Chapter 13
Pressure and Pressure Conversions
What do you know about gases?
 You are probably familiar with different types of gases.
 Air, water vapor, methane, propane, the noble gases, the
halogens, hydrogen, nitrogen, oxygen.
 What about the properties of gases?
 You probably remember saying that gases fill up the space of
their container.
 In order to fill up the space in the container, the gas molecules
must be constantly moving and hitting the inside of the
container.
 The force the particles hit the sides of the container with is
referred to as the pressure of the gas.
Measuring pressure
 One of the earliest devices used to measure pressure
was the barometer.
 The barometer was originally filled with mercury.
 The height the mercury filled the tube determined the
pressure.
 This measurement is called millimeters of mercury
(mmHg)
 This is also referred to as the pressure in torr.
 The pressure exerted by the particles in the atmosphere
directly above the point of interest is referred to as the
standard atmosphere (atm).
 The SI unit for pressure is the Pascal (Pa).
 The pressure in tires is commonly measured in pounds
per square inch.
 1 atm = 760 mmHg = 760 torr = 101,325 Pa = 14.69 psi
Converting between units
 Sometimes it is required to convert between units of
pressure.
 Example
 Convert 525 mmHg to atmospheres.
 525 mmHg = 0.691 atm.
 Convert 16 psi to torr and pascals
 16 psi = 828 torr = 110360 Pa
Manometers
 Another common tool to pressure pressure
is a manometer.
 A manometer is a device that be used to
find the pressure inside an object.
 The manometer is open to the
atmosphere on both sides and filled with
an amount of mercury.
 When an object is placed on one side of
the manometer, the mercury will flow to
the side of the manometer under lower
pressure.
 What would happen to the mercury levels if
an object with less pressure than the
atmosphere is placed on the right side of a
manometer?
 The sum of the pressure in mmHg and
the height difference due to the object
determines the pressure inside the object.
Manometer problems
 Example
 A manometer with one side open to the atmosphere is
connected to a basketball. If the atmospheric pressure is
765 mmHg and the mercury in the manometer is 20 mm
higher on the atmosphere side, what is the pressure of
the gas in the basketball?
20
mm
Chapter 13
Boyle’s and Charles’ Law
Boyle’s Law
 Robert Boyle used a J shaped tube which
was closed on one side to determine the
relationship between the pressure and
volume of a gas.
 He filled the tube with a certain amount of
mercury and noted the volume. He then
added more mercury to the tube and
noticed that the volume of the gas
decreased as more mercury was added.
 He then multiplied the pressure and volume
observations and noticed that the product of
these values remained constant.
 This observation only holds true at a
constant temperature and moles of gas.
Boyle’s Law
 If we remember that gas molecules must be in constant
motion and constantly colliding with the container’s
surface…
 we can visually see how the pressure of the gas must
increase as the volume decreases.
Boyle’s Law
 Because the volume of the gas decreases as the
pressure increases, or
 The volume of the gas increases as the pressure
decreases
 We say that the pressure and the volume of a gas are
inversely proportional to one another.
 We can mathematically represent Boyle’s Law with the
equation P1V1=P2V2
Boyle’s Law practice
 Example
 A sample of neon to be used in a sign has a volume of
1.51 L under a pressure of 635 torr. Calculate the
pressure of the neon gas when it is pumped into the
tubes of the sign at a pressure of 785 torr.
 Example
 If the pressure of 2.4 L of gas in a balloon is 1.35 atm,
what is the pressure if the volume is increased to 5.4 L?
Charles’ Law
 Jacques Charles
 1st person to fill a balloon with hydrogen
gas
 1st person to make a solo hot air balloon
voyage
 Studied the relationship between volume
and temperature
 Determined that the volume of the gas
increases as the temperature of the gas
is raised.
 This means there is a direct correlation
between the volume and temperature of a
gas.
 IMPORTANT- you need all temperatures,
when dealing with gases, to be in Kelvin.
Absolute zero
 From the data collected by Charles, it can be
