The Gas Laws
Some things about gases:
n
n
n
n
n
n
Gases have mass
It is easy to compress a gas
Gases fill their containers completely
Gases diffuse through each other easily
Gases exert pressure
The pressure of a gas depends on its
temperature
Gases may be…
•Monoatomic: Made of one atom, like He
•Diatomic: Made of two atoms, like Cl2 or H2
*This is the case for Br, I, N, Cl, H, O, F
Also known as Miss BrINClHOF
(Brinklehoff)
•Polyatomic: Made up of more than two atoms, like
CO2, NO2, or CH4 (methane)
Gases exhibit certain behaviors:
n
Gases are composed of a large number
of particles that behave like hard,
spherical objects in a state of constant,
random motion.
Basically, gas particles are like billiard balls
in a 3-D pool table, and they are all moving
all over the place all the time in different
directions
n
These particles move in a
straight line until they collide
with another particle or the walls
of the container.
Then they bounce off, and move again- these collisions
are elastic
n
These particles are much much
(double much intended) smaller than
the distance between particles. Most
of the volume of a gas is therefore
empty space.
Compared to the container, the volume of the gas is
zero. So, we say the volume of the container is the
volume of the gas
n
There is no force of attraction
between gas particles or
between the particles and the
walls of the container.
Keep in mind- things aren’t repelled, either….no
attraction, no repulsion…
n
Collisions between gas particles or
collisions with the walls of the container
are perfectly elastic. None of the energy
of a gas particle is lost when it collides
with another particle or with the walls of
the container.
This is why gases take the shape of their container!
The energy of the system is constant as long as the
pressure and temperature remain constant.
n
The average kinetic energy of a
collection of gas particles depends
on the temperature of the gas and
nothing else.
n
Think back to the fact that temperature is a
measure of Kinetic Energy (the random
motion of molecules)
Kinetic Molecular Theory of Gases
(KMT)
1.
2.
Gases consist of very small particles ,
each of which has a mass
The distance separating gas particles
is very large- so much so that we say
the volume of the gas is negligible as
compared to the volume of the
container (the gas itself has no
volume)
KMT, continued
1.
2.
3.
4.
5.
6.
Gases have mass
Gases have no volume
Gas particles are in random, rapid,
constant motion.
Collisions with other gas particles or
the walls of the container are elastic.
The average KE of a gas depends on
the temperature of the gas.
Gas particles do not attract or repel
each other (exert no force on each
other).
Measuring Gases
We measure gases in
several ways…
• Volume
• Temperature
• Pressure
• Number of Moles
=V
=T
=P
=n
Volume (V)
• We usually measure volume in
Liters (L), but sometimes in other
metric units
1L = 1000mL
1L = .001m3
We will use these conversions- be sure
to know them!
What is Temperature?
• Temperature is a measure of heat; more
specifically it is the (average) measure of the
random kinetic energy of the molecules in an
object
• Kinetic energy: Energy of motion
• More motion = More KE = Higher temperatures
•
• Less Motion= Lower KE = Lower temperatures
Temperature (T)
• For most scientists, the Celsius scale
is used
• However, we need to use the Kelvin
scale for gas laws
Why?
• Why this strange and bizarre scale that uses a boiling
point of 373K and a freezing point of 273K for water?
• Well, kiddies, it’s because our “normal” temperature
scales are based upon numbers that make sense to use
(or not)
– (like freezing at 0°C and boiling at 100 °C) or are a bit
more convoluted (like the Fahrenheit scale, where zero
comes from the temperature of ice, water and NH4Cl and
body temperature was 98 °F and still water with ice was 32
°F. )
An Absolute Temperature
Scale
• The Kelvin scale bases temperature on an
absolute scale, where temperatures
correspond to the amount of motion of the
particles
• Absolute zero (O K) is when there is no
molecular motion (at all)
– Scientists have gotten close to O K, but not
quite there
So why do we need to use it
again?
• Calculations using temperature of
zero could be undefined or have no
value (which really can’t be)
• Can’t have negative volumes (from
using negative temperatures)
• The Kelvin scale avoids all of these
issues
The Kelvin Scale
• Is based in Absolute Zero, which is -273°C
• 0K= -273°C
• 273K=0°C
To convert between K and °C,
°C + 273 =K
or K -273 = °C
It’s that simple, which is good since no gas laws
calculations can use °C
Pressure (P)
• Gas pressure is created by the molecules
of gas hitting the walls of the container.
This concept is very important in helping
you to understand gas behavior. Keep it
solidly in mind. This idea of gas molecules
hitting the wall will be used often.
• Pressure is force measured over an area
P=Force/ area
and yes, Physics children,
Force = mass (acceleration)
Units of Pressure
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atmospheres (atm)
millimeters of mercury (mm Hg)
Pascals (= Pa)
kiloPascals (= kPa)
Standard pressure is defined as:
1 atm
1atm =760.0 mm Hg
1 atm=101.325 kPa
Measuring Pressure of
Gases
• Manometers
Manometers
• Measure the pressure of a gas as
compared to the outside world
Moles (n)
• We’ve been here before. Calm down
about it.
• Remember that 1 mole is 6.02E23
pieces of something- in this case,
usually molecules of gas (but
sometimes atoms, if not a diatomic
gas).
• Also, 1 mol gas at STP= 22.4L
• (= means occupies, takes up, etc)
A few guys and their laws….
