Transcript Slide 1

The Gas Laws
Boyle, Charles, Combined, and Ideal
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Kinetic Theory
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Explains the states of matter in terms of
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molecular composition
Spacing
speed
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According to the theory...
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1. Matter composed of small particles
A. chemical properties- depend on
a. composition
b. types of elements / molecules present.
B. physical properties- depend on
a. forces that particles exert on each other
b. distance separating the particles.
2. Particles are in constant motion.
Degree of motion depends on temperature.
3. Total kinetic energy of colliding particles remains constant.
elastic collisions - as indiv. particles collide
some gain Ek and some lose Ek.
Overall Ek is constant.
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States
of
Matter
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Solids
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appear to vibrate around a fixed point
(Extremely short free mean path)
have definite shape
“
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volume
noncompressable
very slow rate of diffusion
crystalline or amorphous in nature
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Liquids
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particles are closer than those of gases
forces of attraction between particles
stronger than those of gases, and
weaker than those of solids.
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Gases
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The Kinetic Theory was developed by studying
an ideal gas, a mathematically perfect gas.
[Particles are treated as 1) point masses; as
having no volume, and 2) as exerting no
attractive forces on each other.
Space occupied by gas depends on
temperature and pressure.
When describing a quantity of a gas
temperature and pressure MUST be specified.
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Standard Temperature & Pressure
S.T.P.
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Standard Temperature
0o C
273 K
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Standard Pressure
760 mm Hg
760 n/m2
760 Torr
101.325 kPa
1 atm
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Properties of Gases
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Particles in a gas are
in rapid, constant
motion.
Gas particles travel in
straight-line paths.
Gas particles fill
containers.
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Properties of Gases
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Exerts Pressure
increases / decreases with a rise / fall
in temperature
Have Low density
1000x less dense than liquid
counterpart
Undergo Diffusion
spread out from area of greater to lesser
concentration until uniform spacing exists
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Properties of Gases
Less Dense
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Atmosphere is denser
as you move closer to
Compression
Earth’s surface.
The weight of
atmospheric gases at
any elevation
compress the gases
below.
Very Dense
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At room temperature gases...
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are molecular
move independently of each other
travel at high speeds
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At 0oC
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travel at about 1000 m/sec.
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undergo elastic collisions
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Goal to goal in .11 sec
alters individual speeds, but not overall Ek.
collide nearly 5 BILLION times per
SECOND!
have different rates of diffusion
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Less concentrated - diffusion rate 
More concentrated - diffusion rate 
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Diffusion rate depends on...
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speed of gases
size of the molecules
attractive forces that may effect the
molecules
At the same temperature:
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the average kinetic energy of all molecules is
the same.
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GAS and PRESSURE
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Gas molecules exert pressure by hitting against
the side of its container.
Degree of pressure dependent on:
1. # of gas particles present*
2. volume [size] of the container*
3. average Ek of the molecules *
[temperature]
Changing any of these conditions changes the
pressure.
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A barometer is a device that is used to
measure atmospheric pressure.
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GAS and PRESSURE
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VOLUME and PRESSURE
To test only ONE variable at a time, the
following must be held constant.
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1. # of gas particles present
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2. average Ek of the molecules
[temperature]
Boyle’s Law animation
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VOLUME and PRESSURE
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We can see that pressure is
inversely proportional to volume
P1
V
PV = k
P1V1 = k
and
P1V1 = P2V2
or
V1 = P2
V2
P1
P2V2 = k
Boyle’s Law
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How are the pressure, volume, and
temperature of a gas related?
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Boyle’s law states that for a given mass of
gas at constant temperature, the volume of
the gas varies inversely with pressure.
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As pressure decreases, volume increases
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DALTON’S LAW of PARTIAL
PRESSURE
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The pressure of each gas in a mixture is
called the partial pressure of that gas.
John Dalton, the English chemist who
proposed the atomic theory, discovered
that the pressure exerted by each gas in a
mixture is independent of that exerted by
other gases present.
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Particle Model for a Gas Collected Over Water
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DALTON’S LAW of PARTIAL
PRESSURE
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Gases produced in the laboratory are often collected
over water. The gas produced by the reaction displaces
the water in the reaction bottle.
Dalton’s law of partial pressures can be applied to
calculate the pressures of gases collected in this way.
Water molecules at the liquid surface evaporate and mix
with the gas molecules. Water vapor, like other gases,
exerts a pressure known as vapor pressure.
