Ch 12 Gases
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Three reasons for studying gases
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1. Some common elements and
compounds exist as gases
2. Our atmosphere is gaseous
3. Gas behavior is easy to understand at
the molecular level, using a mathematical
model, which works for most gasses.
Properties of gases

Gases can be described using four
quantities
P, V, T (in K) and n (moles)
Gas Pressure
A tube is filled with mercury. The tube is
inverted into a dish containing mercury.
The mercury assumes a level in the
tube such that the pressure exerted by
the mass of the column of mercury in
the tube is balanced by the pressure of
the atmosphere pressing down on the
surface of the mercury in the dish.
At seal lever, the mercury-filled barometer
will rise a760 mmHg in the tube. This
unit is sometimes called the torr for
Torricelli inventor of the barometer
Gas Pressure
This Galileo thermometer combines art with science. It
provides an accurate reading of current weather
conditions. Temperature is indicated by the lowest
"floating" sphere in the top grouping. As accurate as
laboratory thermometers. Predict changes in the
weather by referencing fluid rise and fall in the
barometric tube. The hygrometer measures
humidity. How the thermometer works:The colored
floating spheres are "pushed" either up or down
depending on the changing density of the clear fluid
inside the glass thermometer body. When the
temperature goes up, the clear fluid becomes less
dense and rises - forcing the spheres down one by
one. When the temperature goes down, the clear
fluid becomes denser - forcing the spheres upward.
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Gas Pressure
How the barometer works:While not as
accurate as modern day aneroid barometers,
the principle of the early "Water Barometer" is
sound. When atmospheric pressure decreases,
the fluid is pulled upward toward the top of the
barometer tube (low pressure). As atmospheric
pressure increases, the fluid is "pushed down"
(high pressure). Standard atmospheric
pressure at sea level is 29.92".
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Gas Pressure
Water-based barometers This concept of "decreasing
atmospheric pressure predicts stormy weather" was
invented by Lucien Vidie It consists of a glass
container with a sealed body, half filled with water. A
narrow spout connects to the body below the water
level and rises above the water level, where it is open
to the atmosphere. When the air pressure is lower
than it was at the time the body was sealed, the
water level in the spout will rise above the water level
in the body; when the air pressure is higher, the water
level in the spout will drop below the water level in
the body.
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Gas Pressure
An aneroid barometer uses a small,
flexible metal box called an aneroid
cell. This aneroid capsule(cell) is
made from an alloy of beryllium and
copper.[2] The evacuated capsule (or
more usually capsules) is prevented
from collapsing by a strong spring.
Small changes in external air pressure
cause the cell to expand or contract.
This expansion and contraction drives
mechanical levers such that the tiny
movements of the capsule are
amplified and displayed on the face of
the aneroid barometer.
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Gas Pressure
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When the pressure gauge is applied to the valve stem of a tire,
the pressurized air from the tire rushes in and pushes the piston
toward the right. The distance the piston travels is relative to
the pressure in the tire. The pressurized air is pushing the
piston to the right, and the spring is pushing back
Gas Pressure
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The calibrated rod fits inside the spring. The calibrated rod
rides on top of the piston, but the rod and the piston are
not connected and there is a fairly tight fit between the
rod and the stop. When the piston moves to the right, it
pushes the calibrated rod. When the pressure is
released, the piston moves back to the left but the rod
stays in its maximum position to allow you to read the
pressure.
Units of Gas Pressure
1 standard atmosphere = 1 atm
1 atm = 760 mm Hg
The SI unit of Pressure is the pascal (Pa) Pressure = force / area
1 Pa = 1 newton / meter2
a Pa is small so kPa is used
1 atm = 760 mmHg = 101.3 kPa = 1.013 bar
Units of Gas Pressure
Convert 635 mm Hg into atm and kPa
Rank the following in decreasing order
75 kPa, 250 mm Hg, 0.83 bar, 0.63 atm.
Gas Pressure and Volume
Boyle
dbhs.wvusd.k12.ca.us/webdocs/GasLaw/
Gas-Boyle.html
Volume is inversely proportional to Pressure when n and T are constant
P V = constant when n and T are constant
P1V1 = P2V2
www.onr.navy.mil/Focus/blowballast/sub/wor
k4.htm
Gas Temperature and Volume
Charles Law
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www.chm.davidson.edu/ChemistryApplets/GasLaws/CharlesLaw.ht
ml
Gas Temperature and Volume
Charles Law allows
the calculation of
absolute 0 or 0 K
Combined Gas Las
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Combination of Charles and Boyle’s
Law
The ratio between the pressure-volume
constant and the temperature of a
system remains constant.
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Combined Gas Las
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Weather balloons
http://www.ultimatechase.com/chase_ac
counts/Weather_Balloon_Launch.htm
You have a 22 L cylinder of He at a pressure of 150
atm and at 31 oC. How many balloons can you fill,
each with a volume of 5.o L, on a day when the
atmospheric pressure is 755 mmHg and the
temperature is 22 oC?
Avogadro’s Hypothesis
Equal volumes of gases under the same conditions
of temperature and pressure have equal numbers
of molecules.
Four interrelated quantities can be used to describe
a gas: P, V, T, and n. These 4 quantities can be
made into a mathematical equation by introducing
a proportionality constant now labeled R
R = .082 l . atm
mol . K
Ideal Gas Law

