Transcript CHE 104 notes

Packet 7
Gases
last updated: 7/7/2015
CHE 140 Packet 7 - 1
Gas Laws Crossword Handout
Why study gases?
What is our atmosphere composed of?
Gas behavior can be described by fairly
simple math formulas.
Some common elements (oxygen and
nitrogen) are gases.
Many solvents – like
gasoline – easily evaporate.
Those vapors are gases!
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Concept Area I: Terminology
atmosphere, atm
atmospheric pressure
Avogadro’s law
Boyle’s law
Charles’ law
combined gas law
dependent variable
direct relationship
ideal gas law
inverse relationship
kinetic molecular theory, KMT
mmHg
Molar volume
pressure
STP, standard temperature &
pressure
torr
universal gas constant, R
vapor pressure
independent variable
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Concept Area II: Properties of Gases
a. You should understand and be able to
explain the “basics” of KMT.
b. You should be able to explain common
observations with gases; for instance, why
hot air balloons fly, or why a smell fills a
room.
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Kinetic Molecular Theory
We’ve mentioned in chapter 2 that thermal
energy is the kinetic energy of molecules.
Molecules, atoms, and ions are always in
motion unless they are at _______________.
Of course, they are too small to see. So, we
use Kinetic Molecular Theory to explain
what is happening at the submicroscopic
level using the macroscopic properties that
we can see.
First, what determines if our submicroscopic
particles will be a gas, liquid or solid?
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Reviewing The Three States of Matter
The gas particles are zipping around like crazy.
The liquid particles are moving around a bit.
The solid particles are jiggling a little.
Above, a flask of
nitrogen liquid is
allowed to evaporate
into gas.
The gas particles are
very
far
apart.
The liquid particles are spaced out a little.
The solid particles are tightly packed.
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Kinetic Molecular Theory
1. A gas contains a large number of individual
particles that are so small as compared with the
container size that even though the particles
have mass, they have essentially no volume.
2. Average kinetic energy of a particle is
proportional to its temperature in Kelvin.
3. The gas particles constantly move in random
straight line until they collide with each other
or container walls. These collisions are
completely elastic – no energy is lost.
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Implications of Kinetic Molecular Theory
1. How are speed, kinetic energy and temperature
related?
2. What causes pressure according to this theory?
3. How can we increase the pressure of a gas?
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1. How are speed, kinetic energy and temperature related?
The ________ the speed of particles, the
________ kinetic energy they possess,
and the _________ the temperature of
the sample!
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2. What causes pressure according to this theory?
left image: Timberlake page 261
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3. How can we increase the pressure of a gas?
Increase number of collisions by
1.
2.
3.
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To summarize, why does heating a sealed
container of gas increase the pressure?
We are increasing the temperature of the
gas particles, so what is happening to the
speed of the particles? _________________
This will also __________ the number of
collisions with the container walls which in
turn will __________ the pressure!
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Now, why is there less
pressure at higher altitudes?
Because there are
________ gas particles
above items at higher
altitudes.
Yes, that’s right. At any
given time we have an
enormous amount of
pressure from all the
gases in the atmosphere
pushing down on us!
Why aren’t we crushed?
Timberlake page 262 & 264
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OK, but why does a hot air balloon rise?
Like with the sealed container, we are still
increasing the temperature of the gas particles,
however, this time the container size is not fixed.
Thus, the gas particles are allowed to
the volume they take up. Once they
do, the
. in the balloon becomes less,
and it rises!
Yes, we have to remember chapter 1 material!
Remember that
is a measure of
.
.
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Great! Then, are all
particles in a container
moving at the same speed?
According to the MaxwellBoltzmann distribution, ___.
Notice at 273 K, the most
probably speed for N2 is about
500 m/s. At 1000 K, it
increases to about 900 m/s. It
increases to about 1100 m/s at
2000 K.
At all these temperatures,
however, there are particles
moving at many other speeds –
faster & slower.
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Another question: What if the particles aren’t all the same? Would helium gas
and oxygen gas have the same most probable speed?
No, they don’t. Oxygen would move slower
than the other gases shown below. Why is
that?
Tro page 190
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Another
question:
representing He
representing O2
If we have the same
amount of oxygen
and helium in
in separate containers of equal volume at the same
temperature, which container would have the higher
pressure, if either?
Why?
Tro page 190
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One last question:
Which of the following samples of an ideal gas,
all at the same temperature, will have the
greatest pressure?
Why?
