ChaPtEChaPtER 5 :R 5 :
GAS LAWS & GAS LAWS &
KINETIC KINETIC
THEORYTHEORY
SCOPE OF STUDYSCOPE OF STUDY
Gas Laws
& Kinetic
Theory
Gas Laws
& Kinetic
TheoryIdeal Gas
law
Real Gas
Gay-Lussac’s
Law
Boyle’s Law
Charles’ Law
Absolute Temperatur
e
gasesgasesElements that exist as gases at 250C and 1 atmosphere
gasesgases
gasesgases
Gases assume the volume and shape of their containers.
Gases are the most compressible state of matter.
Gases will mix evenly and completely when confined to the same
container.
Gases have much lower densities than liquids and solids.
Physical Characteristics of Gases
gasesgases
By international agreement, the reference element is chosen to be the
most abundant type of carbon, called carbon-12, and its atomic mass is
defined to be exactly twelve atomic mass units, or 12 u.
Atomic mass unit, Atomic mass unit, uu
The molecular mass of a molecule is the sum of the atomic masses of
its atoms.
For instance, hydrogen and oxygen have atomic masses of
1.007 94 u and 15.9994 u, respectively.
The molecular mass of a water molecule (H2O) is:
2(1.007 94 u) + 15.9994 u = 18.0153 u.
Molecular massMolecular mass
AVOGADRO’S AVOGADRO’S NUMBERNUMBER
The number of atoms per mole is known as Avogadro's number NA,
after the Italian scientist Amedeo Avogadro (1776–1856):
Number of molesNumber of molesThe number of moles n contained in any sample is the number of
particles N in the sample divided by the number of particles per
mole NA (Avogadro's number):
The number of moles contained in a sample can also be found from
its mass.
BOYLE’S LAWBOYLE’S LAW
DEFINITIONDEFINITION
The volume of a gas is inversely proportional
to the absolute pressure applied to it when
temperature is constant
BOYLE’S LAWBOYLE’S LAWGRAPH :
BOYLE’S LAWBOYLE’S LAW
P α 1/VP α 1/V
P x V = constantP x V = constant
P1 x V1 = P2 x V2P1 x V1 = P2 x V2
Constant temperature
Constant amount of gas
Constant temperature
Constant amount of gas
FORMULA
Example :
A sample of chlorine gas occupies a volume of 946 mL at a
pressure of 726 mmHg. What is the pressure of the gas (in mmHg)
if the volume is reduced at constant temperature to 154 mL?
BOYLE’S LAWBOYLE’S LAW
P1 x V1 = P2 x V2
P1 = 726 mmHg P2 = ?
V1 = 946 mLV2 = 154 mL
P2 = P1 x V1
V2
726 mmHg x 946 mL
154 mL= = 4460 mmHg
charles’S LAWcharles’S LAW
DEFINITIONDEFINITION
The volume of a gas is directly proportional
to the absolute temperature when the pressure
is constant
charles’S LAWcharles’S LAWGRAPH :
charles’S LAWcharles’S LAW
V α TV α T
FORMULA
V = constant x TV = constant x T
V1/T1 = V2/T2V1/T1 = V2/T2
Temperature must bein Kelvin
Temperature must bein Kelvin
T (K) = t (0C) + 273.15 T (K) = t (0C) + 273.15
charles’S LAWcharles’S LAWA sample of carbon monoxide gas occupies 3.20 L at 125
0C. At what temperature will the gas occupy a volume of
1.54 L if the pressure remains constant?
V1/T1 = V2/T2
V1 = 3.20 L V2 = 1.54 L
T1 = 398.15 K T2 = ?
T2 = V2 x T1
V1
1.54 L x 398.15 K
3.20 L= = 192 K
Gay-lussac’S LAWGay-lussac’S LAW
DEFINITIONDEFINITION
The absolute pressure of a gas is directly
proportional to the absolute temperature
when the volume is constant
Gay-lussac’S LAWGay-lussac’S LAWGRAPH :
Temperature is a measure of average
kinetic energy. As temperature
increases, particles move faster. As
the temperature of a gas increases the
particles will hit the walls with more
force.