extrapolated what the temperature would be of a gas
when the volume is decreased to zero.
 We have to extrapolate because all gases liquefy before
reaching this lowest possible temperature.
 This temperature is called Absolute Zero.
 This is the lowest possible temperature possible
 Is a theoretical value; has not been reached but have gotten
close
 Is the temperature in which there is no molecular motion.
 Temperature is the average kinetic energy of the particles.
Volume and Temperature
 Charles found that the volume of a gas decreased
when the temperature of the gas was decreased. He
also noted that the volume would increase upon
increasing the temperature.
 This is called a direct correlation.
 Both factors increase or decrease together.
 Charles’ Law is summarized in the equation
Practice with Charles’ Law
 Example
 If the volume of a gas at 25 °C is 13.6 L, what is the
volume of the same gas at 35 °C?
 If the volume of a gas is 22.4 L at 25°C, what is the
temperature when the volume is 12.2L?
Chapter 13
Avogadro and Gay-Lussac’s Laws
Avogadro’s Law
 You should remember that Avogadro is most
remembered for his work in defining the number of
molecules/atoms/formula units in a mole.
 He also did work with gases.
 He determined that under constant pressure and
temperature, that the number of moles of a gas is directly
correlated to the volume of a gas.
 His law is summarized in the following equation:
Working with Avogadro’s Law
 Example
 If the volume of 25.0 g of F2 is 15.4 L, what volume would
the gas have if the F2 was decreased to 15.0 g?
 Example
 If the volume of 30.0 g of methane (CH4) is decreased
from 13.2 L to 9.8 L was amount of mass was lost?
Gay-Lussac’s Law
 Gay-Lussac determined the relationship between the
temperature and pressure of a gas.
 He determined that the pressure and temperature of a
gas are directly related.
 His law can be represented mathematically by the
following equation:
 Remember that the temperature has to be in Kelvin when
using this equation.
Using Gay-Lussac’s Law
 Example
 What is the pressure of a gas that was originally at 1 atmosphere
is increased from 39 degrees Celsius to 100 degrees Celsius?
Chapter 13
Combined Gas Law
 Since we have relationships between pressure,
volume, and temperature for all substances, we can
combine all the laws into a short equation.
 This equation is to be used when the number of moles of
a gas are not changing.
 Remember that the temperature need to be in Kelvin.
 This equation was obtained through combining Boyle’s,
Charles’, and Gay-Lussac’s laws according to how they
are arranged.
Working with the Combined
Gas Law
 Example
 Calculate the change in the temperature of a gas that
started at room temperature, when the pressure changes
from 1.2 atm to 2.3 atm and the volume decreases from
10 L to 5 .3 L.
 Determine the change in the pressure of a gas that ends
at 3.2 atm and changes in volume from 5.4 L to 7.5 L with
no temperature change.
Dalton’s Law of Partial
Pressures
 So far we have discussed gases that are not mixed, but
this is not always the case.
 There are many examples of gas mixtures
 Air
 He and O2 in diving tanks
 When dealing with a mixture of gases, the total pressure
of the system can be determined by adding up all of the
pressures of each gas.
Dalton’s Law of Partial
Pressure
Chapter 13
The Ideal Gas Law
Ideal gases
 We have neglected an important issue up to this point.
We have not discussed how we were viewing a gas to
behave.
 Under ideal conditions, we view a gas as
 Being made up of small particles that do not experience any
attraction or repulsion to one another while moving
constantly
 Having perfectly inelastic collisions
 These conditions only hold true under low pressure and high
temperature.
 Why would this be?
Ideal Gases
 If gases do not behave this way, why do we even
bother using them?
 It is because it is easier to work with ideal gases.
 The equation used to describe ideal gases is shown
below:
 This law is similar to the combined gas law except that it
is describing the gas at one state, meaning it is not
changing conditions.
 There is also a few terms thrown in
 n for the number of moles of the gas
 R which is called the gas proportionality constant.
 is equal to 0.08206
Using the Ideal Gas Law