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DALTON’S LAW of PARTIAL
PRESSURE
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Hg originally used to measure the pressure of
gases
Now known to be a carcinogen
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‘Mad as a hatter’
H2O replaced Hg
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several problems exist
Density is 13.6 x greater than mercury
Much more volatile.
Evaporates much faster.
Gases to be tested polluted with water’s vapor
pressure.
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DALTON’S LAW of PARTIAL
PRESSURE
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In a mixture of gases [G1, G2, G3, ...] the
TOTAL pressure of the gas mixture is the
SUM of the pressures of the individual gas
pressures.
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Total Pressure = PressureG1 + PressureG2 + Pressure G3 + ...
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If one of these gases is water
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Total Pressure = PressureG1 + PressureG2 + Pressure Water + ...
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To ‘dry out’ a gas
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Total Pressure = PressureG1 + PressureG2 + Pressure Water + ...
- Pressure Water
Pressure DRY gas = PressureG1 + PressureG2 + ...
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Application of Dalton’s Law
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A gas is collected by water displacement.
It occupies 593 cm3 of space at 45 oC.
The atmospheric [total] pressure is 101.1
kPa. What volume will the dry gas occupy
at 45 oC and standard pressure?
V1 = 593 cm3
V2 = ?
P1[wet] = 101.1 kPa P2 = 101.325 kPa
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P1V1 = P2V2
[101.1kPa*][593 cm3] = [101.325 kPa] V2
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At 45 oC, PH2O = 71.9 mm Hg
Since 760 mm Hg = 101.325 kPa
101.325 kPa = ___x___
760 mm Hg
71.9 mm Hg
9.6 kPa = x
101.1 kPa - 9.6 kPa = 91.5 kPa Pressure of the dry gas
[91.5 kPa][593 cm3] = [101.325 kPa] V2
[91.5 kPa][593 cm3] = V2
[101.325 kPa]
535.5 cm3 = V2
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Example B
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Oxygen gas from the decomposition
of potassium chlorate, KClO3, was
collected by water displacement. The
barometric pressure and the
temperature during the experiment
were 731.0 torr and 20.0°C.
respectively. What was the partial
pressure of the oxygen collected?
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Solution
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Given:
PT = Patm = 731.0 torr
PH2O = 17.5 torr (vapor pressure of
water at 20.0°C)
Patm = PO2 + PH2O
PO2  731.0 torr  17.5 torr  713.5 torr
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Diffusion and Effusion
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constant motion of gas molecules causes
them to spread out to fill any container they are
in.
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gradual mixing of two or more gases due to
their spontaneous, random motion is known as
diffusion.
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Effusion is the process whereby the molecules of
a gas confined in a container randomly pass
through a tiny opening in the container.
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Diffusion and Effusion
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Click here to view diffusion animation
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Click here to view effusion animation
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Graham’s Law of Effusion
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Rates of effusion and diffusion depend on
the relative velocities of gas molecules.
The velocity of a gas varies inversely with
the square root of its molar mass.
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Recall that the average kinetic energy of the
molecules in any gas depends only the
temperature.
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Graham’s Law of Effusion
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From the equation relating the kinetic energy of two different gases
at the same conditions, one can derive an equation relating the
rates of effuses of two gases with their molecular mass:
Average kinetic energy = temperature
Ek = 1/2mv2
Molecule 1 has a Ek1= 1/2mv2
Molecule 2 has a Ek2 =1/2mv2
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Graham’s Law of Effusion
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At the same temperature
Ek1= Ek2
1/2m1v2 = 1/2m2v2
m1v2 = m2v2
m1 = v22
m2 v 1 2
√m1 = v2
 m2 v1
Or
√m1 = rate of effusion of 2
 m2 = rate of effusion of 1
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What are the relative effusion rates
of krypton (Kr) and bromine (Br2)?
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 mKr = vBr2
 mBr2 vKr
 84 =
 160
.72 = vBr2
1
vKr
Therefore, Br2 diffuses slower than Kr, at about
72% of Kr’s speed.
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GAS and TEMPERATURE
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Jacques Charles studied the effect of
temperature on gases
To test only ONE variable at a time, Charles held
the following constant.
1. # of gas particles present
2. gas pressure
From his experiments he discovered that all
gases expand and contract to the same degree,
with a set temperature change.