http://intro.chem.okstate.edu/1314F00/labor
atory/GLP.htm
Ideal Gas Law
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R has a different value for each different
unit of pressure and the other quantities
used. Some values are...
R = 8.314472 m3·Pa·K-1·mol-1
R = 0.08205784 L·atm·K-1·mol-1
R = 62.3637 L·mmHg·K-1·mol-
Ideal Gas Law

The state of an amount of gas is
determined by its pressure, volume, and
temperature according to the equation:
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Ideal Gas Law

A balloon with 1300 mol of H2 is at a
temperature of 23oC and a pressure of
750 mmHg, what is the volume of the
balloon?
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Ideal Gas Law
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As the amount of substance could be given in mass instead of
moles, sometimes an alternative form of the ideal gas law is
useful.
The number of moles (n ) is equal to the mass m() divided by
the molar mass (M):
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Then, replacing gives:
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Density of a Gas
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Given that
D = m/V rearrange the equation to solve for the D of a
gas
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Divide by V
So D = m = PM
V
RT
P = m R T Then get only m on one side
VM
V
Density of a Gas

Calculate the density of CO2 gas. Is it more or less
dense than air.
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Calculating Molar Mass
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Calculate the molar mass (M) of a compound when a
0.100 g sample exerts a pressure of 70.5 mm Hg in a
250 mL container at 22.3 oC. The empirical formula
is CHF2. Calculate the molecular formula.
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Gas Laws and Chemical Reactions
Gas Laws and Chemical Reactions
Use the following reaction to prepare D2.
2 Li(s) + 2 D2O(l) -> 2 LiOD(aq) + D2(g)
Place 0.125 g of Li metal in 15 mL of D2O (d = 1.11 g / mL) . What
amount od D2 (in moles) can be prepared? If dry D2 gas is captured in
a 1450 mL flask at 22.o oC, what is the pressure of the gas in mm Hg?.
D has an atomic mass of 2.0147 g/ mol)
Gas Laws and Chemical Reactions
Write the reaction for the synthesis of ammonia from its elements.
Assume that 355 L of H2 gas at 25oC and 542 mm Hg is combined with
excess N2gas. What amount (mol) of NH3 gas can be produced? If
this amount of NH3 gas is stored in a 125 -L tank at 25 oC, what is the
pressure of the gas?
Gas and Partial Pressures
Dalton’s Law of Partial Pressure
the pressure of each gas in a mixture is called its partial
pressure P
the pressure of a mixture of gases is the sum of the partial
pressures of the different gases
Ptotal = P1 + P2 + P3…..
http://www.chm.davidson.edu/ChemistryApple
ts/GasLaws/DaltonsLaw.html
Dalton’s Law of Partial Pressures
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Dalton’s Law of Partial Pressures
Dalton's Law of Partial Pressures states that for
a mixture of gases in a container, the total
pressure is equal to the sum of the
pressures of each gas. The gas that a diver
breathes must be maintained at a partial
pressure of 0.20 atm of oxygen. More
oxygen could poison the diver, and less
would lead to suffocation. The total
pressure, however, must be equal to the
external pressure to avoid collapsing the
lungs. So, a special valve is used to
equalize the pressure inside the divers lungs
with the external pressure by adding helium
gas. The valve also maintains oxygen levels
by using Dalton's Law.
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Dalton’s Law of Partial Pressures
Dalton’s Law of Partial Pressures
For mixtures of gases, use the quantity mole fraction, X
X is defined as the number of moles of a gas in a mixture divided
By the total number of moles of all gasses. For a mixture of gas A
and gas B and Gas C is written as follows
Combining the above
equation yields the
important equation
Partial Pressure Problems
Mix 15.o g of C2HBrClF2 with 23.g g of O2
The total P is 855 mm Hg Calculate the P
of each gas.
The mixture above is placed in a 5.00 L
tank at 25oC. What is the total P?
What is the P of each gas?
Kinetic -Molecular Theory
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Gases are point masses in space. particles small compared to the space
they occupy.
Particles are in constant random motion
All gases, regardless of their
molecular mass, have the same
average kinetic energy at the
same temperature.
Kinetic -Molecular Theory
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http://www.bcpl.net/~kdrews/kmt/kmt.ht
ml
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http://chemed.chem.purdue.edu/genche
m/topicreview/bp/ch4/kinetic4.html
Kinetic -Molecular Theory
The kinetic energy of a single molecule of mass m is described
Below where u is the speed of that molecule.
Two important assumptions
