomposition of 152 g CaCO3 by
the reaction CaCO3(s) → CaO(s) + CO2(g).
PRACTICE FIFTEEN
A sample of methane gas having a volume of 2.80
L at 25ºC and 1.65 atm was mixed with a sample
of oxygen gas having a volume of 35.0 L at 31ºC
and 1.25 atm. The mixture was then ignited to
form carbon dioxide and water. Calculate the
volume of CO2 formed at a pressure of 2.50 atm
and a temperature of 125ºC.
DETERMINING DENSITY
This modified version of the ideal gas
equation can also be used to solve for the
density of a gas.
PV = nRT bcomes
D = PM
RT
DETERMINING DENSITY
•
D = m = PMM or
V
RT
•
The density of gases is g/L NOT g/mL.
Mnemonic given in notes.
•
D = PMM
RT
PRACTICE SIXTEEN

What is the approximate molar mass of
air?

What is the approximate density of air?
List 3 gases that float in air.
 List 3 gases that sink in air.

PRACTICE SEVENTEEN
The density of a gas was measured at 1.50
atm and 27ºC and found to be 1.95 g/L.
Calculate the molar mass of the gas.
DALTON’S LAW OF PARTIAL
PRESSURES
THE LAW: The pressure of a mixture of
gases is the sum of the pressures of the
different components of the mixture:
Ptotal = P1 + P2 + P3 +.....Pn
DALTON’S LAW OF PARTIAL
PRESSURES
Also uses the concept of mole fraction, χ
χA =
moles of A
moles A + moles B + moles C + . . .
so now, PA = χ A / Ptotal
The partial pressure of each gas in a mixture of
gases in a container depends on the number of
moles of that gas. The total pressure is the SUM
of the partial pressures and depends on the total
moles of gas particles present, no matter what
they are.
DALTON’S LAW OF PARTIAL
PRESSURES
PRACTICE SEVENTEEN
For a particular dive, 46 L He at 25ºC and 1.0 atm and 12 L
O2 at 25ºC and 1.0 atm were pumped into a tank with a
volume of 5.0 L. Calculate the partial pressure of each gas
and the total pressure in the tank at 25ºC.
PRACTICE EIGHTEEN
The partial pressure of oxygen was observed to
be 156 torr in air with a total atmospheric
pressure of 743 torr. Calculate the mole fraction
of O2 present.
PRACTICE NINETEEN
The mole fraction of nitrogen in the air is 0.7808.
Calculate the partial pressure of N2 in air when
the atmospheric pressure is 760. torr.
WATER DISPLACEMENT
It is common to collect a gas by water
displacement which means some of the
pressure is due to water vapor collected
as the gas was passing through the water.
 You must correct for this.
 You look up the partial pressure due to
water vapor in a table by knowing the
temperature.

DALTON’S LAW OF PARTIAL
PRESSURES
PRACTICE TWENTY
A sample of solid potassium chlorate (KClO3) was heated
in a test tube (see the figure above) and decomposed by
the following reaction: 2 KClO3(s) → 2 KCl(s) + 3 O2(g) The
oxygen produced was collected by displacement of water
at 22ºC at a total pressure of 754torr. The volume of the
gas collected was 0.650 L, and the vapor pressure of water
at 22ºC is 21torr. Calculate the partial pressure of O2 in
the gas collected and the mass of KClO3 in the sample that
was decomposed.
KINETIC MOLECULAR
THEORY
Assumptions of the KMT Model:
1. All particles are in constant, random
motion.
2. All collisions between particles are
perfectly elastic.
3. The volume of the particles in a gas is
negligible.
4. The average kinetic energy of the
molecules is its Kelvin temperature.
KINETIC MOLECULAR
THEORY
This neglects any intermolecular forces as
well.
 Gases expand to fill their container,
solids/liquids do not.
 Gases are compressible; solids/liquids are
not appreciably compressible.

KINETIC MOLECULAR
THEORY
Boyle’s Law: If the volume is decreased,
the gas particles will hit the wall more
often, thus increasing pressure.
KINETIC MOLECULAR
THEORY
Charles’ Law: When a gas is heated, the speed
of its particles increase and thus hit the walls
more often and with more force. The only way
to keep the P constant is to increase the
volume of the container.
KINETIC MOLECULAR
THEORY
Gay-Lussac’s Law: When the temperature of
a gas increases, the speeds of its particles increase,
the particles are hitting the wall with greater force
and greater frequency. Since the volume remains
the same this would result in increased gas
pressure.
KINETIC MOLECULAR
THEORY
Avogadro’s Law: An increase in the number
of particles at the same temperature would cause
the pressure to increase if the volume were held
constant. The only way to keep constant P is to
vary the V.
DISTRIBUTION OF
MOLECULAR SPEED
Although the molecules in a sample of gas have
an average KE (and therefore an average speed),
the individual molecules move at various speeds
and they stop and change direction according to
the law of density measurements and isolation
→ they exhibit a distribution of speeds.
 Some move fast, others relatively slowly.
 Collisions change individual molecular speeds
but the distribution of speeds remains the same.