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GAS and TEMPERATURE
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Volume changes by 1/273 of the original volume
for each degree change in temperature.
At 0oC a gas has a volume of 1 m3. If the temperature
is lowered to a -2730C the gas volume would
theoretically be reduced to zero!
absolute zero- the temperature at which a
gas
1] has no volume
2] has no Ek
Gas temperatures are ALWAYS measured in
KELVINS.
Charles Law animation
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Charles’ Law
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GAS and TEMPERATURE
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V  T
V = k
T
V1 = k
V2 = k
T1
T2
Charles’ Law
 V1 = V2
T1
T2
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Charles’ Law
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Charles’s law states that the volume of a fixed
mass of gas is directly proportional to its Kelvin
temperature if the pressure is kept constant.
Temperature in Kelvin (K)
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Charles’ Law
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As the temperature of the water
increases, the volume of the balloon
increases.
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V 1 =V 2
T1 T 2
4.00L = V2
297K 331K
Cross multiply and solve for the missing variable, V2.
The answer is:
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Temperature and Pressure
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Gay-Lussac’s Law
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Joseph Louis Gay-Lussac in the early 1800's.
To test only ONE variable at a time, GayLussac held the following constant.
1. # of gas particles present
2. volume
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Temperature and Pressure
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Pressure and
temperature are
directly proportional
to each other
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P1 = k
T1
P2 = k
T2
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CHANGING MORE THAN ONE
VARIABLE
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It is highly possible that several
environmental factors may change at the
same time.
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The Combined Gas Law
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The combined gas law describes the
relationship among the pressure,
temperature, and volume of an enclosed gas.
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(30.0L)(153kPa) = V2 (101.325kPa)
313K
273K
Cross multiply and solve for V2.
V2 = 39.5L
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IDEAL GASES
* No volume
* Not effected by attractive
forces
*mathematiclly perfect
REAL GASES
* Has volume
* Some attraction
between particles
*variable in selected
situations
Gas Laws Fail when:
1. molecules are forced very close together due to
extremely HIGH PRESSURE. [inter-molecular attraction]
2. molecules move too slowly to pull away from the
attraction generated by other molecules. Molecules are
displaying LOW kinetic energy; LOW TEMPERATURE.
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EXPLOITING GAS TENDENCIES
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Joule-Thomas Effect
Highly compressed gas, allowed to escape through a
small opening causes the temperature to drop.
Explanation:
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when molecules move apart from each other work must be
done.
energy for the work comes from Ek
since Ek is the same as the temp, when it is used the temp drops
aerosol cans cool as the gas escapes
refrigerators
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Low Pressure Gas
High Pressure Gas
Compressor
Evaporator
Condenser
Throttle Valve
Low Pressure Liquid
High Pressure
Liquid
Very NarrowOpening
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Gases and the Mole
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Two identical cubes filled with a gas
Temperature for both cubes is constant [the
same]
Pressure is dependent on ... ?
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Gases and the Mole
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Pressure is dependent on the amount gas
in each box.
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Gases and the Mole
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If the pressure in the boxes are equal and
the amount gas in the boxes are equal,
what can be said about the number of gas
molecules in each box?
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10.2
The Mole–Volume Relationship
Avogadro’s
hypothesis states that equal volumes of
gases at the same temperature and pressure contain
equal numbers of particles.
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Avagadro’s Principle
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Under the same conditions of temperature and
pressure, the number of molecules of ANY GAS
present in a specific volume is equal.
At S.T.P.
1 mole of any gas occupies 22.4 L
1 mole = 22.4 L
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The quantity 22.4 L is called the molar volume of a
gas.
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Avagadro’s Principle
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Remember 1 mole contains 6.02 X 1023
particles.
Therefore, at S.T.P.
1 mole = 22.4 L = 6.02 X 1023 particles
= gram formula wt.
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Ideal Gas Law
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Relates
temperature
pressure
volume
number of particles, or moles
PV = nRT
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Ideal Gas Law
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P = pressure in either kPa, mm Hg or atm
V = volume in L
n = number of moles
R = gas law constant; 8.314 L kPa,
K mol
62.4 L mm Hg , or .0821 L atm
K mol
K mol
T = temperature in Kelvin
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Which equation do I use???
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Given conditions of temperature, pressure,
and/or volume:
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Combine Gas Law
Amount [moles / grams]
is given or ask for:
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Ideal Gas Law
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