Chapter 5
Gases
Unit 5 - Gases
Chemistry II Honors
Characteristics of Gases
•Expands to fill their container
•volume of gas = volume of container
•Highly compressible
•when pressure is applied, volume decreases
•Form homogeneous mixtures with each other
•Considered a fluid
•Low density
•These characteristics happen because individual
molecules are relatively far apart.
Pressure
•occurs because of molecular collision with container
walls
•SI unit -
F
P=
A
2
N/m
- Pascal (Pa)
•Standard atmospheric pressure - at sea level
5
1 atm = 760 mmHg = 1.01x10 Pa = 760 torr
Q: What did Avogadro teach his students in math class?
A: Moletiplication
Pressure
Measuring Pressure
Barometer
Manometer
Pressure
Standard Temperature and Pressure
•Pressure is 1 atm or 760 torr
•Temperature is 0°C or 273 K
•The molar volume of an ideal gas at STP is 22.4 L
THE GAS LAWS
Boyle’s Law
• The volume of a fixed quantity of gas maintained at a constant
temperature is inversely proportional to the pressure
P1V1 = P2V2
THE GAS LAWS
Charles’s Law
• The volume of a fixed amount of gas maintained at constant
pressure is directly proportional to its absolute temperature
V1
V2
=
T1
T2
The Gas Laws
Avogadro’s Law
•Equal volumes of gases at the same temperature and
pressure contain equal numbers of molecules
V1
V2
=
n1
n2
The Gas Laws
Evaluating the Effects of Changes in P, V, n, and T on a Gas
•Suppose we have a gas confined to a cylinder,
indicate how each of these changes will affect.
•The average distance between molecules.
•The pressure of the gas.
•The number of moles of gas in the container.
a.Heat the gas from 298 K to 360 K, while maintaining the
piston in its original position.
b.Move the piston to reduce the volume of the gas from 1 L to
0.5 L.
c. Inject additional gas through the gas inlet valve
The Gas Laws
What happens to the density of a gas as...
•The gas is heated in a constant volume container.
•The gas is compressed at constant temperature.
•Additional gas is added to a constant volume container.
The Gas Laws
Ideal Gas Law
PV = nRT
P - pressure (atm)
T - temperature (K)
V - volume (L)
n - number of moles (mol)
R - gas constant (0.08206 L*atm/mol*K)
Q: How much does Avogadro exaggerate?
A: He makes mountains out of mole hills.
The Gas Laws
Ideal Gas Law
Sample Problem A
•A sample of CaCO3 decomposes upon heating to give
CaO and CO2. The CO2 is collected in a 250 mL flask.
After the decomposition, the gas has a pressure of 1.3
atm at a temperature of 31°C. How many moles of CO2
gas were generated?
The Gas Laws
Relating the Ideal Gas Equation and the Gas Laws
Boyle’s Law
P1V1 = P2V2
Gay-Lussac’s Law
P1
P2
=
T1
T2
PV = nRT
Charles’s Law
V1
V2
=
T1
T2
Combined Gas Law
P1V1
P2V2
=
T1
T2
The Gas Laws
Ideal Gas Law
Sample Problem B
•The gas pressure in an aerosol can is 1.5 atm at 25°C.
Assuming that the gas inside obeys the ideal gas
equation, what would the pressure be if the can were
heated to 450°C?
The Gas Laws
Ideal Gas Law
Sample Problem C
•An inflated balloon has a volume of 6.0 L at sea level
(1.0 atm) and is allowed to ascend in altitude until the
pressure is 0.45 atm. During ascent, the temperature
of the gas falls from 22°C to -21°C. Calculate the
volume of the balloon at its final altitude.
The Gas Laws
Applications of the Ideal Gas Equation
Gas Densities and Molar Mass
d - density
PM
d=
RT
M - molar mass
•The higher the molar mass and pressure, the more
dense the gas.
•The higher the temperature, the less dense the gas.
The Gas Laws
Applications of the Ideal Gas Equation
Sample Problem D
•What is the density of carbon tetrachloride vapor at
714 torr and 125°C?
The Gas Laws
Applications of the Ideal Gas Equation
Sample Problem E
•A series of measurements are made in order to
determine the molar mass of an unknown gas. First, a
large flask is evaluated and found to weigh 134.567 g.
It is then filled and reweighed; its mass is now 137.456
g. Finally, the flask is filled with water at 31°C and
found to weigh 1067.9 g. (The density of water is 0.997
g/mL). Calculate the molar mass of the gas.
Dalton’s Law of Partial Pressures
Dalton’s Law of Partial Pressure
•Total pressure of a mixture of gases equals the sum of
the pressures that each would exert if it were present
alone.