DISTRIBUTION OF
MOLECULAR SPEED
Maxwell’s equation:
Urms means root mean square velocity
which is the measure of the average
velocity of particles in a gas.
 Use the “energy R” or molar gas constant,
8.314 J/K• mol for this equation since
kinetic energy is involved.

DISTRIBUTION OF
MOLECULAR SPEED
By taking the root of the square of the average
velocities, you can acquire the average speed of
gaseous particles.
 The root-mean-square velocity takes into
account both molecular mass and temperature,
two factors that directly affect the KE of a
material.
 What happens if we change to a gas that has a
higher MM?
 What happens if we lower the temperature?

PRACTICE TWENTY-ONE
Calculate the root mean square velocity for
the atoms in a sample of helium gas at
25ºC.
DISTRIBUTION OF
MOLECULAR SPEED
If we could monitor the path of a single
molecule it would be very erratic.
 Mean free path—the average distance a
particle travels between collisions. It’s on the
order of a tenth of a micrometer - very small.
 Examine the effect of temperature on the
numbers of molecules with a given velocity as
it relates to temperature. They heat up,
they speed up.

DISTRIBUTION OF
MOLECULAR SPEED
Drop a vertical line from
the peak of each of the
three bell shaped curves
— that point on the xaxis represents the
AVERAGE velocity of the
sample at that
temperature.
 Note how the bells are
“smashed” as the
temperature increases.

the Maxwell-Boltzmann
Distribution which describes
particle speeds of gases.
GRAHAM’S LAW OF
EFFUSION AND DIFFUSION
Effusion is closely related to diffusion.
 Diffusion is the term used to describe the
mixing of gases. The rate of diffusion is the rate
of the mixing.
 Effusion (pictured at left) is the term used to
describe the passage of a gas through a tiny
orifice into an evacuated chamber as shown on
the right.
 The rate of effusion measures the speed at
which the gas is transferred into the chamber.

GRAHAM’S LAW OF EFFUSION
AND DIFFUSION
Graham's Law of Effusion: The rates of
effusion of two gases are inversely
proportional to the square roots of their
molar masses at the same temperature and
pressure.
If two bodies of different masses have
the same kinetic energy, the lighter
body moves faster.
CALCULATIONS
KE = ½mv2
 ½ mava2 = ½ mcvc2
 ½ mava2 = ½ vc2
mc
 ½ ma = ½ vc2
mc
va2
 ma = vc2
mc
va2

GRAHAM’S LAW OF EFFUSION
AND DIFFUSION
 REMEMBER
rate is a change in a quantity
over time, NOT just the time!
 If they give you time, divide the time into 1
to get the rate.
PRACTICE TWENTY-TWO
Calculate the ratio of the effusion rates of
hydrogen gas (H2) and uranium hexafluoride (UF6),
a gas used in the enrichment process to produce
fuel for nuclear reactors.
PRACTICE TWENTY-THREE
A pure sample of methane is found to effuse through
a porous barrier in 1.50 minutes. Under the same
conditions, an equal number of molecules of an
unknown gas effuses through the barrier in 4.73
minutes. What is the molar mass of the unknown gas?
DIFFUSION
450 m/s
660 m/s
REAL vs. IDEAL GASES
Most gases behave ideally until you reach
high pressure and low temperature.
(Remember, either of these can cause a
gas to liquefy)
 Under very high pressure, real gases
have trouble compressing completely. The
ideal gas law fails. Ideal gases have no
volume, but real gases do.

van der Waals EQUATION

corrects for negligible volume of molecules
and accounts for inelastic collisions leading
to intermolecular forces.
a and b are van der
Waals constants.
Pressure is increased (IMFs lower real
pressure, you’re correcting for this)
 Volume is decreased (corrects the
container to a smaller “free” volume).

INTERPRETATION
When PV / nRT =
1.0, the gas is ideal.
 All of these are at
200K.
 Note the pressures
where the curves
cross the dashed
line [ideality].

INTERPRETATION
This graph is just for
nitrogen gas.
 Note that although
non-ideal behavior is
evident at each
temperature, the
deviations are
smaller at the higher
temperature.

THE AP EXAM
Don’t underestimate the power of
understanding these graphs.
 AP loves to ask questions comparing the
behavior of ideal and real gases - not an entire
free-response gas problem on the real exam.
 Gas Laws are tested extensively in the multiple
choice since it is easy to write questions
involving them! You will most likely see PV = nRT
as one part of a problem in the free response,
just not a whole problem!