Using the ideal gas law when
the gas is changing
 We previously said that the prior equation is only used
when the properties of the gas are not changing.
 Can we still use the ideal gas law when a property
changes.
 We can; we just have to modify the equation slightly.
 You have notice which side of the equation is staying
constant.
 This side will remain the same.
 You will then use one of the other gas laws to find the change.
 It is just easier to use the other gas law though.
Chapter 13
Real vs. Ideal Gases
Kinetic Molecular Theory
 What is the temperature of a substance?
 The average kinetic energy of the substance.
 By this point you should be very familiar with all of the
gas laws brought up in discussion so far.
 What we have not discussed is why gases behave the
way the do.
 The kinetic molecular theory helps to explain this
question.
 The kinetic molecular theory has five main assumptions
 The assumptions in the kinetic molecular theory do not
describe all gases but do help explain the behavior of ideal
gases.
Assumptions of KMT
 Gases consist of tiny particles (atoms or particles).
 These particles are so small, compared to the distance between
them, that the volume (size) of the individual particles can be
assumed to be negligible (zero).
 The particles are in constant random motion, colliding with the
walls of the container. These collisions are viewed as perfectly
elastic and result in the pressure exerted by the gas. The particles
also collide with one another in a perfect elastic collision.
 The particles are assumed not to attract or repel each other
 The average kinetic energy of the gas particles is directly
proportional to the Kelvin temperature of the gas.
Elaboration on Assumption #5
 The fifth assumption of the kinetic molecular theory
states that the average kinetic energy of the gas
particles is directly proportional to the Kelvin
temperature of the gas.
 Kinetic energy is represented by the equation below.
 Since the mass of the particle cannot change without a
reaction occurring, this means that the speed, v, of the
particle must increase with increasing temperature.
Real vs. Ideal
 So what is the difference between real and ideal gases?
 Real gases exist and ideal gases are hypothetical compounds
that obey the ideal gas law.
 An ideal gas contains particles that have no volume or any
interaction with other particles in the same except to collide with
one another.
 There are similarities however,
 The volume of each particle takes up such a small space that it
is almost like having zero volume.
 As the volume decreases though, the percent of the total
volume taken up by the particles is much higher, making it less
ideal.
Ideal vs. real
 What about the pressure of a gas?
 If I reduce the volume of the gas, what will happen to its
pressure?
 When those molecules are closer together and exerting a
greater pressure on the container, what about the distance
between the particles?
 The individual particles that make up the entire gas come closer
to one another.
 This makes it more likely that the particles that make up the
gas will be close enough to one another to have a large effect
on one another.
Gas Stoichiometry
 If we know of a reaction that occurs along with two of
the three following variables,
 The pressure
 Volume
 Temperature
 Along with the mass of a compound,
 We can use stoichiometry to determine the number of moles
of the compound of interest
 We can then use the ideal gas law to find out the answer to
the question.
Standard Temperature and
Pressure (STP)
 When trying to solve problems about gas stoichiometry, it is sometimes
helpful to know the volume of gas occupied by 1 mole of the gas at STP
 STP is achieved when in the pressure of a gas is 1 atm and the
temperature is 0 degrees Celsius.
 Lets determine the volume of a gas at STP
At STP, every mole of gas occupies
22.4 L of space.
Sources

http://commons.wikimedia.org/wiki/File:BoyleLaw_J_TestTube.png


http://www.alibaba.com/product-detail/Manometer_107677058/showimage.html


http://www.atmos.washington.edu/academics/classes/2013Q2/101/LINKShtml/MercuryBarometer.html


http://www.oceansbridge.com/oil-paintings/product/88533/robertboyle


http://www.floridaballoonadventures.com/history-of-hot-air-balloons.html