Leyte National High School
Behavior of Gases
An Overview of the Physical States of Matter
Distinguishing gases from solids and liquids:
• Gas volume changes significantly with pressure
- Solid and liquid volumes are not greatly affected by pressure.
• Gas volume changes significantly with temperature
- Gases expand when heated and shrink when cooled
- The volume change is 50 to 100 times greater for gases than for liquids and solids
• Gases flow very freely
• Gases have relatively low densities
• Gases form a solution in any proportions
- Gases are freely miscible with each other
Pressure
Pressure is the force exerted on a given area,
𝐹
𝑃=
𝐴
Atmospheric pressure arises from the force exerted by atmospheric gases on the Earth’s
surface.
Atmospheric pressure decreases with altitude.
Pressure
The SI unit of pressure is the pascal (Pa), named after Blaise Pascal, a French scientist who
studied pressure: 1 Pa = 1 NΤm2 . A related pressure unit is the bar: 1 bar = 105 Pa = 105 NΤm2 .
Another pressure unit is pounds per square inch (psi, lbsΤin2 ). At sea level, atmospheric pressure
is 14.7 psi.
Pressure
Evangelista
Torricelli
invented
the
barometer, which is made from a glass tube
more than 760 mm long that is closed at
one end, completely filled with mercury, and
inverted into a dish of mercury.
Pressure
Standard
atmospheric
pressure,
which
corresponds to the typical pressure at sea
level, is the pressure sufficient to support a
column of mercury 760 mm high. In SI
units, this pressure is 1.01325 x 105 Pa.
Pressure
Standard
atmospheric
pressure
defines
some common non-SI units used to express
gas pressure, such as the atmosphere
(atm) and the millimeter of mercury (mm
Hg). The latter unit is also called the torr,
after Torricelli: 1 torr = 1 mm Hg.
The Gas Laws
The gas laws describe the physical behavior of gases in terms of 4 variables:
- Pressure (P)
- Temperature (T)
- Volume (V)
- Amount of moles (n)
The Gas Laws
The Pressure-Volume Relationship: Boyle’s Law
Boyle’s law states that the volume of a fixed quantity of gas maintained at constant
temperature is inversely proportional to the pressure.
The Gas Laws
The Pressure-Volume Relationship: Boyle’s Law
1
𝑃∝
𝑉
At fixed T and n,
P decreases as V increases
P increases as V decreases
P1 V1 = P2 V2
The Gas Laws
The Temperature-Volume Relationship: Charles’ Law and Gay-Lussac’s Law
Charles’ law states that the volume of a fixed amount of gas maintained at
constant pressure is directly proportional to its absolute temperature.
The Gas Laws
The Temperature-Volume Relationship: Charles’ Law and Gay-Lussac’s Law
𝑉∝T
At fixed P and n,
V decreases as T decreases
V increases as T increases
V1 V2
=
T1 T2
The Gas Laws
The Temperature-Volume Relationship: Charles’ Law and Gay-Lussac’s Law
P∝T
P1 P2
=
T1 T2
The Gas Laws
The Volume-Amount Relationship: Avogadro’s Law
Avogadro’s law states that the volume of a gas maintained at constant temperature
and pressure is directly proportional to the number of moles of the gas.
V∝n
V1 V2
=
n1 n2
The Gas Laws
Boyle’s law
Charles’ Law
The Gas Laws
Gay-Lussac’s law
Avogadro’s Law
The Gas Laws
The Ideal Gas Equation
We can combine all three expressions to form a single master equation for the
behavior of gases:
or
nT
V∝
P
nT
V=R
P
PV = nRT
This is the ideal gas equation, which describes the relationship among the four
variables P, V, T, and n. An ideal gas is a hypothetical gas whose pressure-volumetemperature behavior can be completely accounted for by the ideal gas equation. No
ideal gas actually exists, but most simple gases behave nearly ideally at ordinary
temperatures and pressures.
The Gas Laws
Gas Behavior at Standard Conditions
STP or Standard Temperature and Pressure specifies a pressure of 1 atm (760 torr) and
a temperature of 0°C (273 K).
Experiments show that under these conditions, 1 mole of an ideal gas occupies 22.414 L,
which is somewhat greater than the volume of a basketball.
Sample Problem 1 (Pressure)
The pressure inside the cabin of an airplane decreases
to 10.9 psi during a high-altitude flight. Convert this
pressure value to units of:
a.millimeters of mercury (mmHg)
b.atmospheres (atm)
c. Kilopascals (kPa)
Sample Problem 2 (Boyle’s Law)
A weather balloon is about to be launched from the
weather station. The balloon has a volume of 56.0 liters
at a pressure of 18.2 psi. Once launched, the balloon
rises to a higher altitude where the pressure has
decreased to 12.7 psi. Determine the volume of the
balloon.
