Gases
Chapter 5
Gas as a Phase
• Remember,
Gases do NOT have a definite size, shape,
or volume. They will form to the size and
volume of a container
They will move and float freely within in all
3 dimensions
Compressibility
• Gases are compressible…
This means that we can squeeze a gas
and alter its size, shape, and even
volume
What happens to a gas’s pressure if I
squeeze it in and shrink (or decrease
its volume)?
A Background
• Gases are very easily manipulated and
controlled
• They are compressible
• We can manipulate a gas’s pressure,
temperature, and even volume (which all have
an effect on each other)
Pressure
• Pressure of a gas is caused by collisions of the
gas particles with the sides of the container
• They are
causing a
driving force
outward and
the faster they
move, the
more collisions
they have…
the more
collisions they
have the
higher the
pressure
Pressure
• Pressure is defined as the amount of force
exerted on a given area
𝐹𝑜𝑟𝑐𝑒
𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 =
𝐴𝑟𝑒𝑎
Or…
𝐹
𝑃=
𝐴
Applications
• Think about ice skating
• The blades are very sharp to
maximize the
pressure exerted
Apply Pressure to Gases
• If I have a sealed container…
– What would happen if I increased the number of
gas particles but did nothing to the size of the
container… how would the pressure be affected?
Pressure Units
• Remember, units are everything!!
• When in doubt, they will tell you what to do!
• There are many units of pressure, all of which
can be converted to and from each other
using conversion factors
A Gas’s Basic Properties
• A sample of gas has 4 basic properties (4
things that are manipulate-able)
– Its pressure (P)
– Its temperature (T)
– Its volume (V)
– The amount in moles (n)
Interrelated Properties
• The “simple” gas laws
describe the relationships
between pairs of these
properties (i.e. P & T, T &
V, V & P, etc.)
• The properties not in the equation are said to be “held
constant” or left unchanged
Boyle’s Law
• Relates VOLUME and PRESSURE
• States that volume is inversely proportional to
pressure… meaning the higher the pressure,
the lower the volume, and vice versa
PV = constant
P1V1 = constant = P2V2
• So… Boyle’s Gas Law is
P1V1 = P2V2
Practice
• A cylinder equipped with a movable piston
has a volume of 7.25 L under an applied
pressure of 4.52 atm. What is the volume of
the cylinder if the applied pressure is
decreased to 1.21 atm?
Practice
• A snorkeler takes a syringe filled with 16 mL of
air from the surface, where the pressure is 1.0
atm, to an unknown depth. The volume of the
air in the syringe at this depth is 7.5 mL. What
is the pressure at this depth?
Charles’s Law
• Relates Volume (V) and Temperature (T)
– MUST hold pressure constant 
• What do you think happens to the volume of a
gas when you increase / decrease the temp??
• What causes pressure? Volume? What
happens to the Kinetic Energy when you warm
something up?
• As you increase temperature, the volume will
increase proportionally
The Kelvin Scale
• When using gas laws (and thermo) ALWAYS use
temp units of Kelvin
• Remember, -273.15⁰C = 0 K (Absolute Zero)
• If we “extrapolate” or “go backwards” on the
graph of T vs V all gases will meet at an identical
volume (meaning does not decrease anymore) at
the temperature of ___________
Charles’s Law
• Charles’s Law states that at a constant P, the
temperature will increase proportionally with
the volume
VαT
• Mathematically:
𝑉1
𝑉2
=𝑘=
𝑇1
𝑇2
Practice with Charles’s Law
• A sample of gas has a volume of 2.80L at an unknown
temperature. When the sample is submerged in ice
water at T = 0.00⁰C, its volume decreases to 2.57 L. What
was its initial temperature (in K and in ⁰C)?
Practice with Charles’s Law
• A gas in a cylinder with a moveable piston has an initial
volume of 88.2 mL. If the gas is heated from 35⁰ C to
155⁰C, what is its final volume (in mL)?
Pressure and Temperature
• What happens to pressure as you increase
temperature? And vice versa??
• As pressure increases, the temperature also
increases
• This is a _______________ relationship
Gay-Lussac’s Gas Law
𝑃1
𝑃2
=𝑘=
𝑇1
𝑇2
Or
𝑃1 𝑃 2
=
𝑇1 𝑇 2
Practice with Gay-Lussac’s Law
• If a marshmallow originally at 37⁰C is placed in
the microwave and warmed to 55⁰C, what was
its initial temperature if it expands to 17.1 mL?
Combining them all 
• Because the four properties all affect each
other, we can combine them all to form one
“super” gas law… known as the combined gas
law
• The Combined Gas Law can be used to
determine (or figure out) all of the others we
have discussed so far…
The Combined Gas Law
• We can set these equations equal to a common variable
and then set them equal to one another
• By doing this, we can derive a COMBINED GAS LAW
P1V1 = P2V2
T1
T2
• This equation enables us to make calculations consisting of
varying pressures, temperatures, and volume (holding
nothing but the number of moles constant).