•Partial Pressure is the pressure exerted by a
particular component of a mixture of gases.
Dalton’s Law of Partial Pressure
PTotal = P1 + P2 + P3 ...
•Helpful when collecting gases over water.
Dalton’s Law of Partial Pressures
Dalton’s Law of Partial Pressure
Sample Problem F
•A gaseous mixture made from 6.00 g of O2 and 9.00 g
CH4 is placed in a 15.0 L vessel at 0°C. What is the
partial pressure of each gas, and what is the total
pressure in the vessel?
Dalton’s Law of Partial Pressures
Partial Pressures and Mole Fractions
mol A
nA
XA =
or X A =
total mol
nTotal
⎛ n1 ⎞
P1 = ⎜
P
=
X
P
t
1 t
⎟
⎝ ntotal ⎠
Q: What do you get when you have a bunch of moles acting like idiots?
A: A bunch of Moleasses.
Dalton’s Law of Partial Pressures
Partial Pressures and Mole Fraction
Sample Problem G
•A study of the effects of certain gases on plant growth
requires a synthetic atmosphere composed of 1.5 mol
percent CO2, 18.0 mol percent O2, and 80.5 mol percent
Ar.
a.Calculate the partial pressure of O2 if the total
pressure is 745 torr.
b.If the atmosphere is to be held in a 120 L space a 295
K, how many moles of O2 are needed?
Dalton’s Law of Partial Pressures
Collecting Gases over Water
Sample Problem H
•A sample of KClO3 is partially decomposed producing O2
gas that is collected over water. The volume of gas
collected is 0.250 L at 26°C and 765 torr total
pressure.
a.How many moles of O2 are collected?
b.How many grams of KClO3 were decomposed?
Dalton’s Law of Partial Pressures
AP EXAM PRACTICE
Sample Problem I
•A rigid 5.00 L cylinder contains 24.5 g of N2(g) and
28.0 g of O2(g).
a.Calculate the total pressure, in atm, of the gas
mixture in the cylinder at 298 K.
b.The temperature of the gas mixture in the cylinder is
decreased to 280 K. Calculate each of the following.
i. The mole fraction of N2(g) in the cylinder.
ii.The partial pressure, in atm, of N2(g) in the cylinder.
Dalton’s Law of Partial Pressures
AP EXAM PRACTICE
Sample Problem I
•A rigid 5.00 L cylinder contains 24.5 g of N2(g) and
28.0 g of O2(g).
c.If the cylinder develops a pinhole-sized leak and some
mole of N ( g )
of the gaseous mixture escapes, would the moles of O ( g )
in the cylinder increase, decrease or remains the
same? Justify your answer.
2
2
Dalton’s Law of Partial Pressures
AP EXAM PRACTICE
Sample Problem I
•A different rigid 5.00 L cylinder contains 0.176 mol of
NO(g) at 298 K. A 0.176 mol sample of O2(g) is added to
the cylinder, where a reaction occurs to produce
NO2(g).
d.Write the balanced equation for the reaction.
e.Calculate the total pressure, in atm, in the cylinder at
298 K after the reaction is complete.
The Kinetic Molecular Theory of Gases
Kinetic Molecular Theory
1.Gases consist of large numbers of molecules that are in
continuous, random motion.
2.The combined volume of all the molecules of the gas is
negligible relative to the total volume in which the gas
is contained.
3.Attractive and repulsive forces between gas molecules
are negligible.
The Kinetic Molecular Theory of Gases
Kinetic Molecular Theory
4.Energy can be transferred during collisions, but the
average kinetic energy does not change, if the
temperature remains the same. (Collisions are elastic.)
5.The average kinetic energy of the molecules is
proportional to the absolute temperature. At any given
temperature the molecules of all gases have the same
average kinetic energy.
The Kinetic Molecular Theory of Gases
Root Mean Square Velocity
•Root Mean Square Velocity (rms, μ) is the speed of a
molecule possessing average kinetic energy.
•rms increases with temperature.
µrms =
3RT
M
Kinetic Energy
1 2
∈= mv
2
Dalton’s Law of Partial Pressures
Root Mean Square Velocity
Sample Problem J
•A sample of O2 gas initially at STP is compressed to a
smaller volume at constant temperature. What effect
does this change have on:
a.The average kinetic energy of O2 molecules.
b.The average speed of O2 molecules.
c.The total number of collisions of O2 molecules with the
container walls in a unit time.