Sample Problem 3 (Charles’ Law)
Will purchases a set of helium balloons at the local
card shop. Each balloon occupies a volume of 15.5 liters
when in the store; but when taken outside, they are
observed to shrink. If the indoor temperature is 28.5°C
and the outside air temperature is -4.2°C, then what is
the new volume of the balloons when taken outside?
Sample Problem 4 (Gay-Lussac’s Law)
A sample of oxygen gas at 62.8°C and 3.85 atm is
heated until its pressure has increased to 6.64 atm.
What is the new temperature (in °C)?
Sample Problem 5 (Ideal Gas Equation)
A 0.316 mol sample of nitrogen gas is placed in a 4.0 L
container at 42°C. What is the pressure, in kPa, of the
nitrogen gas?
Further Applications of the Ideal Gas Equation
Gas Densities and Molar Mass
We can arrange the ideal gas equation to obtain similar units of moles per unit volume:
n
P
=
V
RT
If we multiply both sides of this equation by the molar mass, M, we obtain
nM
PM
d=
=
V
RT
This equation tells us that the density of a gas depends on its pressure, molar mass,
and temperature. The higher the molar mass and pressure, the denser the gas. The
higher the temperature, the less dense the gas.
Sample Problem 6 (Gas Densities)
What is the density of carbon tetrachloride vapor at 714 torr and 125°C?
Further Applications of the Ideal Gas Equation
Gas Stoichiometry
It is useful to be able to calculate the volumes of gases consumed or produced in
reactions. Such calculations are based on the mole concept and balanced chemical
equations.
Sample Problem 7 (Gas Stoichiometry)
Automobile air bags are inflated by nitrogen gas generated by the rapid
decomposition of sodium azide, NaN3 :
2NaN3 (𝑠) → 2Na(s) + 3N2 (g)
If an air bag has a volume of 36 L and is to be filled with nitrogen gas at 1.15 atm and 26
°C, how many grams of NaN3 must be decomposed?
Dalton’s Law of Partial Pressure
John Dalton made an important observation that “The total pressure of a mixture of
gases equals the sum pressures that each would exert if it were present alone.”.
The pressure exerted by a particular component of a mixture of gases is called the
partial pressure of that component. Dalton’s observation is known as Dalton’s law of
partial pressures.
If we let 𝑃𝑇 be the total pressure of a mixture of gases and 𝑃1 , 𝑃2 , 𝑃3 , and so forth
be the partial pressures of the individual gases, we can write Dalton’s law of partial
pressures as:
𝑃𝑇 = 𝑃1 + 𝑃2 + 𝑃3 + …
Sample Problem 8 (Dalton’s Law of Partial Pressure Part 1)
The pressure of a mixture of nitrogen, carbon dioxide, and oxygen is 150 kPa. What is the
partial pressure of oxygen if the partial pressures of nitrogen and carbon dioxide are
100 kPa and 24 kPa, respectively?
Sample Problem 9 (Dalton’s Law of Partial Pressure Part 2)
A mixture of 6.00 g of O2 and 9.00 g of CH4 is placed in a 15.0-L vessel at 0°C. What is the
partial pressure of each gas and what is the total pressure in the vessel?
Kinetic-Molecular Theory of Gases
To understand the physical properties of gases, we need a model that helps us picture
what happens to gas particles when conditions such as pressure or temperature
change. Such a model, known as the kinetic-molecular theory of gases.
1. Gases consist of large numbers of molecules that are in continuous, random motion.
2. The combined volume of all the molecules of the gas is negligible relative to the
total volume in which the gas is contained.
3. Attractive and repulsive forces between gas molecules are negligible.
4. Energy can be transferred between molecules during collisions but, as long as
temperature remains constant, the average kinetic energy of the molecules does
not change with time.
5. The average kinetic energy of the molecules is proportional to the absolute
temperature. At any given temperature, the molecules of all gases have the same
average kinetic energy.
Diffusion and Graham’s Law of Effusion
The dependence of molecular speed on mass has two interesting consequences. The
first is effusion, which is the escape of gas molecules through a tiny hole. Meanwhile,
diffusion, which is the spread of one substance throughout a space or throughout a
second substance.
Thomas Graham discovered that the effusion rate of a gas is inversely proportional to
the square root of its molar mass.
Assume we have two gases at the same temperature and pressure in two containers
with identical pinholes. If the rates of effusion of the two gases are 𝑟1 and 𝑟2 and their
molar masses are 𝑀1 and 𝑀2 , Graham’s law states that
𝑟1
=
𝑟2
𝑀2
𝑀1
a relationship that indicates that the lighter gas has the higher effusion rate.
Sample Problem 10 (Graham’s Law of Effusion)
What is the relative rate of diffusion of ammonia compared to helium? Does ammonia
effuse faster or slower than He?
September 22, 2022
Leyte National High School
Any questions or
clarifications?
September 2, 2022
Leyte National High School
We’re done for the
day!