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Dalton- Partial Pressures
Boyle- Pressure and Volume
Charles- Volume and Temperature
Gay Lussac-Pressure and
Temperature
Graham- Rate of diffusion
Avogadro- moles and volume
And a few laws with no guys…
•
Ideal Gas Law- pressure, volume,
temperature related to number of
moles
•
Combined Gas Laws- relate changes
in pressure, temperature, and volume
in a sealed container (no change in
moles)
Avogadro’s Law
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You’ve heard of him before…
He’s the guy who came up with
the number of particles in a
mole
He related the volume of a gas
to the number of moles
1mol= 22.4L gas at STP
The more moles, the higher the
volume
Dalton’s Law of Partial
Pressures
•
The total pressure in a
sealed container of gas
are the sum of all the
partial pressures of the
gases in the container
•
PT= P1+P2+P3…. For as
many gases are present
Using Dalton’s Law….
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What is partial pressure of oxygen gas in a
container of oxygen, nitrogen, and
hydrogen, if the partial pressure of nitrogen
is 0.68atm, the partial pressure of
hydrogen is 0.24 atm, and the total
pressure is 1.02atm?
PT= P1+P2+P3
PT= Pnitrogen+Phydrogen+Poxygen
1.02atm= 0.68atm + 0.24 atm +Poxygen
1.02atm-0.68atm-0.24atm=Poxygen
Boyle’s Law
•
Relates pressure
and volume,
while
temperature and
number of moles
are constant (so
they do not
appear in the
equation)
Boyle’s Law:
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P1V1=P2V2
In a closed rigid container of a gas at a
constant temperature, the pressure times
the volume remains constant (P1V1=k)
Pressure and volume are inversely related
The P1 is the pressure at the first volume
(V1), while P2 is the pressure at the second
volume (V 2).
Boyle’s Law: P1V1=P2V2
•
The product of
pressure and
volume remains
constant as long as
the temperature
remains constant.
(The number of
moles must also
remain constant.)
Volume
Pressure
• When volume is
high, pressure is low
• When the volume is
low, pressure is high
Using Boyle’s Law
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If a balloon with a volume of 3L is under a
pressure of 1 atmosphere, determine the
new volume if the pressure is changed to
.8 atm.
We are given P1, V1, and P2. We are
asked to find V2
Two key words here are new and
changed- to ID these measurements as
linked (having the same subscript)
What is the new volume?
Charles’ Law
•
Charles’ law relates
volume and
temperature, at a
constant pressure
and number of moles
in a flexible container.
Since the pressure
and number of moles
are constant, they do
not appear in the
equation.
Charles’ law
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•
V1/T1=V2/T2
In a closed container of a gas at a
constant temperature, the pressure
times the volume remains constant
(V1/T1=k)
The T1 is the temperature at the first
volume (V1) while T2 is the temperature
at the second volume (V 2).
Charles’ Law
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V1/T1=V2/T2
V1T2=V2T1
can be rearranged to read
Why would we care to rearrange this?
This means no division in the equation.
You can use it either way, just remember
that they are DIRECTLY
PROPORTIONAL.
Charles’ Law
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As the temperature increases, the volume
increases.
As the temperature decreases, the volume
decreases.
Temperature and volume are
proportionally related.
Chuck’s law (still…)
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Think again about temperature- it is the
KE of the gas particles.
Think about what the volume is a result
of: the force that the gas molecules are
exerting of the container
Think about how if something hits
another thing at a higher speed- it hits
with more force. More force is pushing
harder. Pushing harder means further.
This means greater volume when we
are dealing with a flexible container!
Gay Lussac’s Law
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Relates pressure and temperature,
when volume is kept constant
(P1/T1=k)
P1/T1= P2/T2 Or P1T2=P2T1
As the temperature increases, the
pressure increases.
As the temperature decreases, the
pressure decreases.
Combined Gas Law (Putting it all
together)
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(P1V1)/ T1=(P2V2)/T2
Takes all other gas laws into account,
even if you can’t see them here (they
cross out of the equation)
When in doubt about most of the
guy’s laws, you can use this one,
because when the pressure, volume,
or temperature is constant, you have
the law you need.
Ideal Gas Law
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First, a few words about ideal gases:
Ideal gases follow the gas laws at ALL
pressures and temperatures
Ideal gases cannot be liquefied by cooling
and/ or applying pressure
KMT assumes that all gas molecules
have no attraction to each other, and
has no volume
These above statements aren’t true
However, in most cases, all gases behave
like ideal gases, so the gas laws hold true
in most cases
The Ideal Gas Law
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PV=nRT
n= number of moles
R= ideal gas constant
– R=.0821 atm L/ mol K
– R= 62.4 mmHg L/ mol K
– R= 8.31E3 Pa L/ mol K
Why so many Rs? Different measurements of
pressure
Graham’s Law of Effusion
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Diffusion: tendency of ions and
molecules to move from an area of
high concentration to an area of low
concentration
Effusion: Gases escaping from a tiny
hole in a container (because of
diffusion or pressure differences)
– The rate of effusion of a gas is inversely
proportional to the square root of its
molar mass
More on Graham’s Law…
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KE= ½mv2
So, when two bodies having the same
KE but different masses, the smaller
one must be moving faster….why
does this matter?
If two gases in a container have the
same temperature (the same KE), the
lighter one must be moving faster
Graham’s Law
Rate A
_______
Rate B
√ molar mass B
=
______________
√ molar mass A
Lighter gases effuse faster- that’s why party
balloons filled with He are must faster to
deflate than those filled with air (air is mostly
heavier N2 and O2)