Temperature is a measure of average
kinetic energy. As temperature
increases, particles move faster. As
the temperature of a gas increases the
particles will hit the walls with more
force.
FORMULA
P α TP α T
Gay-lussac’S LAWGay-lussac’S LAW
P = constant x TP = constant x T
P1/T1 = P2/T2P1/T1 = P2/T2
Constant volume
Constant amount of gas, n
Constant volume
Constant amount of gas, n
Gay-lussac’S LAWGay-lussac’S LAWA gas has a pressure at 2.0 atm at 18°C. What is the newpressure when the temperature is 62°C? (V and n constant).
1. Set up a data table; Conditions 1 Conditions 2
P1 = 2.0 atm P2 =
T1 = 18°C + 273 T2 = 62°C + 273
= 291 K = 335 K
?
Gay-lussac’S LAWGay-lussac’S LAW
2. Solve Gay-Lussac’s Law for P2:
P1 = P2
T1 T2
P2 = P1 x T2
T1
P2 = 2.0 atm x 335 K = 2.3 atm 291 K
Temperature ratioincreases pressure
Ideal gas LAWIdeal gas LAW
Exhibits certain theoretical properties. Specifically, an
ideal gas :
Obeys all of the gas laws under all conditions.
Does not condense into a liquid when cooled.
Shows perfectly straight lines when its V and T & P and
T relationships are plotted on a graph.
Ideal gas LAWIdeal gas LAWDEFINITIONDEFINITION
The absolute pressure of an ideal gas is directly
proportional to the Kelvin temperature and the number of
moles of the gas and is inversely proportional to the volume
of the gas.
V
nRTP OR
Ideal Gas Equation
P V = n R T
Universal Gas ConstantVolume
No. of moles
Temperature
Pressure
R = 0.0821 atm L / mol K
R = 8.314 kPa L / mol K
Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 366
PV = nRT
P = pressureV = volumeT = temperature (Kelvin)n = number of molesR = gas constant
Standard Temperature and Pressure (STP)
T = 0 oC or 273 K
P = 1 atm = 101.3 kPa = 760 mm Hg
Solve for constant (R)
PV nT
= R
Substitute values:
(1 atm) (22.4 L) (1 mole)(273 K)
R = 0.0821 atm L / mol K or R = 8.31 kPa L / mol K
R = 0.0821 atm L mol K
Recall: 1 atm = 101.3 kPa
(101.3 kPa)
( 1 atm)= 8.31 kPa L mol K
1 mol = 22.4 L @ STP
Ideal gas LAWIdeal gas LAW
How many moles of H2 is in a 3.1 L sample of H2
measured at 300 kPa and 20°C?
Task 1 :
PV = nRT
P = 300 kPa, V = 3.1 L, T = 293 K
(300 kPa)(3.1 L) = n (8.31 kPa•L/K•mol)(293 K)
(8.31 kPa•L/K•mol)(293 K)
(300 kPa)(3.1 L)= n = 0.38 mol
Solution :
Ideal gas LAWIdeal gas LAW
How many grams of O2 are in a 315 mL container that has a
pressure of 12 atm at 25°C?
Task 2 :
Solution :PV = nRT
P= 1215.9 kPa, V= 0.315 L, T= 298 K
(8.31 kPa•L/K•mol)(298 K)
(1215.9 kPa)(0.315 L)= n = 0.1547 mol
0.1547 mol x 32 g/mol = 4.95 g
Ideal gas LAWIdeal gas LAWWhat is the volume that 500 g of iodine will occupy under the
conditions: Temp = 300oC and Pressure = 740 mm Hg?
Step 1) Write down given information.
mass = 500 g iodine
n = 1.9685 mol I2
T = 573 K (300oC)
P = 0.9737 atm (740 mm Hg)
R = 0.0821 atm . L / mol . K
V = ? L
Task 3 :
Solution :
Ideal gas LAWIdeal gas LAW
Step 2) Equation: PV = nRT
Step 3) Solve for variable
V =nRT
P
Step 4) Substitute in numbers and solve
V (1.9685 mol)(0.0821 atm . L / mol . K)(573 K)
0.9737 atm=
V = 95.1 L I2
Ideal gas LAWIdeal gas LAW If the amount of gas does not change:
NkTTN
RNnRTPV
A
AN
Nn
Number of molecules
KJ1038.1
mol106.022
KmolJ31.8 23123
AN
Rk
Boltzmann’s constant.
