Standard Atmospheric Pressure -
Corresponds to the typical pressure at sea level.
This
pressure is equal to 1.01325 x 10
5
Pa, 760 mm Hg, 760 torr, 1 atm, and 101.325 kPa
10.3 The Gas Laws
The four variables needed to define the physical state of a gas are temperature, T, pressure, P,
volume, V, and the amount of gas, which is usually expressed in moles, n.
Boyle's Law -
The volume of a fixed quantity of gas maintained at constant temperature is
inversely proportional the pressure. V = constant x 1/P; PV = constant.
Charles' Law -
The volume of a fixed amount of ga maintained at constant pressure is directly
proportional to its absolute temperature (on the Kelvin scale).
V = constant x T; V/T = constant
Avogadro's Hypothesis -
Equal volumes of gases at the same temperature and pressure
contain equal number of molecules.
From this,
Avogadro's Law
was established, which said
t
he
volume of a gas maintained at constant temperature and pressure is directly proportional to the
number of moles of the gas.
Gay-Lussac's
law of combining volumes
, provided the basis for both
of these, which said that at a given temperature and pressure the volumes of gases that react
with on another are in the ratios of small whole numbers.
10.4 The Ideal-Gas Equation
The Ideal-Gas Equation -
PV = nRT; Made by combining the three gas laws, An
ideal gas
is a
hypothetical gas whose pressure, volume, and temperature behavior is completely described by
the ideal-gas equation.
The term
R
is called the
gas constant
, whose value depends on the
units of P,V, n, and T.
Temperature is expressed in Kelvins, Pressure in atm's, Volume in liters,
and the quantity of gas,
n
, in moles.
Standard Temperature and Pressure (STP) -
0 degrees Celsius and 1 atm.
10.5 Further Applications of the Ideal-Gas Equation
The ideal gas law can also be used to determine the density of a gas, by multiplying both
sides of the equation (n/V) = (P/RT) by M, the molar mass, which is the number of grams in one
mole of a substance. The resulting equation (nM/V) is equivalent to m/V (mass divided by
volume), which is the same thing as density.
Thus, the density of gas is given by the equation
PM/RT.
10.6 Gas Mixtures and Partial Pressures
Dalton's Law of Partial Pressures -
The total pressure of a mixture of gases equals the sum of
the pressures that each would exert if it were present alone.
The pressure exerted by a particular
component of a mixture of gass is called the
partial pressure
.
The law has the equation P
t
=
n
t
(RT/V), where P
t
is the total pressure exerted by the gas(es), and n
t
is the total number of moles
in the gas(es)
Partial Pressures and Mole Fractions -
Because each gas in a mixture behaves independently,
we can relate the amount of a given gas in a mixture to its partial pressure.
For a mixture, n
1
/n
2
is
called the mole fraction of gas 1, which is denoted as X
1
.
The
mole fraction,
X, expresses the
ratio of the number of moles of one component to the total number of moles in the mixture.
The