Tro page 190
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Concept Area III: Calculations with Gases
a. You need to know what STP conditions are.
b. You need to know how to convert between
millimeters of mercury, torr and atmospheres.
c. You should be able to explain and use the
following laws: Boyle’s Law, Charles’ Law,
Combined Gas Law, and the Ideal Gas Law.
d. You should be able to combine gas calculations
with stoichiometry problems.
e. You are not responsible for Dalton’s Law of
partial pressures.
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STP: Standard Temperature & Pressure
We have defined some standard conditions.
They are:
temperature:
pressure:
Be sure to memorize these values!
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What four variables will define a gas’ state?
Amount
measured in ___________________
symbol/variable used: ____
Temperature – measured in
measured in ___________________
symbol/variable used: ____
Volume – measured in
measured in ___________________
symbol/variable used: ____
Pressure – measured in
measured in ___________________
symbol/variable used: ____
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Pressure, P
P
force
F

area
A
Where F is in newtons (N) and A is in
square meters (m2). So, the SI unit for
pressure is N/m2 = pascal (Pa).
For gasses, we typically compare their
pressure against that of the atmosphere, so
we use relative pressure instead of total
pressure.
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Pressure
At 0º C and where the
force of gravity is
9.80665 m/s2, the
atmosphere exerts a
pressure that will cause
a column of mercury in
a barometer to be 760
mm tall. This is defined
as one atmosphere, atm.
So, we now know that
760 mm Hg = 1 atm.
Timberlake page 264
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Pressure Conversions
Okay, so we just learned that normal atmospheric
pressure creates a column of mercury 760 mmHg tall, so
What about other units for pressure?
Also, just for your information
760 mmHg = 101,325 Pa = 29.921 in Hg = 1.01325 bar
Now, how do we convert these equalities to conversion
factors?
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Gas Laws Demos Handout
Gas Laws Demos
Pressure
Gun
Blowing up
Balloon
Imploding
Pop Can
Balloon on
Erlenmeyer
Inflating
Basketball
Brief description
of demo set-up
Observations –
what happened
What two
variables are
involved (circle
the one we’re
changing – the
independent
variable)
Are the variables
directly
proportional or
inversely
proportional?
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Volume versus Pressure
Boyle’s Law
At constant T, P1V1 = P2V2.
Boyle noticed that as the volume
decreased on a closed container
of gas, that the pressure increased.
Upon further investigation, he found
their relationship: the volume of gas varies
inversely with its pressure.
What demonstration corresponds with this?
Also note, gas canisters use this principle so
that we can store the gas in a smaller container.
Many times, the gas is under such high
pressure that it is condensed into liquid!
updated bottom image on Timberlake page 267
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Why is Boyle’s Law
important to scuba
divers?
This very question was
asked of the main
character in Men of
Honor.
Well, what would happen
if divers held their breath
while going back up to
the surface?
bottom image Timberlake page 277
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Temperature versus Volume
Charles’ Law
V1 V2

T1 T2
At constant P,
.
Charles decided to study the effect of
temperature on volume. He found their
relationship to be linear: V a T.
What demonstration corresponds with this?
Remember, can’t have
negative volumes, so
can’t use a
temperature scale
with negative values.
Always use Kelvin!
updated top right image on Timberlake page 270
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Temperature versus Pressure
Amonton’s Law or Gay-Lussac’s Law
Our last relationship could be derived from
the previous to give: P1  P2
T1
T2
If we think back to KMT,
we should have no problem
with this relationship!
What demonstration
corresponds with this?
updated image Timberlake page 273
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Moles versus Volume
Avogadro’s Law
•
•
•
•
•Avogadro hypothesized that different gases if
compared at the same Temperature and Pressure
would have the same number of molecules in equal
Volumes.
So, if we have 1 mol of He and 1 mol of CO2, Avogadro believed those
two differently sized and massed molecules would take up the same
volume (if T and P were constant).
This idea was finally accepted (four years
after Avogadro died) in 1860.
So, at STP (Standard Temperature &
Pressure) which is 0ºC and 1 atm, 1 mol
of gas will have a volume of
22.4 L. Note, only three sig figs.
What demonstration corresponds with this?
updated images on Timberlake pages 279 & 280
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Graphing!
Let’s graph all these relationships on the
second page of the Gas Laws Demos
handout!
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See the P vs. V graph is not linear.
But, if we graph V vs. 1/P, the graph
is linear! Why is that?
Also, why is the volume on the x-axis
on the left but on the y-axis up
above?
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Note with this V vs. T graph
that we can extrapolate back
to –273.15ºC.
Why would that be?
Even though this graph is in ºC, in
calculations we must use Kelvin in
calculations! This graph is just to
help visualize where the concept
of absolute zero came from.