Ideal gas LAWIdeal gas LAWTask 4: Hydrogen atom mass.
Use Avogadro’s number to determine the mass of a hydrogen atom.
Solution :
Dive the mass of 1 mol by the number of atoms in a mole; the mass is 1.67 x
10-27 kg.
Task 5: How many molecules in one breath?
Estimate how many molecules you breathe in with a 1.0-L breath of air.
Solution :
1 L is about 0.045 mol, and contains about 3 x 1022 molecules.
Absolute Absolute temperaturetemperature
Temperature measured using the Kelvin scale where zero
is absolute zero.
Kelvin scale is a thermodynamic (absolute) temperature scale
where absolute zero, the theoretical absence of all thermal energy,
is zero (0 K).
Kelvin unit and its scale, by international agreement, are defined
by two points: absolute zero, and the triple point.
Absolute Absolute temperaturetemperature
Absolute zero is the temperature at which nothing could be colder and no
heat energy remains in a substance - exactly 0 K and −273.15 °C.
The triple point of water is, by definition, exactly 273.16 K and 0.01 °C.
This definition does three things:
It fixes the magnitude of the kelvin unit as being exactly 1 part in
273.16 of the difference between absolute zero and the triple point of
water;
It establishes that one kelvin has exactly the same magnitude as a one-
degree increment on the Celsius scale;
It establishes the difference between the two scales’ null points as being
exactly 273.15 kelvins (0 K ≡ −273.15 °C and 273.16 K ≡ 0.01 °C).
Absolute Absolute temperaturetemperature
Triple Point of water :
The point where water in the solid, liquid and gas states can
coexist in equilibrium. The pressure of triple point is 4.58
torr and the temperature is 0.01 degree Celsius.
Triple Point of water :
The point where water in the solid, liquid and gas states can
coexist in equilibrium. The pressure of triple point is 4.58
torr and the temperature is 0.01 degree Celsius.
Absolute Absolute temperaturetemperature
Phase diagram of water.Phase diagram of water.
Absolute Absolute temperaturetemperature
The absolute temperature, T at any points for an ideal gas is defined :The absolute temperature, T at any points for an ideal gas is defined :
where : P = Pressure in the thermometer when it is at point
where T is determined
PTP = Pressure of gas in the thermometer at the
triple point temperature of water
REAL gas REAL gas DEFINITIONDEFINITION
Most like an ideal gas when the real
gas is at low pressure and high
temperature.
REAL gas REAL gas At high pressures gas particles are close therefore the volume of
the gas particles is considered.
At low temperatures gas particles have low kinetic energy
therefore particles have some attractive force
In real gases, particles attract each other reducing the pressure
Real gases behave more like ideal gases as pressure approaches
zero.
Example : Dry ice, liquid oxygen and nitrogen
Kinetic theory of gas Kinetic theory of gas
Kinetic Molecular Theory (KMT) for an ideal gas states
that all gas particles:
are in random, constant, straight-line motion.
are separated by great distances relative to their size; the
volume of the gas particles is considered negligible.
have no attractive forces between them.
have collisions that may result in the transfer of energy
between gas particles, but the total energy of the system
remains constant.
Kinetic Molecular Theory (KMT) for an ideal gas states
that all gas particles:
are in random, constant, straight-line motion.
are separated by great distances relative to their size; the
volume of the gas particles is considered negligible.
have no attractive forces between them.
have collisions that may result in the transfer of energy
between gas particles, but the total energy of the system
remains constant.
The average translational kinetic energy of the molecules in an
ideal gas is directly proportional to the temperature of the gas.
The average translational kinetic energy of the molecules in an
ideal gas is directly proportional to the temperature of the gas.
Kinetic theory of gas Kinetic theory of gas
The average speed of molecules in a gas as a function of
temperature:
The average speed of molecules in a gas as a function of
temperature:
The end The end “NEVER STAND
BEGGING FOR THAT WHICH YOU HAVE POWER TO EARN”
-MIGUEL DE CERVANTES-
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