V (liters)
Dalton’s Law of Partial Pressures
AP Exam Practice
Sample Problem K
T (kelvins)
•
Samples
areatplaced
in indicated
1 L in the diagram
(e) Samples
of CO(g)of
andCO(g)
CO2(g) areand
placedCO2(g)
in 1 L containers
the conditions
below.containers at the conditions indicated in the diagram
below.
a.Indicate
whether
the
average
kinetic
energy
of
the
(i)
Indicate whether the average kinetic energy of the CO2(g) molecules is greater than, equal to,
CO
(g)
molecules
is energy
greater
than,
equalJustify
to, your
or answer.
less
or2less
than
the average kinetic
of the CO(g)
molecules.
than the average kinetic energy of CO(g) molecules.
(ii)
Indicate whether the root-mean-square speed of the CO2(g) molecules is greater than, equal to,
Justify
answer. speed of the CO(g) molecules. Justify your answer.
or less thanyour
the root-mean-square
V (liters)
Dalton’s Law of Partial Pressures
AP Exam Practice
Sample Problem K
T (kelvins)
•
Samples
areatplaced
in indicated
1 L in the diagram
(e) Samples
of CO(g)of
andCO(g)
CO2(g) areand
placedCO2(g)
in 1 L containers
the conditions
below.containers at the conditions indicated in the diagram
below.
b.Indicate
whether
the
root-mean-square
speed
of
the
(i)
Indicate whether the average kinetic energy of the CO2(g) molecules is greater than, equal to,
CO
(g)
molecule
is greater
equal Justify
to, or
than
or2less
than
the average kinetic
energy of thethan,
CO(g) molecules.
yourless
answer.
the root-mean-square speed of the CO(g) molecule.
(ii)
Indicate whether the root-mean-square speed of the CO2(g) molecules is greater than, equal to,
Justify
answer. speed of the CO(g) molecules. Justify your answer.
or less thanyour
the root-mean-square
V (liters)
Dalton’s Law of Partial Pressures
AP Exam Practice
Sample Problem K
T (kelvins)
•
Samples
areatplaced
in indicated
1 L in the diagram
(e) Samples
of CO(g)of
andCO(g)
CO2(g) areand
placedCO2(g)
in 1 L containers
the conditions
below.containers at the conditions indicated in the diagram
below.
c.Indicate
whether
the
number
of
CO
2(g) molecule is
(i)
Indicate whether the average kinetic energy of the CO2(g) molecules is greater than, equal to,
greater
equal
to, orof the
less
than
theJustify
number
of
or less thanthan,
the average
kinetic energy
CO(g)
molecules.
your answer.
CO(g) molecules. Justify your answer.
(ii)
Indicate whether the root-mean-square speed of the CO2(g) molecules is greater than, equal to,
or less than the root-mean-square speed of the CO(g) molecules. Justify your answer.
Daily Objectives
Chemistry II Honors
Today, I will be able to
compare and contrast diffusion and effusion.
describe the behavior of real gases.
•
•
LO 2.4, 2.5, 2.6, 2.12, 3.4, 5.2, 5.4
Effusion and Diffusion
Effusion and Diffusion
•Dependance of molecular speeds on mass leads to
effusion and diffusion.
•Effusion is the escape of a gas molecule through a tiny
hole.
•Diffusion is the spreading of one
substance throughout a space or
throughout a second substance.
EFFUSION AND DIFFUSION
Graham’s Law of Effusion
Rate1
=
Rate 2
M2
M1
Effusion and Diffusion
Graham’s Law of Effusion
Sample Problem L
•An unknown gas composed of homonuclear diatomic
molecules effuses at a rate that is only 0.355 times that
of O2 at the same temperature. Calculate the molar
mass of the unknown and identify it.
Real Gases
Real Gases
•Deviate from ideal behavior
•Do not behave ideally at high
pressures and low
temperatures
•Do have finite volumes and
attract one another
•The greater the intermolecular
forces (IMF), the more the gas
deviates from ideal behavior. (polar, hydrogen bonding,
ionic, etc.)
Real Gases
van der Waal’s Equation
nRT
⎛ n⎞
P=
− a⎜ ⎟
⎝V⎠
V − nb
correction for volume of molecules
(decreases volume as a function of
the number of molecules)
2
correction for molecular attraction
(decreases pressure as volume
decrease and the number of
molecules increases)
Real Gases
van der Waal’s Equation
⎛
an ⎞
P
+
V
−
nb
=
nRT
(
)
2 ⎟
⎜⎝
V ⎠
2
P - pressure
V - volume
T - temperature
R - gas constant
a, b - specific coefficients for each gas
Values for a and b generally increase with an increase in mass of
molecule and an increase in complexity of its structure
Real Gases
AP Exam Practice
Sample Problem M
a.From the standpoint of the kinetic-molecular theory,
discuss briefly the properties of gas molecules that
cause deviations from ideal behavior.
b.At 25ºC at 1 atmosphere pressure, which of the
following gases shows the greatest deviation from ideal
behavior? Give two reasons for your choice.
