Transcript THE GAS LAWS - Clayton State University

Spencer L. Seager
Michael R. Slabaugh
www.cengage.com/chemistry/seager
Chapter 6:
The States of Matter
Jennifer P. Harris
PHYSICAL PROPERTIES OF MATTER
• All three states of matter have certain properties that help
distinguish between the states. Four of these properties are
density, shape, compressibility, and thermal expansion.
DENSITY
• Density is equal to the mass of a sample divided by the volume
of the same sample.
mass
density 
volume
OTHER PHYSICAL PROPERTIES
• SHAPE
• The shape matter takes depends upon the physical state of
the matter.
• COMPRESSIBILITY
• Compressibility is the change in volume of a sample of
matter that results from a pressure change acting on the
sample.
• THERMAL EXPANSION
• Thermal expansion is the change in volume of a sample of
matter resulting from a change in the temperature of the
sample.
CHARACTERISTIC PROPERTIES OF THE
THREE STATES OF MATTER
KINETIC MOLECULAR THEORY OF MATTER
• The kinetic molecular theory of matter is a useful tool for
explaining the observed properties of matter in the three
different states of solid, liquid and gas.
• Postulate 1: Matter is made up of tiny particles called
molecules.
• Postulate 2: The particles of matter are in constant motion
and therefore possess kinetic energy.
• Postulate 3: The particles possess potential energy as a
result of repelling or attracting each other.
• Postulate 4: The average particle speed increases as the
temperature increases.
• Postulate 5: The particles transfer energy from one to
another during collisions in which no net energy is lost from
the system.
KINETIC ENERGY
• Kinetic energy is the energy a particle has as a result of being
in motion.
• Kinetic energy (KE) is calculated using the equation:
mv
KE 
2
2
In this equation, m is the mass of a particle and v is its
velocity.
POTENTIAL ENERGY & FORCES
• POTENTIAL ENERGY
• Potential energy is the energy a particle has as a result of
being attracted to or repelled by other particles.
• COHESIVE FORCE
• A cohesive force is an attractive force between particles. It
is associated with potential energy.
• DISRUPTIVE FORCE
• A disruptive force results from particle motion. It is
associated with kinetic energy.
THE SOLID STATE
• The solid state is characterized by a high density, a definite
shape that is independent of its container, a small
compressibility, and a very small thermal expansion.
THE LIQUID STATE
• The liquid state is characterized by a high density, an indefinite
shape that depends on the shape of its container, a small
compressibility, and a small thermal expansion.
THE GASEOUS STATE
• The gaseous state is characterized by a low density, an
indefinite shape that depends on the shape of its container, a
large compressibility, and a moderate thermal expansion.
A KINETIC MOLECULAR VIEW OF SOLIDS,
LIQUIDS, AND GASES
THE GAS LAWS
• The gas laws are
mathematical equations
that describe the behavior
of gases as they are
mixed, subjected to
pressure or temperature
changes, or allowed to
diffuse.
• The pressure exerted on
or by a gas sample and the
temperature of the sample
are important quantities in
gas law calculations.
PRESSURE
• PRESSURE
• Pressure is defined as a force pushing on a unit area of
surface on which the force acts.
• In gas law calculations, pressure is often expressed in units
related to the measurement of atmospheric pressure.
• STANDARD ATMOSPHERE OF PRESSURE
• A pressure of one standard atmosphere is the pressure
needed to support a 760-mm (76.0-cm) column of mercury in
a barometer.
• ONE TORR OF PRESSURE
• One torr of pressure is the pressure needed to support a 1mm column of mercury in a barometer. A pressure of 760 torr
is equal to one standard atmosphere.
OFTEN-USED UNITS OF PRESSURE
TEMPERATURE
• The temperature of a gas sample is a measurement of the
average kinetic energy of the gas molecules in the sample.
• The Kelvin temperature scale is used in all gas law
calculations.
• ABSOLUTE ZERO
• A temperature of 0 K
is called absolute zero.
It is the temperature at
which gas molecules
have no kinetic energy
because all motion
stops. On the Celsius
scale, absolute zero is
equal to -273°C.
PRESSURE, TEMPERATURE, & VOLUME
RELATIONSHIPS FOR GASES
• Mathematical equations relating the pressure, temperature, and
volume of gases are called gas laws.
• All of the gas laws are named after the scientists who first
discovered them.
BOYLE'S LAW
• Boyle's law is a gas law that describes the pressure and volume
behavior of a gas sample that is maintained at constant
temperature.
• Mathematically, Boyle's law is written as follows:
k
P
v
or
PV  k
In these equations, P is the pressure, V is the volume, and k
is an experimentally determined constant.
CHARLES'S LAW
• Charles's law is a gas law that describes the temperature and
volume behavior of a gas sample that is maintained at constant
pressure.
• Mathematically, Charles's law is written as follows:
V  k' T
or
V
 k'
T
In these equations, V is the volume, T is the temperature in
Kelvin, and k' is an experimentally determined constant.
THE COMBINED GAS LAW
• Boyle's law and Charles's law can be combined to give the
combined gas law that is written mathematically as follows:
PV
 k' '
T
In this equation, P, V and T have the same meaning as
before and k'' is another experimentally determined constant.
• The combined gas law can be
expressed in another useful form
where the subscript i refers to an
initial set of conditions and the
subscript f refers to a final set of
conditions for the same gas sample.
Pi Vi Pf Vf

