0.020 m^3 of gas expands to
0.040 m^3. Its initial pressure was
5.0×10^5 Pa. Assume its
temperature is constant. What is
its final pressure?
PiVi = PfVf
Pf = PiVi/Vf
Pf = (5.0×10^5 Pa)(0.020 m^3 )/0.040 m^3
Pf = 2.5 × 10^5 Pa
19.4 - Avogadro’s number and moles
Avogadro’s number: 6.022×10
23
.
Mole: The amount of a substance that contains
Avogadro’s number of particles.
The concept of moles is used in the study of gases. You might find that this section
reviews what you learned in a chemistry class, where this concept also figures
prominently.
Physicists often need to deal with large quantities of molecules when they analyze
gases. For instance, one cubic meter of air at sea level contains about 3×10^25
molecules. In addition, scientists may need to quantify a given amount of gas by its
number of molecules rather than its mass. To do so, they use moles and Avogadro’s
number.
One mole is defined as the amount of a substance containing the same number of
particles as there are atoms in 12 grams of carbon-12. Carbon-12 is one form, or
isotope, of carbon, having six protons and six neutrons in its nucleus. Scientists have
determined that there are, to six significant figures, 6.022 14×10^23 atoms in 12 grams of
carbon-12, and have named this value Avogadro’s number (after the 19th century Italian
physicist Amedeo Avogadro). Avogadro’s number is indicated by NA.
A mole contains about 6.022×10^23 particles of a substance. The abbreviation for mole is
“mol”. The concept of the mole is important enough that the mole is one of the seven
fundamental units of the Système Internationale.
Avogadro’s number specifies the number of particles per mole of a substance. It can be
applied to any kind of object. For example, if you had Avogadro’s number of golf balls,
or one mole, you would have 6.022×10^23 balls (and their mass would be 2.8×10^22 kg).
Of course, moles are more typically used to specify the number of molecules in a
quantity of gas. Moles are used to focus on the number of molecules, not their mass.
For example, a mole of hydrogen atoms contains the same number of atoms as a mole
of lead, even though one mole of lead atoms weighs 207 times more than the hydrogen
atoms. If you have studied chemistry, you may be familiar with combining substances in terms of their molar amounts to achieve the correct
ratio of molecules.
The following discussion will prove useful if you need to use atomic mass units. The atomic massscalerelates moles and the mass of individual
molecules. The atomic mass unit, symbolized by u, is based on carbon-12. By definition, one atom of carbon-12 has a mass of exactly 12
atomic mass units, or 12 u. One atomic mass unit equals 1.660 54×10í^27 kg. Since Carbon-12 contains six protons and six neutrons, which
have about the same mass and make up almost all the mass of the atom, the mass of a proton or neutron is approximately one atomic mass
unit.
A particle with an atomic mass of 24 u is twice as massive as a carbon-12 atom. This means a mole of the 24 u substance will have twice as
Avogadro’s number
Number of atoms in 12 g of carbon-12
NA = 6.022×10^23 particles
Mole
Contains Avogadro’s number of
particles