Page 251 - Schaum's Outline of Theory and Problems of Applied Physics

236 KINETIC THEORY OF MATTER [CHAP. 20

SOLVED PROBLEM 20.6
Find the water vapor density of air at 25 C whose relative humidity is 50 percent.
◦
3
◦
From Fig. 20-1 we see that the saturated water vapor density at 25 C is about 23 g/m . Since
actual vapor density
Relative humidity =
saturation vapor density
we have here
Actual vapor density = (relative humidity)(saturation vapor density)
3
= (0.50)(23 g/m ) = 11.5 g/m 3

SOLVED PROBLEM 20.7
The dew point is the temperature at which air with a certain water vapor density would be saturated and
moisture would start to condense. Dew point is useful in predicting fog: When the air temperature is near
◦
the dew point and is decreasing, fog is likely to occur. What is the dew point of air at 25 C whose relative
humidity is 50 percent?
3
The water vapor density of the air is 11.5 g/m as found in Prob. 20.6. From Fig. 20-1 air with this vapor density
is saturated at about 13 C, so this temperature is the dew point here.
◦

ATOMS AND MOLECULES
Elements are the fundamental substances of which all matter is composed. There are over 100 known elements,
of which a number are not found in nature but have been prepared in the laboratory. Elements cannot be
transformed into one another by ordinary chemical or physical means, but two or more elements can combine to
form a compound, which is a substance whose properties are different from those of its constituent elements.
The ultimate particles of an element are called atoms, and those of a compound that exists in the gaseous
state are called molecules. The molecules of a compound consist of the atoms of the elements that compose it
joined in a specific arrangement. Each molecule of water, for instance, contains two hydrogen atoms and one
oxygen atom, as its symbol H 2 O indicates. Many compounds in the solid and liquid states do not consist of
individual molecules, as discussed later. Elemental gases may consist of atoms (helium, He; argon, Ar) or of
molecules (hydrogen, H 2 ; oxygen, O 2 ).
The masses of atoms and molecules are expressed in atomic mass units (u), where

1 atomic mass unit = 1u = 1.660 × 10 −27 kg
The mass m of a molecule is the sum of the masses of the atoms of which it is composed; thus m(H 2 O) =
2m(H) + m(O).

THE MOLE

The samples of matter used in both industry and the laboratory involve so many atoms or molecules that counting
them is out of the question. Instead the mass of a particular sample is used as a measure of its quantity, and it is
necessary to relate this mass to the number of atoms or molecules in the sample.
When the masses of two samples of different substances stand in the same proportion as their molecular
masses, they contain the same number of molecules. To use this fact, the mole is defined as follows: A mole
of any substance is that amount of it whose mass is equal to its molecular mass expressed in grams instead of
atomic mass units.
Thus a mole of water has a mass of 18 g since a water molecule has a mass of 18 u. A mole of an elemental
substance that consists of individual atoms rather than molecules is that amount of it whose mass is equal to its
atomic mass expressed in grams (Fig. 20-2). In SI units the amount of a substance corresponding to a mole is
taken as a basic unit and written as 1 mol.