CH4 SO2 O2 H2
c.Real gases approach ideality at low pressure, high
temperature or both. Explain these observations.
propane. Assume that air is 21.0 percent O2 by volume.
o
(c) The heat of combustion of propane is 2,220.1 kJ/mol. Calculate the heat of formation, Hf , of propane given
o
o
that Hf of H2O(l) = 285.3 kJ/mol and Hf of CO2(g) = 393.5 kJ/mol.
(d) Assuming that all of the heat evolved in burning 30.0 grams of propane is transferred to 8.00 kilograms of
.
water (specific heat = 4.18 J/g K), calculate the increase in temperature of water.
Real Gases
AP Exam Practice
1996 Sample Problem N
Represented
above
are
five
each
filled
toatmosphere
the
Represented
above are five identical
balloons,
each
filledballoons,
to the same volume
at 25°C
and 1.0
pressure with
the pure
gas indicated.
same
volume
at 25ºC and 1.0 atmosphere pressure
pure
gas indicated.
(a) Whichwith
balloonthe
contains
the greatest
mass of gas? Explain.
a.Which
balloon
contains
the
greatest
massExplain.
of gas?
(b) Compare
the average
kinetic energies
of the gas
molecules
in the balloons.
Explain.
(c) Which balloon contains the gas that would be expected to deviate most from the behavior of an ideal gas?
Explain.
b.Compare the average kinetic energies of the gas
molecules
infilled,
theallballoons.
Explain.
(d) Twelve
hours after being
the balloons have
decreased in size. Predict which balloon will be the
smallest. Explain your reasoning.
propane. Assume that air is 21.0 percent O2 by volume.
o
(c) The heat of combustion of propane is 2,220.1 kJ/mol. Calculate the heat of formation, Hf , of propane given
o
o
that Hf of H2O(l) = 285.3 kJ/mol and Hf of CO2(g) = 393.5 kJ/mol.
(d) Assuming that all of the heat evolved in burning 30.0 grams of propane is transferred to 8.00 kilograms of
.
water (specific heat = 4.18 J/g K), calculate the increase in temperature of water.
Real Gases
AP Exam Practice
1996 Sample Problem N
Represented
above
are
five
each
filled
toatmosphere
the
Represented
above are five identical
balloons,
each
filledballoons,
to the same volume
at 25°C
and 1.0
pressure with
the pure
gas indicated.
same
volume
at 25ºC and 1.0 atmosphere pressure
pure
gas indicated.
(a) Whichwith
balloonthe
contains
the greatest
mass of gas? Explain.
c.Which
balloon
contains
the
gas that
would
be expected
(b) Compare
the average
kinetic energies
of the gas
molecules
in the balloons.
Explain.
to
deviate
most
from
the
behavior
of
an
ideal
gas?
(c) Which balloon contains the gas that would be expected to deviate most from the behavior of an ideal gas?
Explain.
Explain.
(d) Twelve hours after being filled, all the balloons have decreased in size. Predict which balloon will be the
smallest. Explain your reasoning.
propane. Assume that air is 21.0 percent O2 by volume.
o
(c) The heat of combustion of propane is 2,220.1 kJ/mol. Calculate the heat of formation, Hf , of propane given
o
o
that Hf of H2O(l) = 285.3 kJ/mol and Hf of CO2(g) = 393.5 kJ/mol.
(d) Assuming that all of the heat evolved in burning 30.0 grams of propane is transferred to 8.00 kilograms of
.
water (specific heat = 4.18 J/g K), calculate the increase in temperature of water.
Real Gases
AP Exam Practice
1996 Sample Problem N
Represented
above
are
five
each
filled
toatmosphere
the
Represented
above are five identical
balloons,
each
filledballoons,
to the same volume
at 25°C
and 1.0
pressure with
the pure
gas indicated.
same
volume
at 25ºC and 1.0 atmosphere pressure
pure
gas indicated.
(a) Whichwith
balloonthe
contains
the greatest
mass of gas? Explain.
d.Twelve
hours
afterofbeing
filled, all
balloons
(b) Compare
the average
kinetic energies
the gas molecules
in thethe
balloons.
Explain.
have
decreased
in
size.
Predict
which
balloon
will
be
the
(c) Which balloon contains the gas that would be expected to deviate most from the behavior of an ideal gas?
smallest. Explain your reasoning.
Explain.
(d) Twelve hours after being filled, all the balloons have decreased in size. Predict which balloon will be the
smallest. Explain your reasoning.