Download Lecture 3 (Dec.7) - University of Manitoba Physics Department

Chapter 14: The Ideal Gas Law and Kinetic Theory
Fluids – Chapter 11 - cover
14.1: Molecular Mass, the Mole and Avogadro’s Number.
14.2: The Ideal Gas Law.
14.3: Kinetic Theory of Gases.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
To facilitate comparison of the mass of one atom with another, a mass
scale known as the atomic mass scale has been established.
Fluids – Chapter 11
The unit is called the atomic mass unit (symbol u).
Based on the mass of a reference element : the most abundant isotope of
carbon, (“carbon-12”), whose atomic mass is defined to be exactly 12u.
1 u  1.6605 10 27 kg
The atomic mass is given in atomic
mass units. For example, a Li atom
has a mass of 6.941u.
14.1 Molecular Mass, the Mole, and Avogadro’s Number
One mole of a substance contains as many particles as there are
atoms in 12 grams of the isotope carbon-12.
Fluids – Chapter 11
The number of atoms per mole is known as Avogadro’s number, NA.
N A  6.022  10 mol
23
number of
moles
1
number of
atoms
N
n
NA
14.1 Molecular Mass, the Mole, and Avogadro’s Number
The number of moles contained in a sample can be found from its
mass:
Fluids – Chapter 11
n
mparticle N
mparticle N A

m
Mass per mole
The mass per mole (in g/mol) of a substance has the same numerical
value as the atomic or molecular mass of the substance (in atomic
mass units).
For example Hydrogen has an atomic mass of 1.00794 g/mol, while
the mass of a single hydrogen atom is 1.00794 u.
(1.00794 is the “gram molecular weight” of H)
14.1 Molecular Mass, the Mole, and Avogadro’s Number
Example 1 The Hope Diamond and the Rosser Reeves Ruby
Fluids – Chapter 11
The Hope diamond (44.5 carats) is almost pure carbon. The Rosser
Reeves ruby (138 carats) is primarily aluminum oxide (Al2O3). One
carat is equivalent to a mass of 0.200 g.
Determine
(a) the number of carbon atoms in the Hope diamond.

m
44.5 carats0.200 g  1 carat 
n

 0.741 mol
Mass per mole
12.011 g mol


N  nN A  0.741 mol 6.022  10 23 mol1  4.46 10 23 atoms
14.1 Molecular Mass, the Mole, and Avogadro’s Number
Example 1 The Hope Diamond and the Rosser Reeves Ruby
Fluids – Chapter 11
The Hope diamond (44.5 carats) is almost pure carbon. The Rosser
Reeves ruby (138 carats) is primarily aluminum oxide (Al2O3). One
carat is equivalent to a mass of 0.200 g.
Determine
(b) the number of Al2O3 molecules in the ruby.
Mass/mole (Al2O3 ) = 2 x Mass/mole (Al) + 3 x Mass/mole (O)


N  nN A  0.271 mol 6.022 10 23 mol1  1.63 10 23 atoms
Chapter 14: The Ideal Gas Law and Kinetic Theory
Fluids – Chapter 11 - cover
14.1: Molecular Mass, the Mole and Avogadro’s Number.
14.2: The Ideal Gas Law.
14.3: Kinetic Theory of Gases.
14.2The Ideal Gas Law
An ideal gas is an idealized model for real gases that have sufficiently
low densities.
Fluids – Chapter 11
The condition of low density means that the molecules are so far apart
that they do not interact except during collisions, which are effectively
elastic.
Observations:
At constant volume
the pressure
is proportional to
the temperature.
14.2The Ideal Gas Law
An ideal gas is an idealized model for real gases that have sufficiently
low densities.
Fluids – Chapter 11
The condition of low density means that the molecules are so far apart
that they do not interact except during collisions, which are effectively
elastic.
Observations:
Pumping up a tire (approximately
constant temperature and volume):
Adding more gas molecules
increases the pressure.
14.2The Ideal Gas Law
An ideal gas is an idealized model for real gases that have sufficiently
low densities.
Fluids – Chapter 11
The condition of low density means that the molecules are so far apart
that they do not interact except during collisions, which are effectively
elastic.
Observations:
Pressure of an ideal gas can be
increased by reducing the volume
of the container.
(1 bar = 100 kPa)
14.2The Ideal Gas Law
THE IDEAL GAS LAW
Fluids
–
Chapter
11
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.
Universal gas constant:
R  8.31 J mol  K 
14.2The Ideal Gas Law
THE IDEAL GAS LAW (Alternative)
Fluids
–
Chapter
11
The absolute pressure of an ideal gas is directly proportional to the Kelvin
temperature and the number of molecules of the gas and is inversely
proportional to the volume of the gas.
 R 
T  NkT
PV  nRT  N 
 NA 
n
N
NA
Boltzmann’s constant:
8.31 J mol  K 
R
 23


1
.
38

10
J K
k
23
1
N A 6.022 10 mol