The Combined Gas Law
𝑃 1 𝑉1 𝑃 2 𝑉2
=
𝑇1
𝑇2
Simply cover up the variable that is held
constant to reveal the other gas laws
The Combined Gas Law
𝑃1𝑉1 𝑃2𝑉2
=
𝑇1
𝑇2
If you saw this as…
𝑃1𝑉1𝑇2 = 𝑃2𝑉2𝑇1
Would it be easier to “cross-multiply” ??
Practice with the Combined
• A soda bottle has a volume of 1.50 L at 25ºC
at standard pressure (1.00 atm). The bottle is
then taken to the bottom of the ocean to a
temp of 1.00ºC and a pressure of 0.67 atm.
What will the new volume of this bottle be?
Problems with these
• No gas perfectly obeys all four of these laws under all
conditions
• These assumptions work well for most gases and most
conditions
• One way to model a gas’s behavior is to assume that
the gas is an ideal gas that perfectly follows these laws
– Does not condense to a liquid at low temps
– Does not have forces or attraction or repulsion between
the particles
– And is composed of particles that have no volume
Volume-molar relationships
• Avogadro!!
• States at the same temperature and pressure, balloons of
the same volume with contain the SAME number of moles
of gas, REGARDLESS of the gasses identity.
• H2, O2, CO2, it does not matter!!
• 1 mole of gas = 22.41 L. The mass of a gas at 0ºC and 1 atm
(STP) is equal to the gas’s molecular (molar) mass
V = kn, where k is the proportionality constant
Relationship between V and n
(number of moles)
• What happens when the amount of gas
changes?
– Not a trick question…
• The volume will go up as the amount of gas (in
moles) goes up
Proportionally or Inversely ??
Avogadro’s Law
• As long as the pressure and temperature are
held constant
𝑉1
𝑉2
=𝑘=
𝑛1
𝑛2
This relationship proposed that the volume of 1
mol of gas (at STP) is = 22.41 L
Avogadro’s Law Practice
• A 4.65 L sample of helium gas contains 0.225 mol of
helium. How many additional moles of helium gas must
be added to the sample to obtain a volume of 6.48 L?
Assume constant temperature and pressure.
Avogadro’s Law Practice
• A chemical reaction occurring in a cylinder equipped with
moveable piston produces 0.621 mol of a gaseous
products. If the cylinder contained 0.120 mol of gas
before the reaction and had an initial volume of 2.18 L,
what was it volume after the reaction?
Practice
• The gauge pressure in a tire is 28 psi, which
adds to atmospheric pressure of 14.0 psi.
What is the internal tire pressure in kPa?
• A gas sample has a volume of 125 mL at 91.0
kPa. What will its volume be at 101 kPa?
Practice
• A gas at 65ºC occupies 4.22 L. At what Celsius
temperature will the volume be 3.87 Liters, at
the same pressure?
• A scientist warms 26 mL of gas at 0.0ºC until
its volume is 32 mL. What is its new
temperature in Kelvin?
Practice
• A sample of hydrogen exerts a pressure of
0.329 atm at 47ºC. What will the pressure be
at 77ºC, assuming constant volume?
• A cylinder of gas at 55 kPa and 22ºC is heated
until the pressure is 655 kPa. What is the new
temperature??
Practice
• A balloon has a volume of 1.25 liters and a temperature of
20ºC. The pressure when filled was 1.05 atm. The balloon
was released and allowed to float away, reaching 1.87
kilometers where the pressure is 0.667 atm and a
temperature of -100 C, what would the new volume of the
balloon be?
The Ideal Gas Law
• Combining the properties into one single
“snap shot” of a gas scenario derives the
“ideal gas law”
PV = nRT
• “R” is known as the ideal gas constant. It is
the same for all gases and depends on (or is
determined by) the units of PRESSURE
PV=nRT
P = Pressure
V = Volume
n = number of moles of gas
R = Universal gas constant
8.314 L*kPa*mol-1*K-1
or 0.0821 L*atm*mol-1*K-1
T = Temperature of gas
** If you are given a unit of pressure that you
cannot find an R value for (or cannot remember)
what are your options??
CONVERT TO A BETTER PRESSURE UNIT!!
Practice Converting
Convert the following:
1.87 atm to torr
715 mmHg to torr
814 mmHg to atm
132 psi to mmHg
Practice
• How many moles of argon are there in 20.0 L, at 25ºC and 101 kPa?
• How many moles of air are in 1.00 L at -23ºC and 101 kPa?
• A weather balloon is inflated with 12.0 g of He at -23ºC and 100.0
kPa. What is its volume?
STP
• Standard Temperature and Pressure (STP) is used
in chemistry to stay uniform
273 K (0⁰C) and 1 atm of pressure
• What would the volume of a 1 mole of gas be at
STP?