Ti
Tf
THE COMBINED GAS LAW
• Crushing Soda Can Demonstration
GAS LAW EXAMPLE
• A gas sample has a volume of 2.50 liters when it is at a temperature of
30.0°C and a pressure of 1.80 atm. What volume in liters will the sample
have if the pressure is increased to 3.00 atm, and the temperature is
increased to 100°C?
• Solution: The problem can be solved:
• using the combined gas law.
• by identifying the initial and final conditions.
• making sure all like quantities are in the same units.
• expressing the temperatures in Kelvin.
• Thus, we see that the combined gas law must be solved for Vf.
GAS LAW EXAMPLE (continued)
• The result is:
Pi Vi Tf
Vf 
TiPf
• Substitution of appropriate values gives:
Vf

1.80 atm 2.50 liters 373 K 

 1.85 liters
303 K 3.00 atm
AVOGADRO’S LAW
• Avogadro’s law states that equal volumes of gases
measured at the same temperature and pressure contain
equal numbers of molecules.
• STANDARD CONDITIONS
• STP = standard temperature and pressure
• 0°C (273 K)
• 1.00 atm
• MOLAR VOLUME AT STP
• 1 mole of any gas molecules
has a volume of 22.4 L at STP.
THE IDEAL GAS LAW
• The ideal gas law allows calculations to be done in which the amount
of gas varies as well as the temperature, pressure, and volume.
• Mathematically, the ideal gas law is written as follows:
PV= nRT
In this equation, P is the pressure of a gas sample, V is the
sample volume, T is the sample temperature in Kelvin, n is
the number of moles of gas in the sample, and R is a
constant called the universal gas constant. A commonlyused value for R is:
L atm
0.0821
mol K
• In calculations, the quantities V, P, and T must be expressed in units
that match the units of R, liters (L), atm, and Kelvin, respectively.
IDEAL GAS LAW CALCULATIONS
• Example 1: A 2.50 mole sample of gas is confined in a 6.17 liter
tank at a temperature of 28.0°C. What is the pressure of the gas
in atm?
• Solution: The ideal gas equation is first solved for P:
nRT
P
V
The known quantities are then substituted into the equation,
making sure the units cancel properly to give units of atm in the
answer:
L atm 

2.50 mol  0.0821
301K 
mol K 

P
 10.0 atm
6.17 L 
IDEAL GAS LAW CALCULATIONS
(continued)
• Example 2: A 4.00 g sample of gas is found to exert a pressure of
1.71 atm when confined in a 3.60 L container at a temperature of
27°C. What is the molecular weight of the gas in grams per mole?
• Solution:
• The molecular weight is equal to the sample mass in grams
divided by the number of moles in the sample.
• Because the sample mass is known, the molecular weight can
be determined by calculating the number of moles in the
sample.
• The ideal gas equation is first solved for n:
PV
n
RT
• The known quantities are then substituted into the equation,
making sure units cancel properly to give the units of mol for the
answer.
IDEAL GAS LAW CALCULATIONS
(continued)
n
1.71 atm3.60 L
L atm 

 0.0821
300 K 
mol K 

 0.250 mol
• The units are seen to cancel properly to give the number of
moles as the answer. The molecular weight is calculated by
dividing the number of grams in the sample by the number of
moles in the sample:
4.00 g
g
mw 
 16.0
0.250 mol
mol
IDEAL GASES vs. REAL GASES
• No ideal gases actually exist.
• If they did exist, they would behave
exactly as predicted by the gas laws
at all temperatures and pressures.
• Real gases deviate from the
behavior predicted by the gas laws,
but under normally encountered
temperatures and pressures, the
deviations are small.
• Consequently, the gas laws can be
used for real gases.
• Interparticle attractions make gases
behave less ideally.
• The gas laws work best for gases
made up of single atoms or nonpolar
molecules.