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The Combined Gas Law
What was found to be the single mathematical
expression for our four variables? (That’s the third
question on our handout.)
Hopefully you have noticed that that if we combine
Boyle’s Law, Charles’ Law and Avogadro’s Law we
get the Combined Gas Law: P1V1 P2 V2
n1T1

n2 T2
We can use this law to determine how one variable
changes when the other three are held constant.
Helpful problem solving hint: if problem doesn’t
mention a variable, assume it remains constant!
Remember, we only care about final and initial states.
The initial state is usually called “1” and the final state
is usually called “2”.
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Practice time!
A happy child gets a balloon at the mall. The balloon has a
maximum capacity of 5.00 L. To save on helium costs,
mall policy dictates that the balloons be filled only to
4.77 L. The mall keeps the temperature at a comfortable
22.00 ºC.
1.
Will our child still be happy upon exiting the mall if the outside
temperature is 34.20 ºC, in other words, will the balloon pop?
2.
If the balloon survives to the car, will it survive the interior
temperature of the car, 37.50 ºC?
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Another problem applying the combined gas law:
If a 20.0 lb bag of pure NH4NO3 were detonated,
what total volume of gases would be produced
at 25.0ºC and 751 torr?
2 NH4NO3(s) → 2 N2(g) + 4 H2O(g) + O2(g)
Note: the notes page for this slide show this problem worked out!
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Some problems (with answers) for home practice:
1. 3.83 L
2. 2.19 L
(don’t use
Celcius or
get wrong
answer of
2.65 L)
3. 1.43 g
4. 26.2 L
5. 0.470 g C
1. 8.73 L of Freon gas has a pressure of 735 mmHg.
What will be the volume if the pressure increases to
1675 mmHg?
2. If a gas occupies 2.15 L at 24.5ºC, how much volume
will it take up at 30.2ºC?
3. What’s the weight of 1.00L of O2 at STP?
4. What volume does 1 mol of gas fill at 30.0ºC at 720
torr?
5. Given the following reaction: 2C + O2 → 2 CO, how
many grams of carbon are needed to react completely
with 500 mL O2 gas at 30.0ºC and 740 torr? *Can also
use the ideal gas law to solve this one, and probably would use it
once we’ve learned.
Note: the notes page for this slide shows these problems worked out!
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What if conditions aren’t changing and we just want to
know the value of the one variable we don’t know (like in
that last problem)?
The Ideal Gas Law
Remember that single mathematical expression we found
for our four variables on the worksheet?
We can combine all of our relationships into one
expression:
nT
V
P
Then, introduce a proportionality constant, R, to get an
equality. R is called the gas constant and is equal to
8.314472 J/mol·K or 0.082057 L·atm/mol·K.
 nT 
V  R 
 P 
or
PV  nRT
CHE 140 Packet 7 - 38
PV  nRT
P is pressure – in atm
V is volume – in L
n is number of moles – in mol
R is the gas constant – 0.082057 L·atm/mol·K
T is temperature – in K
CHE 140 Packet 7 - 39
Solving that earlier problem with PV=nRT:
If a 20.0 lb bag of pure NH4NO3 were detonated,
what total volume of gases would be produced
at 25.0ºC and 751 torr?
2NH4NO3(s) → 2 N2(g) + 4 H2O(g) + O2(g)
Note: the notes page for this slide show this problem worked out!
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A crazy example with PV=nRT!
An experiment was done where the oxygen consumption
was measured while male cockroaches were running on
treadmills at different speeds. They found that in one
hour an average cockroach running at 0.08 km/hr
consumed 0.8 mL of oxygen (per gram of their weight)
at 1 atm and 24 ºC. So, how many moles of oxygen
would be consumed in one hour by a 5.2 g cockroach
running at that speed?
Note: the notes page for this slide show this problem worked out!
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Some problems (with answers) for home practice:
1. 9.17 L
1. 22.0 g of CO2 at 286ºC and 2.50 atm.
2. 30.0 kg
What is the volume of the CO2?
3. 0.096 atm 2. How many kilograms of helium does a balloon have if
the volume of the balloon is 1.51×105 L, the pressure
is 1.20 atm and the temperature is 22 ºC?
3. Iron reacts with hydrochloric acid to produce iron(II)
chloride and hydrogen gas. The hydrogen gas from
the reaction of 2.2 g of iron with excess acid is
collected in a 10.0-L flask at 25 ºC. What is the
pressure of the hydrogen gas in this flask?
Fe(s) + 2 HCl(aq) → FeCl2(aq) + H2(g)
Note: the notes page for this slide shows these problems worked out!
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The End of Packet 7
Any Questions?
CHE 140 Packet 7 - 43