Kinetic theory of matter

One mole contains 6.022×10<sup>23</sup> atomsUsing very clever experiments, in 1895 French physicist Jean Perrin determined that there were about 6×1023 atoms in 1 g of hydrogen, the lightest element. Subsequent experiments have refined Avogadro’s number to its modern value of NA = 6.022×1023. The number is named in honor of the Italian scientist and teacher Amadeo Avogadro. One mole is defined as Avogadro’s number. For example, one mole of hydrogen atoms is 6.022×1023 atoms. The mole is one of the seven fundamental quantities of the SI system. Read the text aloud Show More about moles and elements
(23.4) N A =6.022× 10 23
NA  = number of atoms in one mole
You use statistics to calculate an average of a set of numbers, such as the average rent for an apartment in a certain city. The kinetic theory of matter uses statistics to analyze the average behavior of trillions of individual atoms. Kinetic theory shows how the average behavior of 1023 particles produces observable properties such as temperature and pressure. A fundamental result of kinetic theory is that the average energy of a single atom resulting from random thermal motion in any particular direction is given by equation (23.5), where kB is Boltzmann’s constant and T is the absolute temperature in kelvins. Equation (23.5) relates the microscopic property of an atom’s thermal energy U to its macroscopic property of temperature T. Read the text aloud
(23.5) E= 3 2 k B T
E  = energy (J)
kB  = Boltzmann’s constant = 1.38×10−23 J/K
T  = absolute temperature (K)
Thermal energy
per atom
If we did not have the historical measure of temperature in “degrees,” then we might instead use equation (23.5) to define temperature in units of energy. A temperature of 20ºC (293 K) is equivalent to 6.07×10−21 joules per particle, for example. Think of Boltzmann’s constant and Avogradro’s number as numerical “bridges” between the microscopic world of atoms and molecules and macroscopic properties such as density, temperature, and pressure. Boltzmann’s constant has a very small value at 1.38×10−23 J/K, which indicates that individual atoms have very small energies. Read the text aloud Show Thermal energy per atom
One mole of carbon has a mass of 12 g. What is the mass of a single atom?
Asked: mass of a single atom
Given: 12 g = 1 mole of carbon atoms
Relationships: 1 mole = 6.022×1023 particles
Solution: 12 g mol × 1 mol 6.022× 10 23  atoms =1.99× 10 23  g/atom
Answer: 1.99×10−23 g/atom
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