𝑛𝑅𝑇
𝑃
𝑉=
=
𝐿∗𝑎𝑡𝑚
(1.00𝑚𝑜𝑙)(0.08206
)(273K)
𝑚𝑜𝑙∗𝐾
1.00 atm
Question
• Assuming ideal gas behavior, which of the
following gas samples will have the greatest
volume at STP?
a) 1 g H2
b) 1 g O2
c) 1 g Ar
Recall Density
• What was density equal to?
𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠
𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑚𝑜𝑙𝑎𝑟 𝑣𝑜𝑙𝑢𝑚𝑒
• With the help of some algebra magic  we can derive
the following relationship:
𝑑=
𝑃𝑴
𝑅𝑇
(with M being the molar mass)
• Any relationship you know can be
“substituted” in to help solve problems
• For example… you know that
𝑚𝑎𝑠𝑠
𝑛=
𝑀
and so
𝑚𝑎𝑠𝑠 𝑚
𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 =
𝑚𝑜𝑙𝑒𝑠 𝑛
Practice
• A sample of gas has a mass of 0.311 g. Its volume is
0.225 L at a temperature of 55⁰C and a pressure of
886 mmHg. What is its molar mass?
• GET YOUR UNITS IN ORDER FIRST!!
• Using the R=0.08206L*atm*mole-1*K-1 you see you must convert
to atmospheres from mmHg
Hint: Solve for “n” and then use the mass to find the
molar mass
Gases are ADDITIVE
• Because gases (at the same conditions)
behave in the same way, we can add them
together
• Dalton’s Law of Partial Pressures:
𝑃𝑡𝑜𝑡𝑎𝑙 = 𝑃𝑎 + 𝑃𝑏 + 𝑃𝑐 +. . .
Practice
• A mixture of CO2, CO, H2, and N2 are floating
around in a reagent bottle. The pressure of
the system is 0.25 atm. The pressures of the
gases are 0.002 atm, 0.058 atm, 0.084 atm,
and unknown, respectively. Calculate the
pressure of the N2 component.
Practice
• A 1-Liter mixture of He, Ne, and Ar has a total pressure of
662 mmHg at 298 K. If the partial pressure of helium is
341 mmHg and the partial pressure of neon is 112
mmHg, what mass of argon is present in the mixture?
Vapor Pressure
NOW FOR THE FUN STUFF!!
Gas STOICHIOMETRY!!
Gas Stoich
• Because there is an “n” in the ideal gas law
(number of moles) we can make
stoichiometric conversions using reactions
• What volume (in liters) of hydrogen gas, measured at
a temperature of 355 K and a pressure of 738 mmHg,
is required to synthesize 35.7 g of methanol?
___CO(g) + ___H2(g)  ___CH3OH(g)
• In the following reaction, 4.58 L of O2 was formed at
P = 745mmHg and T = 308K. How many grams of
Ag2O must have decomposed?
___Ag2O(s)  ___Ag(s) + ___ O2(g)
Kinetic Molecular Theory
• There are a few rules (or assumptions) for gases
to follow
1. Gases move in a straight line until they hit
something
2. The size of the particle is negligible
3. The average kinetic energy or a particle is
proportional to temperature in Kelvins
4. The collision of one particle with another (or with
the walls) is completely elastic (meaning they
bounce straight back and unaffected)
Gas Motion
• Diffusion – the movement of particles from
regions of higher density to regions of lower
density.
– Odor of ammonia smelling up the room
– Involves an increase in entropy (measure of
randomness)
• Effusion – the passage of a gas under pressure
through a tiny opening
– Like out of a leaking tire
• The smaller the gas particle, the faster it will
move (on average)
• The larger it is, the slower it travels
Wasn’t that fun??
Problems with Gases
• No gas perfectly obeys all of these laws under all
conditions
• These assumptions work well for most gases and most
conditions
• One way to model a gas’s behavior is to assume that
the gas is an ideal gas that perfectly follows these laws
– Does not condense to a liquid at low temps
– Does not have forces or attraction or repulsion between
the particles
– And is composed of particles that have no volume
• A real gas deviates from the ideal gas behavior at low
temperature and high pressure
• The volume of the particles themselves is close to the
total volume, so the actual volume will be higher than
calculated.
• So, with regards to the Ideal Gas Law, low temperature
and high pressure is BAD!!
– Condensation and particle attractions as they get closer
Remember This!!!
Ideal vs. Real
• These laws and assumptions are great for
ideal gases but what about real gases?
•
•
•
•
Real gases do interact with one another…
Real gases do come into contact with one another…
Real gases do have mass…
Real gases (the particles themselves) do have
volume…
• Real gases do condense into liquids at low temps…
All Done 
• Do you have gas yet?? ASSIGNED PRACTICE
PROBLEMS ARE A MUST IN THIS UNIT!!