1. Not all molecules have the same speed
2. As temp increases, the number of high speed molecules increases.
The avg KE of a sample of gas molecules depends only on T
Kinetic -Molecular Theory
A sample of gas molecules with avg speed u some molecules
Have speed u1 other molecules have u2, therefore
N is the total number of molecules
(n1 + n2 …)
Therefore, the avg KE of molecules is
related to u2 the avg of The squares of
their speeds (called mean square
speed) So the avg KE is described
below
Kinetic -Molecular Theory
http://chemed.chem.purdue.edu/genchem/topicreview/
bp/ch4/kinetic4.html#kinetic
http://www.chm.davidson.edu/ChemistryApplets/
KineticMolecularTheory/Maxwell.html
Kinetic -Molecular Theory
Kinetic -Molecular Theory
This equation relates mass, average speed, and temperature
The square root of the mean square speed, called the
Root-mean-square, or rms speed. Where T is in Kelvins
And related to molar mass, M,
Called the Maxwell equation where R = 8.3144 J / K . Mol
All gases have the same average KE at the same Temp
However, smaller molecules have greater rms speed
Kinetic -Molecular Theory
Graham’s Law of Effusion
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Diffusion is the mixing of molecules of
two or more gases due to their
molecular motions.
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Effusion is the movement of gas
through a tiny opening in a container
into another container.
Graham’s Law of Diffusion
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A molecule of an ideal gas moves
from point A to point B. The molecule
ignores the other molecules present.
It moves in a straight line path until
it collides against the wall,
bounces off, and continues to travel
in a new straight-line path, again,
ignoring other molecules that it
passes by. It behaves like it is a
billiard ball that was hit once on an
empty table.Using the expression
for the root mean square velocity
(v = square root of (3RT/M)),
at room temperature, the typical
velocity should be about 100 - 1000 m/sec.
One finds, however, that measured diffusion
rates are much slower than the
typical velocities of molecules
in an ideal gas.
Graham’s Law of Diffusion
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Diffusion times are
longer because the
average time between
collisions between
molecules is very
short. These collisions
prevent the molecules
from traveling in a
straight line motion.
Thus, it takes longer
for one molecule to
go from point A
to point B.
Graham’s Law of Effusion
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Graham’s Law of Effusion
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Graham found experimentally that the
rate of effusion of a gas is inversely
proportional to the square root of the
mass of its particles.
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Rate1 is the rate of effusion of the first gas.
Rate2 is the rate of effusion for the second gas.
M1 is the molar mass of gas 1
M2 is the molar mass of gas 2.
Nonideal Behavior: Real
Gases
Real Gases: • Are affected by intermolecular
forces of attraction (otherwise, a gas could not
become a liquid)
• Undergo non-elastic collisions
• Do occupy space These differences between how
a real gas and and ideal gas act are negligible
except at high pressures and low temperature.
Real Gases
• In the real world, the behavior of gases only
conforms to the ideal-gas equation at relatively
high temperature and low pressure.
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Nonideal Behavior: Real Gases
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Nonideal Behavior: Real Gases
Thus, for real
gases, the
following should
be expected
when the volume
of the container
becomes small
that the
molecules are
forced to be
closer to each
other:
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Nonideal Behavior: Real Gases
In real life,
condensati
on occurs.
At some
point in the
PV
diagram,
the vapor
turns into
liquid:
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Nonideal Behavior: Real Gases
Intermolecular interactions
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Nonideal Behavior: Real Gases
Intermolecular interactions
excluded volume (molecules take up space)
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Nonideal Behavior: Real Gases
Van der Waals Equation
van der Waals equation of state:
(P + (n2a/V2)) (V - nb) = nRT
a and b are the van der Waals constants
(characteristic of the gas under study)
a corrects for intermolecular interaction,
the density (n/V) is included since at higher densities,
there should be greater opportunity for
intermolecular interactions
b corrects for the volume of each molecule.
Nonideal Behavior: Real Gases
Van der Waals Equation
At large V, (n2a/V2) approaches zero.
And V-nb approaches V.
At low V (high P), the correction factors become
important.
Nonideal Behavior: Real Gases
Van der Waals Equation
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